An appendix to the fourth issue of the
“Proceedings of the Tomsk Technological Institute of Emperor Nicholas II.”

On the Question

of the Relation Between the Partial Density of the Solvent in a Solution and the Vapor Pressure of the Solution.

A study by

Ya. I. Mikhailenko.

Kiev.
Litho-Typography of I. I. Chokolov, Fundukleevskaya Street, house No. 22.
1905.

The question of the relation between the partial densities of the solvent in the liquid and vapor phases, to which the present study is devoted, constitutes a part of a more general topic—the relation between the partial density of the solvent in solution and the osmotic pressure of the dissolved substance.

Both topics have scarcely been touched upon in contemporary chemical literature. The works of Nernst, Donnan, Charpy, and others should be regarded merely as notes or as incidental thoughts and, in any case, not as attempts at the systematic development of a definitely posed problem. Nernst, in formulating his well-known proposition that the vapor pressure of a solution is proportional to the active mass of the solvent, was hardly aware that by this proposition he was taking the first step toward posing the question of the change in the density of a liquid under the forces of osmotic pressure—at least, the term “partial density of the solvent in solution” appears to have been introduced for the first time in this book.

I was led to the investigation of the problem—to express the partial density of the solvent in solution as a function of the osmotic pressure—in 1898 by the observation of the approximate equality of the partial densities of the solvent in solution and in vapor, an observation made by me for aqueous salt solutions quite independently. During the period 1898–1905 I published a series of articles in which this topic was already subjected to systematic development. These works continue at the present time as well. Some of these articles have been included in this book as materials. Two works have not been included: 1) “Methods for Determining the Vapor Pressure of Solutions.” Kiev, 1901, and 2) “The Relation between the Vapor Pressure of a Solution and Its Osmotic Pressure.” Kiev, 1904.

The proposed book contains, in approximate form, a derivation of the relation between the partial density of the solvent in solution and the pressure of its vapor and, in addition, an investigation of the concrete cases in which the derived relation proved applicable, in some cases—no. For such an investigation it was necessary to collect and evaluate a vast body of experimental material, which was partly gathered from the literature and partly obtained by my own work on measuring the density and vapor pressure of solutions. In collecting the experimental material and in evaluating the vapor-pressure data obtained by different investigators and by different methods, the work “Methods for Determining the Vapor Pressure of Solutions” proved necessary; it constituted a classification and description of methods for measuring the vapor pressure of solutions and a list of works, and in the subsequent collection and evaluation of experimental material on the vapor pressure of solutions it was of great service to me.

The first and second chapters of the book contain the derivation of the relation being sought, theoretical investigations and considerations, and their verification against experimental material; the greater part of the contents of these chapters appears in print for the first time.

The third and fourth chapters contain an account of my own experiments on measuring the density and elasticity of the vapor of solutions. Measurements of the specific gravity of solutions and of the elasticity of the vapor of solutions in organic solvents, as well as an investigation of the temperatures of the vapor and of the boiling liquid, appear in print for the first time.

By deriving, in an approximate form, the relation between the densities of the solvent in the liquid and vapor phases, I do not consider the problem posed to be exhausted. Preparatory work on finding this relation in exact form, and also on establishing the functional dependence between the partial density of the liquid solvent and the osmotic pressure, is under way. One of these works, “The Relation between the Elasticity of the Vapor of a Solution and Its Osmotic Pressure,” which gives a derivation of this relation in exact form, has already been printed; the others are nearing completion. Also unfinished remains the development of the problem of calculating molecular weight from the density of a solution, the solution of which is closely connected with the solution of the preceding general problems. These investigations, when completed, will constitute the contents of the next work.

Tomsk, January 21, 1905.

Chapter I.

Derivation of the relation between the partial density of the solvent in a solution and the elasticity of its vapor by application of the law of active masses to the equilibrium between the solution and its vapor.

Definitions of the concepts of a solution and of a chemical compound. In chemistry two types of physically homogeneous associations of several bodies are distinguished: 1) a solution and 2) a chemical compound.

A solution is defined as a physically homogeneous association of several bodies, the ratio between whose masses may vary continuously without disturbing the homogeneity of the association.

A chemical compound is defined as a physically homogeneous association in which the ratio between the masses of the components may vary only discontinuously, namely, according to the law of definite proportions.

The distinction between these two types of associations, long established in chemistry, cannot, however, necessarily be understood in the sense that both types of these associations are essentially different from one another. On the contrary, both formerly and at the present time one may note a constant tendency to consider both types of associations in connection with one another. Thus, the chemical theory of solutions seeks to represent a solution as a chemical compound in a state of decomposition; the so-called physical theory of solutions, on the contrary, seeks to represent a chemical compound as an equilibrium system existing under special conditions, so to speak fixed by certain forces—essentially the same as a solution. In general, both the one theory and the other, though by different paths, proceed toward one and the same goal, namely, to show that the distinction between a solution and a chemical compound is purely formal, serving only for purposes of classification, and that both types of associations are particular cases of equilibrium between the components of an association—an equilibrium that obeys, in both cases, the same general laws.

Partial density of the solvent. One of the essential properties of the association that is called a solution is its complete homogeneity. If every action on the solution by external forces is excluded—for example, the forces of gravity, magnetic and electric forces, capillarity, and others—then every given volume of the solution, all other things being equal, must be homogeneous.

conditions, both in its physical properties, e.g., density, color, refractive index, etc., and in composition, is identical to any other volume of this same solution. If at some place in the solution the ratio between the components constituting this solution is changed, e.g., if one or another component is added or removed, then a movement of masses immediately begins in the solution, the result of which movement is the restoration of the former homogeneity of the solution.

In the study of a solution two points of view may be adopted. The first consists in regarding the solution as a new body, in which there are none of those individuals that served for the formation of the solution—the solution is a new individual, i.e., a new combination of atoms previously combined in the form of separate bodies. The second point of view consists in regarding the solution as an association not of atoms, but of individuals—consequently, the solution is assumed to contain the individuals (molecules) that served for the formation of the solution as such. Both points of view represent two logical methods of analyzing the phenomenon of solution; they do not contradict one another, although they are different, and they lead to one and the same goal—to give as complete and precise a scheme of the phenomenon as possible. The investigator may use either method equally, depending on which of them, in application to the given particular case, will be simpler or more fruitful. In the present investigation the second point of view on the solution is adopted, namely, that the solution is an association of chemical individuals.

From the definition of “solution” as a wholly homogeneous association of bodies it follows that each of the components of this association is distributed quite uniformly throughout the volume occupied by the solution; hence its volume is at the same time the volume of the entire association. Since the ratio between volume and mass is generally called density, the ratio between the mass of a given component of the association and the volume in which it is distributed may be called the partial density of the given component in the solution, i.e., its density at the time when it participates in the association. Since the volume of the solution is in general different from the volume of each of the ingredients of the solution, in the act of dissolution all bodies forming the solution change their density, just as a gas changes its density depending on the pressure under which it is found.

If the density of the solution and its composition are known, then the partial density in the solution (in the liquid phase of the solution) of some component \(A_1\), \(A_2\), etc., of the solution will be expressed as follows:

\[ s_{A_1}=S\times \frac{c_{A_1}}{100+c_{A_1}+c_{A_2}+\ldots},\qquad s_{A_2}=S\times \frac{c_{A_2}}{100+c_{A_1}+c_{A_2}+\ldots},\ \text{etc.;} \tag{1} \]

or

\[ s_{A_1}=S\times \frac{\pi_{A_1}}{100};\qquad s_{A_2}=S\times \frac{\pi_{A_2}}{100}\ldots\ \text{etc.} \]

Here the notation is:

\(S\)—specific gravity of the solution;

\(s_{A_1}, s_{A_2}, \ldots\)—partial densities in the solution of the components \(A_1, A_2\);

\(c_{A_1}, c_{A_2}, \ldots\)—ratios between the masses of the components \(A_1, A_2,\ldots\) and the mass-

of some arbitrarily chosen component of a mixture adopted as 100; \(\pi_{A_1}\), \(\pi_{A_2}\), etc. are the contents of the components \(A_1\), \(A_2\), etc. in 100 weight parts of the solution.

Partial density, as is evident from the method of calculating it, is a concept analogous to that of ordinary density.

As is known, besides the ordinary concept of density, theoretical chemistry introduces also the concept of true density. Namely, according to the atomic-molecular theory of matter, mass does not fill the volume occupied by it continuously; gaps remain between atoms and molecules. Therefore the visible volume occupied by a mass is composed of the proper volume (voluma) occupied by atoms and molecules, and of the volume in which these molecules and atoms perform their oscillations (covolyum). The true density of a compound will consequently be the ratio between the mass and the volume occupied by the hypothetical molecules of the given compound. For calculating this volume, theoretical chemistry, as is known, offers a number of methods.

By partial density—the concept with which we shall operate in this investigation—is meant the ratio between the mass of a component of a solution and the visible volume which it occupies. How this mass is placed in the volume of the solution—whether it consists of molecules distributed in the intervals between the molecules of other components of the mixture, or whether it penetrates the masses of these components—does not concern this concept of partial density.

In some special cases the concept of partial density just stated will prove insufficient; in these cases we shall arrive at the concept of “true” partial density.

Calculation of the partial density of dissolved bodies by formulas (1) will show that solids, on dissolving, change their density to the density of stretched liquids or of compressed and rarefied gases, i.e., to the density which the given solid would have if, by means of some forces at the temperature of the solution, it were converted into a liquid or vapor, which were then, by means of the same forces, compressed or stretched.

Liquids, in the act of dissolving, change their density to the density of stretched liquids or of compressed and rarefied gases.

Gaseous bodies, on dissolving, either decrease their density or increase it.

The change of density by bodies in the act of association according to the type of a solution is one of the most characteristic signs of association of this type. In the theory of solutions this sign may be adopted as central, and one may attempt to represent all the other properties of a solution as in one way or another connected with the magnitude of this change in density.

In the proposed work one such attempt has been made, namely, an attempt to represent the magnitude of the elasticity of the vapor of a solution as a function of the changed density of the solvent in the solution.

The partial specific density of the solvent in the liquid phase is equal to the specific density of the solvent in the gaseous phase. Let there be given an association, of the solution type, of two bodies; let one of these bodies necessarily be a volatile liquid, and the other body a nonvolatile liquid or a nonvolatile solid.

According to the generally accepted nomenclature, the body which, with a given mass of another body, can form solutions in quantities varying up to infinity is called the solvent. The body which, with a given mass of another body, can form solutions in quantities varying within certain limits is called the dissolved substance.

Such a distinction between the dissolved substance and the solvent should not, however, be understood in the sense that there is a profound difference between the dissolved substance and the solvent. This distinction is based on a purely accidental feature. Indeed, if the bodies form solutions with one another in all proportions, then such a distinction disappears of itself. It is more correct to accept that all components participating in the association of a solution play the same role in this association, and that there is essentially no difference between the dissolved substance and the solvent. Thus, from this point of view, the use of the term solvent would seem superfluous and even undesirable. But, on the other hand, the significance of each member in a given association is determined first of all by its mass and only then by its individual qualities. Since there is no term that would indicate the mass of the body participating in the association, it may be useful to retain the term solvent to designate the mass of the component, i.e. to apply it to that component which is present in great excess and whose altered density may be regarded as the density of a stretched liquid. In this and only in this sense will the term solvent be used below.

Thus, when a nonvolatile body is dissolved in a volatile solvent, the density of the solvent changes. If the composition of the solution is expressed by the ratio \((c)\) of the mass of the dissolved body to the mass of the solvent, taken as 100, then the density of the solvent in the solution \(s_1\) (partial density of the solvent) according to equation (1) is expressed as follows:

\[ s_1 = S \times \frac{100}{100+c} \tag{2} \]

If the composition of the solution is expressed by the content of dissolved substance in 100 wt. parts of solution \((\pi)\), then the density of the solvent in the solution is expressed as follows:

\[ s_1 = S \times \frac{100-\pi}{100} \tag{3} \]

For example, the partial density of a 31.64% aqueous solution of cane sugar, whose density at \(17.5^\circ\) is equal to 1.13759, is calculated as follows:

\[ s_1 = 1.13759 \times \frac{100-31.64}{100} = 0.77766, \]

i.e. the water in this solution has a greatly reduced density; it is as if stretched by certain forces.

We represent the equilibrium between a liquid and its vapor as a mobile equilibrium:

Liquid ⇄ Vapor.

Namely, we assume that in a unit of time as much liquid evaporates as vapor condenses into liquid. If by \(V\) we denote the rate of vapor formation, and by \(V'\) the rate of vapor condensation, then in the case of equilibrium:

\[ V = V'. \]

Let us make the assumption that in an equilibrium system consisting of a solution and the vapor of the solvent, the vapor is in equilibrium not with the association—solution, but with the pure liquid solvent, which has merely changed its density (as a result of the dissolution in it of a foreign body). Let us also assume that the rates of vapor formation and condensation at constant temperature are proportional to the mass in a unit volume. Then:

\[ \begin{aligned} V_0 &= Ks_0, & V'_0 &= K'\vartheta_0,\\ V_1 &= Ks_1, & V'_1 &= K'\vartheta_1,\\ V_2 &= Ks_2, & V'_2 &= K'\vartheta_2, \end{aligned} \]

\[ \ldots\ldots\ldots\ldots \]

and so on, where

\(s_0, s_1, s_2 \ldots\) are the partial densities of the solvent in the solution;

\(\vartheta_0, \vartheta_1, \vartheta_2 \ldots\)—the densities of the vapor;

\(K\) and \(K'\)—constant quantities (coefficients of proportionality).

When equilibrium is established,

\[ Ks_0 = K'\vartheta_0 \]

\[ Ks_1 = K'\vartheta_1 \]

\[ \ldots\ldots\ldots \]

and so on.

And from this it follows that

\[ \frac{s_1}{s_0} = \frac{\vartheta_1}{\vartheta_0} \qquad \text{and} \qquad \tag{4} \]

\[ \frac{s_1}{\vartheta_1} = \frac{s_0}{\vartheta_0} = Const. \tag{5} \]

i.e. the ratio between the densities of the solvent in the liquid and gaseous phases remains unchanged for an entire series of solutions and is equal in magnitude to the ratio between the densities of the liquid and vapor for the pure solvent.

Since, without great error, it may be assumed that

\[ \frac{\partial_1}{\partial_0}=\frac{p_1}{p_0}, \]

then expression (4) may be written as follows:

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0} \quad \text{or} \tag{6} \]

\[ \frac{s_0-s_1}{s_0}=\frac{p_0-p_1}{p_0} \tag{7} \]

These expressions also establish the relation between the density of the solution and the elasticity of its vapor. They may conveniently be formulated as follows: the relative (specific) elasticity of the vapor of a solution is equal in magnitude to the relative (specific) density of the solvent in the liquid phase of the solution (its partial density), and the relative lowering of the elasticity of the vapor of the solution is equal to the relative lowering of the density of the solvent undergone by it in the act of dissolution.

Expressions (4), (5), (6), (7) can in exactly the same way be derived, obviously, for any other component of the solution, e.g., \(A_2\), etc., provided, of course, that the other components of the solution are nonvolatile.

For the case in which the first component of the solution is a liquid and the second component a gas, expression (6) has long been known under the name of Henry’s law and is expressed by saying that the solubility of a gas is proportional to the pressure of the gas.

Starting from Henry’s law, expressions (4) (5) (6) (7), as applied to the solvent, may be derived in the following way.

Let there be given a solution, for example, of ether vapor in nitrobenzene. Let the elasticity of the ether vapor above the solution be \(p_1\). Let the content of ether in a unit volume of the liquid phase of the solution be \(s_1\).

According to Henry’s law,

\[ s_1 = a p_1, \]

where

\(a\) is a constant quantity.

We shall gradually increase the content of ether in the solution; since ether and nitrobenzene mix in all proportions, the concentration of ether in the liquid phase can be continuously increased to a value differing infinitely little from the concentration of pure liquid ether, i.e. the value \(s_0\). During such a gradual increase in the concentration of ether, the ether will finally become the solvent instead of the dissolved substance, and, if throughout the entire increase in the concentration of ether in the liquid phase \(a\) remains unchanged, then, since the transition from solution to pure liquid can be effected continuously, it will retain the same value for pure ether as well, i.e.

\[ s_0 = a p_0 \]

And from this it follows that:

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0}. \tag{6} \]

The quantity \(\alpha\) is called the coefficient of solubility of the vapor or gas. From the preceding it follows that, for those vapors of bodies for which Henry’s law is justified over a wide interval of concentrations, one should expect that the coefficient of solubility of the gas will be equal or very close to the ratio between the densities of the vapor or gas condensed into the liquid and its saturated vapor.

Discussion of the derivation of the relation \(\dfrac{s_1}{s_0}=\dfrac{p_1}{p_0}\). Expressions (4), (5), (6), and (7) are derived under the assumption that the law of mass action is applicable in the case of equilibrium between a solution and its vapor.

But the law of mass action can be derived from the two principles of thermodynamics only for a substance in a state of infinite dilution (rarefied gases and dilute solutions). In application to real gases and strong solutions the law of mass action must have a more complicated expression. Consequently, one cannot expect equality (6) to be strictly exact, since in deriving it the law of mass action was applied to the solvent, i.e., to that component of the solution whose concentration (spatial concentration) is a concentration of the order of strongly compressed gases or expanded liquids. However, one may hope that this correction term will not be very large, since experience shows that the application of the law of mass action in its simple formulation to even very strong solutions nevertheless gives quite satisfactory results. As an example, one may point to the application of the law of mass action to the reaction of formation of esters from acids and alcohols.

The second assumption made in deriving equation (6) is that the molecular weight of the solvent in the liquid and gaseous phases is taken to be the same, i.e., the assumption is made that the solvent does not associate. Indeed, if the solvent were associated, i.e., if its liquid and gaseous phases were mixtures of simple and polymeric molecules, then with any change in the volume of the solvent occurring upon a change in the concentration of the solution, the equilibrium between the simple and polymeric molecules would be disturbed; in a solution of each new concentration the solvent would represent, as it were, a new body. Obviously, the constants of the processes of evaporation and condensation would also change with the concentration of the solution, and the derivation of equation (6) would be invalid.

Let, in the liquid phase, the solvent, for example acetic acid, consist of double molecules \((C_2H_4O_2)_2\), and in the vapor phase of simple molecules \(C_2H_4O_2\). Since in the liquid phase there are double molecules \((C_2H_4O_2)_2\), then, according to the phase rule, they will be present, even if in an exceedingly small amount, also in the vapor phase, and between these molecules and the simple ones in the vapor phase an equilibrium must be established according to the equation:

\[ (C_2H_4O_2)_2 \rightleftarrows 2C_2H_4O_2. \]

Applying the law of mass action to this equilibrium system, we obtain:

\[ C_{C_2H_4O_2}^{\prime\,2}=K C'_{(C_2H_4O_2)_2}, \tag{8} \]

where \(C'_{C_2H_4O_2}\) and \(C'_{(C_2H_4O_2)_2}\) are the spatial concentrations of the corresponding molecules in the gaseous phase.

Between the concentrations of double molecules in the liquid phase and of double molecules in the gaseous phase there exists the following gradation:

\[ C_{(C_2H_4O_2)_2}=K_1 C'_{(C_2H_4O_2)_2}, \]

where \(K_1\) is to be a constant, and \(C'_{(C_2H_4O_2)_2}\) is the concentration of double molecules in the liquid phase.

Expressing in equation (8) the concentration of double molecules in the vapor phase through the concentration of double molecules in the liquid phase, we obtain:

\[ \frac{C_{C_2H_4O_2}^{\prime\,2}}{C_{(C_2H_4O_2)_2}} = \frac{K}{K_1} = \mathrm{Const}. \tag{9} \]

In the liquid phase, besides double molecules, simple molecules should as a rule also exist, just as in the vapor phase, besides simple molecules, double ones should exist. Assuming that in the liquid phase the number of simple molecules, and in the gaseous phase the number of double molecules, is negligible, one may take the density of the solvent in the liquid phase to be proportional to the concentration of double molecules, i.e. to the quantity \(C_{(C_2H_4O_2)_2}\), and the elasticity of the solvent vapor in the gaseous phase to be proportional to the number of simple molecules in the gaseous phase, i.e. to the quantity \(C'_{C_2H_4O_2}\). Then equation (9) may be written as follows:

\[ \frac{p^2}{s}=\mathrm{Const}. \]

And hence it follows that

\[ \frac{s_1}{s_0}=\frac{p_1^2}{p_0^2}=\mathrm{Const}. \tag{10} \]

Thus, for the case when the solvent in the liquid phase consists only of double molecules, and in the gaseous phase only of simple molecules, the relation between the elasticity of the vapor of the solution and the partial density of the solvent in the solution takes the form (10). If, both in the liquid and in the gaseous phase, the number of unassociated and associated molecules is considerable, this same relation assumes a new, still more complex form.

The remarks just made concerning the derivation of the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) may be formulated as follows: the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) is strictly exact in

in the case when the solvent is not associated at all and when the solvent obeys the laws of ideal gases even at spatial concentrations close to the spatial concentration of its liquid state.

The deviation of real gases from the laws of Mariotte–Boyle, Gay-Lussac, and Avogadro, as is known, is explained in two ways: either by the volume of the gas molecules and the attraction between them (van der Waals), or by the association of gas molecules (Planck).

If we adopt the second scheme, then the conclusion concerning the derivation of equality (6) may be formulated generally, namely as follows: the equality

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0} \]

will be strictly exact for the case of solutions in liquids that are not associated at all; if the solvent is associated, equality (6) will be either inaccurate or incorrect—depending on the degree of association of the solvent. The degree of association of the dissolved substance obviously does not affect the derivation of equality (6).

To these remarks one more must be added, namely: is the assumption correct that the vapor of a solution of a nonvolatile substance in a volatile solvent is in equilibrium only with the solvent in the liquid phase, and not with the entire solution; otherwise, do the nature of the dissolved substance and its concentration exert their share of influence on the value of the elasticity of the vapor of the solution or not? For example, will solutions of two different substances in one and the same solvent, in which the solvent has one and the same partial density, have the same or a different vapor pressure?

To this remark one might answer that, if the equilibrium between the liquid solvent and its vapor were influenced by the dissolved substance (its nature and concentration), this would mean that the active mass of the given substance is determined not by its spatial concentration alone, but depends also on the nature and concentrations of other substances present in the same medium, and above all, of course, on the nature of the solvent itself. On the one hand, the everyday application of the law of mass action in its usual formulation to a whole series of very complex equilibrium systems, with quite satisfactory results, seems completely to remove the concern stated above. On the other hand, a series of such facts as the influence of the medium on the rate of reaction (Menshutkin), the phenomenon of unequal solubility of one and the same substance in equal volumes of different solvents, distribution phenomena, the noted influence of indifferent substances on various equilibrium systems, etc., do not allow this remark to be entirely disregarded. It is possible that, precisely for the particular case of equilibrium under discussion, the influence of the nature and concentration of the dissolved substances cannot be neglected.

Let us suppose that the nature and concentration of the dissolved substance exert an influence on the rate of transition of the liquid solvent into the vapor-like state.

Then the rate of vaporization \(V\) will be expressed as follows:

\[ V=K_1 s_{A_1}\times K_2 s_{A_2} \]

where \(s_{A_1}\) and \(s_{A_2}\) are the partial densities of the solvent and of the dissolved

bodies, and \(K_1\) and \(K_2\) are constants depending only on the nature of the pair of bodies forming the solution.

The rate of the process of condensation of the vapor \(V'\) will be expressed as:

\[ V' = K'_1 p_1 \]

Whence, for the case of equilibrium, one obtains:

\[ K_1 s_{A_1} \times K_2 s_{A_2} = K'_1 p_1 \quad \text{or} \]

\[ \frac{s_{A_1} \times s_{A_2}}{p_1} = \frac{K'_1}{K_1 \times K_2} = \mathrm{Const}. \tag{11} \]

Thus, in the event that the nature and concentration of the dissolved substance had an effect on the equilibrium between the vapor and the solvent, the relation between the density of the solution and the elasticity of its vapor would be expressed by equality (11).

How the actual relation between the density of the solution and the elasticity of its vapor is expressed—or, in other words, between the density of the solvent in the liquid and gaseous phases—in one of the formulations just analyzed, or in a more complex form, can be answered only by experiment carried out on a broad scale.

A thermodynamic derivation of the relation between the partial density of the solvent in a solution and the elasticity of its vapor was given by N. N. Schiller: namely, he showed that, for those solutions for which Babo’s law is valid, this relation is expressed by the equality:

\[ \frac{s_1}{s_0} = \frac{p_1}{p_0}.^{1)} \]

Experimental verification of the possible relations between the density of the solvent in a solution and the elasticity of its vapor. In the experimental verification of the possible relations derived above between the densities of the solvent in the liquid and gaseous phases of a solution, a whole series of difficulties had to be encountered.

The numerical data for the values of the vapor elasticity of solutions turned out to be comparatively very few in the literature; whereas specific weights were most often determined at temperatures of \(0^\circ\), \(15^\circ\), and \(25^\circ\), the vapor elasticities of solutions were most often measured at temperatures close to the boiling points of the solvents; the data from measurements of vapor elasticity proved in general to contain a large error, sometimes to such an extent that the vapor elasticities of the same solutions, determined by different authors or by different methods, did not agree at all with one another; finally, systematic measurements of the specific gravity of solutions in organic solvents were almost entirely absent from the literature; while accidental isolated measurements were scattered through articles on the most varied topics, and to find them, in the absence of any guiding indication, was very difficult.

\(^{1)}\) Schiller. Zh. R. Phys.-Chem. Soc. 30, 79. 1898; 31, 93. 1899.

Since the vapor pressures and the partial densities had to be compared at one and the same temperature, in order to avoid recalculations—which, moreover, could not always be made because the expansion coefficients of the solutions were unknown—I assumed that the relative vapor pressure of solutions does not depend on temperature (Babo’s law).

As is known, this proposition, in its strict form, is applicable only to those solutions whose dilution is accompanied by a zero thermal effect (Kirchhoff). There are hardly many such solutions. But experiment shows (Emden) that the influence of the thermal effect of dilution on the relative vapor pressure of a solution is so small that even in the case of aqueous salt solutions, whose dilution is accompanied in general by a clearly perceptible thermal effect, the method of measuring vapor pressure is in some cases entirely incapable of detecting it, and in other cases the correction may be neglected; moreover, the dilution of solutions in organic solvents is in the majority of cases accompanied by a quite negligible thermal effect, in some cases close to zero (Linebarger). Thus the error made by introducing Babo’s law into the calculations could not appreciably affect the results of the comparisons.

In Table I are compared aqueous solutions of salts that crystallize without water of crystallization.

The specific gravities \((S)\) for a given concentration \((c)\) were calculated from the parabolas derived by D. I. Mendeleev from a comparison of specific gravities determined by various investigators¹. The accuracy with which the specific gravities are given is \(\pm 0.0002\). The concentration of the solutions \((c)\) is expressed as the ratio of the mass of the dissolved substance to the mass of the solvent, taken as 100.

The density of the solvent in the solution (partial density) was calculated by the formula:

\[ s_1 = S \times \frac{100}{100 + c} \tag{12} \]

The vapor-pressure data for the solutions were taken from the works of Emden² and Tammann³. The probable error in the determination of the relative vapor pressure is greater than \(\pm 0.001\).

Aqueous Solutions.

Electrolyte solutions.

1. Salts crystallizing without water of crystallization.

Table I.

$c$	$S \dfrac{15^0}{4^0}$	$s_1 \dfrac{15^0}{4^0}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	Name of the observer of vapor pressure
Potassium chloride KCl.	Potassium chloride KCl.	Potassium chloride KCl.	Potassium chloride KCl.	Potassium chloride KCl.	Potassium chloride KCl.
10,051	1,0588	0,9621	0,9629	0,956	Emden
20,040	1,1112	0,9256	0,9264	0,909	Emden
Potassium bromide KBr.	Potassium bromide KBr.	Potassium bromide KBr.	Potassium bromide KBr.	Potassium bromide KBr.	Potassium bromide KBr.
24,63	1,1577	0,9289	0,9297	0,934	Tammann
35,4	1,2174	0,8991	0,8998	0,903	Tammann
68,57	1,3691	0,8125	0,8131	0,816	Tammann
Potassium iodide KI.	Potassium iodide KI.	Potassium iodide KI.	Potassium iodide KI.	Potassium iodide KI.	Potassium iodide KI.
13,09	1,0910	0,9647	0,9655	0,978	Tammann
35,97	1,2349	0,9082	0,9089	0,930	Tammann
96,34	1,5326	0,7806	0,7812	0,792	Tammann
Sodium chloride NaCl.	Sodium chloride NaCl.	Sodium chloride NaCl.	Sodium chloride NaCl.	Sodium chloride NaCl.	Sodium chloride NaCl.
5,067	1,0339	0,9840	0,9848	0,967	Emden
14,705	1,0939	0,9537	0,9545	0,906	Emden
26,636	1,1583	0,9147	0,9155	0,819	Emden
Sodium bromide NaBr.	Sodium bromide NaBr.	Sodium bromide NaBr.	Sodium bromide NaBr.	Sodium bromide NaBr.	Sodium bromide NaBr.
18,24	1,1299	0,9556	0,9564	0,947	Tammann
31,93	1,2225	0,9267	0,9274	0,889	Tammann
41,01	1,2717	0,9018	0,9026	0,845	Tammann
Sodium iodide NaI.	Sodium iodide NaI.	Sodium iodide NaI.	Sodium iodide NaI.	Sodium iodide NaI.	Sodium iodide NaI.
13,22	1,0701	0,9451	0,9459	0,973	Tammann
43,97	1,3023	0,9046	0,9053	0,882	Tammann
57,48	1,3777	0,8748	0,8755	0,836	Tammann

\(c\)	\(S\frac{15^\circ}{4^\circ}\)	\(s_1\frac{15^\circ}{4^\circ}\)	\(\frac{s_1}{s_0}\)	\(\frac{p_1}{p_0}\)	Name of the observer of vapor pressure
		Ammonium chloride \(NH_4Cl\).
6,06	1,0168	0,9587	0,9594	0,969	Tammann
28,52	1,0644	0,8282	0,8289	0,836	Tammann
24,38	1,0572	0,8500	0,8506	0,862	Tammann
		Ammonium bromide \(NH_4Br\).
14,52	1,0726	0,9366	0,9374	0,956	Tammann
28,87	1,1377	0,8828	0,8835	0,905	Tammann
		Potassium nitrate \(KNO_3\).
5,029	1,0296	0,9803	0,9811	0,983	Emden
14,885	1,0844	0,9436	0,9445	0,956	Emden
25,011	1,1348	0,9077	0,9085	0,932	Emden
		Sodium nitrate \(NaNO_3\).
9,976	1,0618	0,9656	0,9665	0,956	Emden
19,680	1,1169	0,9330	0,9340	0,926	Emden
41,75	1,2238	0,8634	0,8642	0,853	Emden
		Lithium nitrate \(LiNO_3\).
15,92	1,0847	0,9357	0,9365	0,916	Tammann
59,06	1,2608	0,7927	0,7933	0,632	Tammann
		Potassium sulfate \(K_2SO_4\).
5,008	1,0382	0,9883	0,9893	0,983	Emden
10,021	1,0750	0,9774	0,9783	0,974	Emden
		Potassium chromate \(K_2CrO_4\).
25,35	1,1767	0,9387	0,9405	0,950	Tammann
48,90	1,3091	0,8792	0,8808	0,895	Tammann
67,83	1,3963	0,8130	0,8145	0,850	Tammann

\(c\)	\(S \dfrac{15^\circ}{4^\circ}\)	\(s_1 \dfrac{15^\circ}{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	Name of the observer of the vapor pressure.
		Ammonium sulfate \((NH_4)_2SO_4\).	Ammonium sulfate \((NH_4)_2SO_4\).
13,93	1,0711	0,9402	0,9411	0,966	Tammann
33,20	1,1479	0,8618	0,8625	0,922

The data presented in Table I show that, for aqueous solutions of salts crystallizing without water of crystallization, it may be assumed that the equality \(\dfrac{s_1}{s_0} = \dfrac{p_1}{p_0}\) is satisfied approximately, and the better, the more dilute the solution. For dilute solutions the deviations lie within the limits of experimental error. For some salts \(\dfrac{p_1}{p_0}\) is greater than \(\dfrac{s_1}{s_0}\), for others it is smaller. Comparatively too large deviations are observed for solutions of sodium chloride.

Other probable relations between the partial density of the solvent and the elasticity of its vapor—formulas (10) and (11)—are not at all satisfied, as is easily seen from the following comparison for solutions of potassium bromide.

Table II.

Potassium bromide \(KBr\).

\(c\)	\(S \dfrac{15^\circ}{4^\circ}\)	\(s_1 \dfrac{15^\circ}{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	\(\dfrac{p_1^2}{p_0^2}\)	\(\dfrac{s_1 s_2}{p_1}\)
24,63	1,1577	0,9289	0,9297	0,934	0,8721	0,1018
35,40	1,2174	0,8991	0,8998	0,903	0,8154	0,3168
68,57	1,3691	0,8125	0,8131	0,816	0,6659	0,5541

2. Salts crystallizing with water of crystallization.

In Table III a comparison is made for salts crystallizing from aqueous solutions in the form of hydrates. In calculating the partial density by formula (12), it was assumed that the solution contains either these or other hydrates.

Table III.

\(c\)	\(S \dfrac{15^\circ}{4^\circ}\)	\(s_1 \dfrac{15^\circ}{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	Name of the observer of vapor pressure
Zinc sulfate \(ZnSO_4\).
14.865 \(ZnSO_4\)	1.1436	0.9956	0.9964	0.976	Emden
29.988 \(ZnSO_4 \cdot 7H_2O\)	1.1436	0.8798	0.8805	0.976	Emden
16.80 \(ZnSO_4 \cdot H_2O\)	1.1436	0.9795	0.9802	0.976	Emden
26.654 \(ZnSO_4\)	1.2503	0.9872	0.9880	0.959	”
60.036 \(ZnSO_4 \cdot 7H_2O\)	1.2503	0.7812	0.7818	0.959	”
30.54 \(ZnSO_4 \cdot H_2O\)	1.2503	0.9579	0.9585	0.959	”
Copper sulfate \(CuSO_4\).
6.156 \(CuSO_4\)	1.0606	0.9991	0.9998	0.989	Emden
9.998 \(CuSO_4 \cdot 5H_2O\)	1.0606	0.9643	0.9651	0.989	Emden
6.901 \(CuSO_4 \cdot H_2O\)	1.0606	0.9921	0.9929	0.989	Emden
11.916 \(CuSO_4\)	1.1160	0.9971	0.9979	0.982	”
19.990 \(CuSO_4 \cdot 5H_2O\)	1.1160	0.9301	0.9308	0.982	”
13.45 \(CuSO_4 \cdot H_2O\)	1.1160	0.9837	0.9845	0.982	”
16.778 \(CuSO_4\)	1.1611	0.9943	0.9006	0.976	”
28.922 \(CuSO_4 \cdot 5H_2O\)	1.1611	0.9951	0.9014	0.976	”
18.60 \(CuSO_4 \cdot H_2O\)	1.1611	0.9790	0.9798	0.976	”
Calcium chloride \(CaCl_2\).
12.55 \(CaCl_2\)	1.0955	0.9728	0.9736	0.931	Emden
28.22 \(CaCl_2 \cdot 6H_2O\)	1.0955	0.8549	0.8556	0.931	Emden
17.15 \(CaCl_2 \cdot 2H_2O\)	1.0955	0.9351	0.9359	0.931	Emden
19.99 \(CaCl_2\)	1.1461	0.9552	0.9557	0.882	”
48.96 \(CaCl_2 \cdot 6H_2O\)	1.1461	0.7694	0.7700	0.882	”
27.45 \(CaCl_2 \cdot 2H_2O\)	1.1461	0.8993	0.9000	0.882	”

\(c\)	\(S\frac{15^0}{4^0}\)	\(s_1\frac{15^0}{4^0}\)	\(\frac{s_1}{s_0}\)	\(\frac{p_1}{p_0}\)	Name of the observer of the vapor pressure.
20.211 \(CaCl_2\)	1.1476	0.9546	0.9554	0.877	”
49.64 \(CaCl_2.6H_2O\)	1.1476	0.7669	0.7675	0.877	”
28.64 \(CaCl_2.2H_2O\)	1.1476	0.8921	0.8928	0.877	”
Magnesium chloride \(MgCl_2\).	Magnesium chloride \(MgCl_2\).	Magnesium chloride \(MgCl_2\).	Magnesium chloride \(MgCl_2\).	Magnesium chloride \(MgCl_2\).	Magnesium chloride \(MgCl_2\).
10.73 \(MgCl_2\)	1.0815	0.9767	0.9775	0.937	Tammann
26.13 \(MgCl_2.6H_2O\)	1.0815	0.8575	0.8581	0.937	Tammann
14.43 \(MgCl_2.2H_2O\)	1.0815	0.9449	0.9456	0.937	Tammann
19.00 \(MgCl_2\)	1.1385	0.9566	0.9574	0.864	”
51.80 \(MgCl_2.6H_2O\)	1.1385	0.7500	0.7506	0.864	”
26.20 \(MgCl_2.2H_2O\)	1.1385	0.8876	0.8882	0.864	”
36.09 \(MgCl_2\)	1.2410	0.9119	0.9126	0.653	”
13.08 \(MgCl_2.6H_2O\)	1.2410	0.5376	0.5380	0.653	”
49.77 \(MgCl_2.2H_2O\)	1.2410	0.7870	0.7876	0.653	”
Barium chloride \(BaCl_2\).	Barium chloride \(BaCl_2\).	Barium chloride \(BaCl_2\).	Barium chloride \(BaCl_2\).	Barium chloride \(BaCl_2\).	Barium chloride \(BaCl_2\).
11.10 \(BaCl_2\)	1.0937	0.9847	0.9854	0.975	Tammann
13.27 \(BaCl_2.2H_2O\)	1.0937	0.9656	0.9663	0.975	Tammann
12.30 \(BaCl_2.H_2O\)	1.0937	0.9750	0.9757	0.975	Tammann
31.50 \(BaCl_2\)	1.2533	0.9530	0.9537	0.921	Tammann
39.10 \(BaCl_2.2H_2O\)	1.2533	0.9010	0.9017	0.921	Tammann
35.20 \(BaCl_2.H_2O\)	1.2533	0.9268	0.9275	0.921	Tammann

From Table III it follows that the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) is sharply not justified if, in calculating \(s_1\), it is assumed that these salts are present in solution in the anhydrous state or in the form of those hydrates in which they crystallize from saturated solutions.

For solutions of calcium chloride and magnesium chloride, the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) is justified only in the case where it is assumed that in the sol—

solutions there are the hydrates \(CaCl_2 \cdot 2H_2O\) and \(MgCl_2 \cdot 2H_2O\); for solutions of copper sulfate and zinc sulfate this equality is justified if one assumes that in the solution there are the hydrates \(CuSO_4 \cdot H_2O\) and \(ZnSO_4 \cdot H_2O\), i.e. in unsaturated solutions there are the most stable hydrates, capable of withstanding the dissociating power of the solvent.

It follows from this that comparison of the partial density of the solvent in the liquid phase with the elasticity of its vapor can serve as a method for deciding the question of the state in which the dissolved substance is present in the solution.

The question of the state in which dissolved substances are present belongs to the number of questions as interesting and important as they are obscure, confused, and to this day stubbornly resistant to final solution. Parallel to the two principal points of view on solutions, one may also note two currents of thought in the question of the state of dissolved substances. The advocates of the chemical theory of solutions (Mendeleev, Pickering, Kahlenberg, Jones) try to prove that dissolved substances are present in solution in the form of neutral molecules chemically combined with the solvent, namely hydrates and solvates¹. The creators of the physical theory of solutions assume that dissolved substances are present in solution either in the form of ions or in the form of neutral molecules not chemically combined with the solvent. Neither the one view nor the other exhausts the question of the state of dissolved substances. It is possible that dissolved substances are present in solution in the form of hydrated ions².

The method of comparing the partial densities of the solvent in the liquid and gaseous phases, without at all touching upon the question of the state in which the dissolved substance is present—whether in the form of ions or in the form of neutral molecules—decides the question of whether the entire solvent of the solution is associated with the dissolved substance according to the type of a solution, or whether part of it is associated according to the type of a chemical compound. Between associations of the one and the other type we draw a sharp boundary, and it is obvious, entirely possible, that part of the solvent will be associated according to one type and part according to the other.

The difference between a solvent associated with a dissolved substance according to the type of a chemical compound and according to the type of a solution may be explained as follows. In those cases where part of the solvent of the solution is chemically bound, we cannot separate the solvent and the dissolved substance by a process that is reversible in all its parts and continuous; when all the solvent has been removed and only its chemical compound with the solvent remains, the process must be interrupted and a new process begun, one or several successive processes, depending on the character of the hydrate; each of these processes, in its turn, will also be continuous and reversible.

If comparison of the partial densities of the solvent in the liquid and gaseous phases gives an answer as to what part of the solvent is bound chemically, investigation of the electrical conductivity will further show whether this solvent is bound to the neutral molecules of the dissolved substance or to ions.

The calculation of the amount of solvent \((x)\) bound to the dissolved substance and, consequently, of the complex \((c+x)\) that is present in solution, by the method of comparing the partial densities of the solvent in the liquid and gaseous phases of the solution, is carried out as follows.

Let, upon dissolving \((c)\) parts by weight of a substance in 100 parts by weight of solvent, \((x)\) weight units of the solvent enter into interaction with \((c)\) parts by weight of the dissolved substance.

Then

\[ s_1=\frac{100-x}{V}, \]

where \(V\) is the volume of the solution.

Let

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0}=\mu. \]

Since

\[ V=\frac{100+c}{S}, \]

it follows from this that

\[ x=100-\mu\frac{s_0}{S}(100+c) \tag{13} \]

For example, calculation of \(x\) by formula (13) for solutions of zinc sulfate and calcium chloride gives the following results.

For a solution of zinc sulfate containing 14.865 g of anhydrous salt per 100 g of water:

\[ \frac{p_1}{p_0}=\mu=0.976\quad \text{(Emden);} \]

\[ S\frac{15^\circ}{4^\circ}=1.1436; \]

whence

\[ x=100-0.976\times\frac{0.9992}{1.1436}\times114.865=2.05\ \text{g}. \]

Consequently, in a solution with 14.865 g of zinc sulfate, 2.05 g of water are chemically bound, and with the molecule \(ZnSO_4(161)\) there are bound 22 g, i.e., one molecule \((H_2O=18)\).

For a solution of calcium chloride containing 12.55 g of anhydrous salt per 100 g of water:

\[ \frac{p_1}{p_0}=\mu=0.931\quad \text{(Emden);} \]

\[ S \frac{15^\circ}{4^\circ}=1.0955. \]

Hence

\[ x=100-0.931 \times \frac{0.9992}{1.0955}\times 112.5=4.41\ \text{g}; \]

with the molecule \(CaCl_2\) (111), therefore, 38, i.e. two molecules of water \((2H_2O=36)\), are chemically bound.

Thus, the calculation of the quantity of water chemically bound in solution to the molecules of salts that crystallize with water of crystallization gives the curious result that in solution there are not higher hydrates at all, as might have seemed, but, on the contrary, either anhydrous salts or the most stable hydrates; i.e., the excess water acts not in a hydrating, but in a dissociating manner.

I think this fact may be explained in the following way. Recently Schiller has shown that, under pressure on the boundary surface between a liquid and its vapor, the vapor pressure of the liquid increases¹. The same conclusion may be applied also to crystallohydrates, namely in this form: pressure on a crystallohydrate increases the pressure of its dissociation. Liquids may be regarded as strongly compressed gases enclosed, as it were, in vessels whose walls, capable of withstanding enormous pressures, consist of the surface layer of the liquid. A manometer immersed in a liquid therefore does not reveal this pressure, because when the manometer is immersed in the liquid the surface layer of the liquid is not disturbed; where the manometer is placed, the liquid is only pushed aside—the shape of the vessel alone changes, but the vessel still remains whole and closed. A particle of crystallohydrate, actually penetrating into the medium of the liquid beyond this envelope, enters an atmosphere of high pressure, the result of which is the dissociation of the crystallohydrate. The more concentrated the solution, the less concentrated the solvent, and the smaller its partial pressure. At a certain degree of concentration there finally comes a moment when this pressure is no longer able to dissociate the crystallohydrate—the crystallohydrate remains undissociated. Thus it is possible that, in strong solutions, crystallohydrates with a higher water content are present, and it is entirely understandable that precisely these hydrates will crystallize from saturated solutions.

The investigation of the question of the hydration (solvation) of dissolved substances does not constitute the principal task of this work. This question is very complex, has its own extensive literature, and deserves special investigation. The application of the method found to a number of concrete cases, and a comparison of the results obtained with the results of other methods, likewise did not enter into our work, since this again would have expanded too greatly the scope and volume of the work. Such an investigation may constitute the content of one of our future works. Here I would like only to point out that the general conclusion given by the method—namely, that with dilution hydration falls—finds confirmation in a number of works by other

researchers who arrived at the same conclusion by entirely different methods. Thus, Smits¹, discussing the results of his work on measuring the vapor elasticity of solutions, says: “Bei kleinen concentrationen kommt Hydratbildung nicht“... “Bei grösseren koncentrationen nimmt die Hydratbildung zu“....

Bancroft², objecting to Nernst (Theoretische Chemie 430) on the influence of concentration on hydration, asserts that with dilution of the solution the decomposition of hydrates takes place.

Jones und Getman³, who calculated hydrates from the freezing temperatures of solutions, came to the same conclusions.

Lobry de Bruyn and Lobry de Bruyn u. Jungius⁴, investigating the state of the hydrates \(NiSO_4 \cdot 7H_2O\), \(NiSO_4 \cdot 6H_2O\), and \(NiSO_4 \cdot 3H_2O\) in solutions in methyl alcohol, and obtaining the result that in these solutions there exists the most stable hydrate \(NiSO_4 \cdot H_2O\), transferred the same conclusion also to aqueous solutions.

Colson⁵, investigating the chemical relations of aqueous solutions of zinc sulfate, assigns to it the formula \(HSO_4 \cdot Zn - O - Zn, SO_4H\), which may be represented as the hydrate \((ZnSO_4)_2 \cdot H_2O\).

Aqueous solutions of nonelectrolytes.

Solutions of cane sugar.

The vapor elasticities of aqueous sugar solutions were measured by me.⁶

The partial density was calculated according to the formula:

\[ s_1 = S \times \frac{100-\pi}{100}, \qquad \text{where} \tag{14} \]

\(S\)—density of the solution,

\(\pi\)—content of sugar in 100 parts by weight of solution.

The densities of sugar solutions were taken from the “Tables” of Landolt und Börnstein.

Table IV.

Aqueous solutions of cane sugar.

$n$ = number of gram-molecules per 1000 g of water	$\pi\%$	$S \dfrac{17.5^\circ}{17.5^\circ}$	$s_1 \dfrac{17.5^\circ}{17.5^\circ}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	$V_{sp}$	$V_{mol}$
0.200	6.40	1.02535	0.95950	0.9595	0.9961	0.5585	191.0
0.800	21.48	1.08995	0.85583	0.8558	0.9846	0.5587	191.2
1.400	31.64	1.13759	0.77766	0.7777	0.9720	0.5554	190.0
1.800	38.10	1.16971	0.72405	0.7240	0.9635	0.5578	190.7
2.400	45.08	1.20618	0.66243	0.6624	0.9443	0.5507	188.1
3.000	50.64	1.23610	0.610139	0.6101	0.9287	0.5481	187.4

It is evident from the table that the equality $\dfrac{p_1}{p_0} = \dfrac{s_1}{s_0}$ is very far from being satisfied for sugar solutions. Still less are the other probable forms of relations between vapor pressure and partial density satisfied [equalities (10) and (11)].

Since the equality just cited, as follows from the preceding, is satisfied fairly closely for a whole series of aqueous salt solutions, it was important to determine the reasons why it is not satisfied for aqueous sugar solutions.

As has just been shown, the accuracy of the equality $\dfrac{p_1}{p_0} = \dfrac{s_1}{s_0}$ may be affected by the formation of hydrates in the solution.

If the dissolved substance forms a hydrate, then the partial density calculated by the formula $s_1 = S \times \dfrac{100-\pi}{100}$ will be incorrect; consequently, the ratio $\dfrac{s_1}{s_0}$ will also be incorrect.

Indeed, let $\pi$ parts by weight of the substance be dissolved in $100-\pi$ parts by weight of the solvent. Let $x$ parts by weight of the solvent be consumed in the formation of the hydrate. Then the partial density will evidently be expressed as follows:

\[ s_1 = S \times \frac{(100-x)-\pi}{100} \tag{15} \]

If formulas (14) and (15) are compared, it is obvious that the quantity \(s_1\), calculated by formula (15), will be smaller than \(s_1\) calculated by formula (14).

For example, if 12.555 grams of anhydrous calcium chloride salt are dissolved in 100 grams of water, then the partial density calculated by formula (14) will be:

\[ s_1 = 1.0955 \times \frac{100 - 11.26}{100} = 0.9728. \]

If one makes the assumption that the hydrate \(CaCl_2 \cdot 6H_2O\) has formed in the solution, then the partial density calculated by formula (15) will be:

\[ s_1 = 1.0955 \times \frac{100 - 22.01}{100} = 0.8549. \]

But for sugar solutions the value of \(s_1\), calculated by formula (14), is too small; the formation of a hydrate would lower it still more. Consequently, the cause of the difference is not hydration.

Nor can the difference be explained by the assumption of hydrolysis.

The matter would stand as if the quantity of water contained in a unit volume of solution does not occupy the whole volume, but only a certain part of it, while the other part is occupied by sugar; in other words—the sugar molecules are not permeable to water.

If one adopts the assumption that the dissolved body occupies in the solution a certain volume, impermeable to the solvent, then, for the calculation of the partial volume \((s_1)\), formula (14) may be used only in the case when this volume can be neglected, for example, in the case of dilute solutions, or if the true specific volume of the dissolved body is small. In other cases, a correction for this volume must be introduced into the formula for calculating the partial density.

Namely, if \(\pi\) grams of a substance are dissolved in \(100-\pi\) g of solvent, and if the specific volume (the volume of 1 gram) of the substance in solution is denoted by \(V_{sp}\), then the partial density of the solvent is expressed as follows:

\[ s_1 = S \times \frac{100-\pi}{100-\pi S V_{sp}} \tag{16} \]

It is evident from the formula that the correction will be the greater, the greater the quantity \(\pi S V_{sp}\), i.e., the stronger the solution \((\pi\%)\), the greater the true specific volume of the dissolved body \((V_{sp})\), and the higher the specific gravity of the solution \((S)\). The quantity \(V_{sp}\), by assumption, must not depend on the concentration.

Let us try to calculate the quantity \(V_{sp}\) (the true specific volume of the dissolved body in solution) and \(V_{mol}\) (the true molecular volume of the dissolved body in solution) for sugar solutions.

We shall find the quantity \(V_{sp}\) from the following equality:

\[ \frac{p_1}{p_0} = \frac{s_1}{s_0} = \frac{S(100-\pi)}{s_0(100-\pi S V_{sp})}. \]

If we assume that the equality \(\dfrac{p_1}{p_0}=\dfrac{s_1}{s_0}\) holds, then the true specific volume \(V_{sp}\) is equal to:

\[ V_{sp}=\frac{100}{\pi S}-\frac{p_0}{p_1}\times\frac{(100-\pi)}{\pi s_0} \tag{17} \]

And \(V_{mol}\), i.e. the true molecular volume, is equal to:

\[ V_{mol}=V_{sp}\times M , \tag{18} \]

if \(M\) denotes the molecular weight.

In Table IV these quantities are given under the symbols \(V_{sp}\) and \(V_{mol}\). As we see, the true specific volume, and consequently also the molecular volume, of sugar changes very little with concentration. I would sooner explain the somewhat smaller values for very concentrated solutions by errors in determining the ratio \(\dfrac{p_1}{p_0}\) for concentrated solutions than by an actual change of the specific volume with concentration.

The true molecular volume of sugar, calculated from atomic volumes, taking for sugar the usual structural formula, and for the atomic volumes Traube’s numbers¹, is 221.9.

Sugar was the first aqueous solution of a nonelectrolyte investigated by me with respect to the equality \(\dfrac{s_1}{s_0}=\dfrac{p_1}{p_0}\). Similar relations are apparently shown by aqueous solutions of other nonelectrolytes as well.

Tables V and VI give data for aqueous solutions of glycerin and urea.

Table V.

Aqueous solutions of glycerin.

\(n=\) number of gram-mol. per liter	\(z\%\)	\(S \dfrac{15^\circ}{15^\circ}\)	\(s_1 \dfrac{15^\circ}{15^\circ}\)	\(\dfrac{p_1}{p_0}\)	\(\dfrac{s_1}{s_0}\)	\(V_{sp}\)	\(V_{mol}\)
\(n\)	\(\%\)
1.0277	8.64	1.0211	0.9329	0.9820	0.9329	0.5669	52.16
0.5038	4.430	1.0108	0.9660	0.9912	0.9660	0.5647	51.95
0.2441	2.195	1.0054	0.9834	0.9956	0.9834	0.5545	51.01
0.1180	1.074	1.0027	0.9920	0.9979	0.9920	0.5514	50.74

\(S \dfrac{15^\circ}{15^\circ}\) are taken from the Tables of Landolt und Börnstein;

\(s_1 \dfrac{15^\circ}{15^\circ}\) are calculated by the formula \(s_1 = S \times \dfrac{100-\pi}{100}\);

\(\dfrac{p_1}{p_0}\) are calculated from the observations of Dieterici, Wied. Ann. 67. 865. 1899.

\(V_{sp}\) and \(V_{mol}\) have the same meaning as in Table IV.

The true molecular volume of glycerin, calculated from atomic volumes, taking Traube’s numbers, \(=61{,}4\).

Table VI.

Aqueous solutions of urea.

\(\pi\%\)	\(S \dfrac{15^\circ}{4^\circ}\)	\(s_1 \dfrac{15^\circ}{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	\(V_{sp}\)	\(V_{mol}\)
0,8228	1,00148	0,99320	0,9940	0,9975	0,5	30
6,09	1,01619	0,95430	0,9551	0,9824	0,4347	26,08 ¹)

\(S \dfrac{15^\circ}{4^\circ}\) observed by Traube, Liebig’s Ann. 290. 94, 1896.

\(\dfrac{p_1}{p_0}\) interpolated from the observations of Dieterici, Wied. Ann. 67. 865, 1899.

The remaining designations are the same as in the preceding table.

The true molecular volume of urea, calculated from atomic volumes, taking Traube’s numbers, \(=30{,}8\).

It is characteristic that in all three cases for the true specific volume (\(V_{sp}\)) almost one and the same number is calculated (about 0,5), although the substances themselves belong to different classes and have different molecular weights (342, 92, 60). That is, as though the correction for each gram of dissolved substance is one and the same for all aqueous solutions, independently of the nature of the dissolved substance.

¹) The comparatively large difference between the molecular volumes of glycerin calculated for different concentrations may here be explained by the fact that urea in aqueous solutions undergoes hydrolysis.

The hypothesis of an apparent and a true volume is not in contradiction with those conceptions of the structure of matter which may be regarded as generally accepted.

Thus, Traube¹, investigating deviations from Kopp’s rule, which consists in the fact that the molecular volume of a compound body in the liquid state is equal to the sum of the atomic volumes of the elements composing it, came to the conclusion that in the visible volume of liquids one must distinguish the volume occupied by the molecules themselves of the given body (true volume) and the volume in which the molecules perform their vibrations (covolume).

Klausius and Mossoti, studying the dielectric properties of bodies, arrived at an analogous conclusion and gave a formula for calculating the true volume of a substance from its dielectric constant.

H. A. Lorentz and L. Lorentz² derived a formula for calculating the true volume from the refractive index of a light wave.

Kanonnikov³ devotes a series of articles to the calculation of the “true density of chemical compounds and its relation to their composition and structure.”

The kinetic theory of gases and liquids likewise treats of the true volume and gives methods for calculating it, etc.

The hypothesis of the true volume is employed here as the simplest hypothesis. How fruitful it will prove to be, and whether the correction for the volume occupied by the dissolved body will constitute that correction term which remained to be found in order finally to establish the relation between the densities of the solvent in the liquid and gaseous phases, or whether this correction term must be sought also in other properties of the solvent—this will be shown by further investigations in the same direction.

Here we shall note only that, for aqueous solutions, account must moreover be taken of those molecular changes, hitherto little investigated, which water undoubtedly undergoes when something is dissolved in it. At the present time, by the hypothesis of the association of water (Röntgen, de Coppet, Witt, Sutherland), these enigmatic phenomena are beginning little by little to be illuminated, and perhaps in the near future it will be possible to introduce them into the calculation.

Aqueous solutions of colloids.

The investigation of the partial density of colloids was of special interest. As is known, colloidal solutions are often regarded as a transition from true solutions to true emulsions. The lowering, by dissolved colloids, of the vapor pressure and freezing temperature of the solvent is so insignificant that in some cases it cannot be detected at all.

¹ Traube, Grundriss der physikalischen Chemie. 1904.
² Wied. Ann. II, 70.
³ Kanonnikov. Zh. R. Phys.-Chem. Soc. 31 (1) 573, 1899; 32 (1), 639, 1900; 33 (1) 61; (1) 95; (1) 743. 1901.

If, in calculating the partial density of the solvent in colloidal solutions, it should turn out that the partial density of the solvent in the solution is equal or very close to the density of the pure solvent, then this would indicate that colloidal solutions are, in essence, true solutions and that formula (14), adopted for calculating the partial density of the solvent, is in general correct. If, in calculating the partial density of the solvent in a solution, it should turn out that its partial density is considerably lower than the partial density of the pure solvent, then this could serve as an indication either that formula (14), adopted for calculating the partial density, is in general not correct, or that colloids are true emulsions.

Since I was unable to find suitable material in the literature, only one aqueous solution of tannin was investigated.

The specific gravities of aqueous tannin solutions were determined, at my suggestion, by my collaborator in the measurement of the specific gravity and vapor pressure of iodine solutions in organic solvents, student Zeltenprom. The material for the investigation was a preparation from the factory of C. A. F. Kahlbaum, purified by special methods. It was dried in a desiccator over phosphorus anhydride, after which the solution was prepared.

The specific gravities were measured at \(25^\circ\) with Mendeleev pycnometers modified by me, observing all precautions and with all corrections, described in detail in Chapter III of this book.

The vapor pressures of aqueous tannin solutions were calculated by me from the well-known formula:

\[ \frac{n_1}{n_1+n_2}=\frac{p_0-p_1}{p_0}, \tag{19} \]

in which \(n_1\) denotes the number of molecules of the dissolved substance, \(n_2\)—the number of molecules of the solvent, \(p_0\)—the vapor pressure of the pure solvent, \(p_1\)—the vapor pressure of the solution.

The calculation of the vapor pressure of aqueous tannin solutions by this formula requires knowledge of the molecular weight of tannin. In the literature we find a whole series of values for the molecular weight of tannin, determined by various authors from the lowering of the freezing point of its solutions, namely: 1322 (Sabaneev)¹), 2643 (Paterno), 3700 (Paterno)²). The differences are due, on the one hand, to the fact that tannin is a mixture of chemical individuals, which gives no guarantee that the material used for the investigation always had one and the same composition, and, on the other hand, to the influence on the result of errors in measuring the magnitude of the lowering of the freezing point, a very small magnitude.

For calculating the relative value of the vapor pressure \(\frac{p_1}{p_0}\) of tannin solutions, I adopted the molecular weight of tannin as \(2000\).

In Table VII are collected: specific gravities \(S \frac{25^\circ}{4^\circ}\), partial densities

¹) Sabaneev, Journ. Russ. Phys.-Chem. Soc., 1890.
²) Paterno, Zeitschr. phys. Chem. 4, 457. 1889.

$s_1 \dfrac{25^\circ}{4^\circ}$, the relative vapor pressure $\dfrac{p_1}{p_0}$, and the true specific volume of tannin in the solution, $V_{sp}$, calculated by formula (17).

TABLE VII.

Аqueous solutions of tannin.

$n\%$	$S\dfrac{25^\circ}{4^\circ}$	$s_1\dfrac{25^\circ}{4^\circ}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	$V_{sp}.$
2,256	1,00601	0,9838	0,9865	0,9998	0,59
6,614	1,02341	0,9558	0,9582	0,9995	0,66
7,567	1,02729	0,9496	0,9523	0,9993	0,61
10,01	1,03722	0,9333	0,9360	0,9990	0,61
15,40	1,06001	0,8968	0,8995	0,9984	0,61
20,17	1,08131	0,8632	0,8658	0,9977	0,61
25,41	1,10475	0,8053	0,8076	0,9969	0,61
29,84	1,12619	0,7722	0,7745	0,9962	0,61
35,80	1,14806	0,7371	0,7393	0,9950	0,63
40,24	1,16930	0,6987	0,7008	0,9940	0,63

A comparison of the specific partial densities of water in the liquid and gaseous phases for aqueous solutions of tannin, as follows from Table VII, generally gives the same results as the corresponding comparisons for aqueous solutions of nonelectrolytes. The equality $\dfrac{s_1}{s_0} = \dfrac{p_1}{p_0}$ is sharply not satisfied if, in calculating the partial density, no correction is introduced for the volume of the tannin molecules. If such a correction is introduced, then the specific volume of tannin, calculated by formula (17), turns out to be a quantity independent of the concentration of the solution and very close (0.61) to the specific volume calculated for nonelectrolytes (0.55). It may be supposed that this relatively small difference is due to the fact that the accepted molecular weight of tannin does not quite exactly correspond to reality (is larger).

The investigated cases of aqueous solutions of nonelectrolytes are, of course, far too few (I was unable to find more extensive material) for the conclusions drawn to be regarded as final. Nevertheless, these conclusions may perhaps serve as a reason and stimulus for further work on the measurement of the specific weights and vapor pressures of solutions.

Solutions in Organic Solvents.

1) The solvent is not associated; the dissolved substance is not volatile.

Table VIII.

Solutions in ether.

\(c\)	\(\dfrac{S^{12.9^\circ}}{4^\circ}\)	\(\dfrac{s_1^{12.9^\circ}}{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	Name of the observer of vapor pressure and density
			Naphthalene \(C_{10}H_8\).
0	0.7206	0.7206	1.0000	1.0000	Noyes and Abbot ¹)
1	0.7232	0.7165	0.9943	0.993
5	0.7330	0.6981	0.9688	0.970
10	0.7443	0.6766	0.9390	0.945
20	0.7663	0.6386	0.8862	0.901
24	0.7746	0.6247	0.8669	0.885
			Azobenzene \(C_{12}H_{10}N_2\).
0	0.7206	0.7206	1.0000	1.0000	Noyes and Abbot ¹)
1	0.7234	0.7163	0.9940	0.995
5	0.7345	0.6995	0.9707	0.980
10	0.7473	0.6794	0.9428	0.962
20	0.7704	0.6420	0.8909	0.929
			Benzophenone \(C_{13}H_{10}O\).
0	0.7210	0.7210	1.0000	1.0000	Goodwin and Burgers ²)
1	0.7236	0.7164	0.9937	0.996
5	0.7351	0.7001	0.9710	0.979
10	0.7492	0.6811	0.9446	0.962
20	0.7741	0.6451	0.8947	0.933

¹) Noyes and Abbot, Zeitschr. phys. Chemie 23, 56. 1897.
²) Goodwin and Burgers, Zeitschr. phys. Chemie 28, 99.

$c$	$S\dfrac{12{,}9^\circ}{4^\circ}$	$s_1\dfrac{12{,}9^\circ}{4^\circ}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	Name of the observer of the vapor pressure and density
		Diphenylamine $C_{12}H_{11}N$.
0	0,7210	0,7210	1,0000	1,0000	Goodwin und Burgers.
1	0,7238	0,7166	0,9939	0,995	(loco cit).
5	0,7357	0,7007	0,9718	0,976
10	0,7494	0,6813	0,9449	0,955
16	0,7645	0,6591	0,9141	0,931

Aniline $C_6H_5NH_2$.

wt.%	$S\dfrac{15^\circ}{4^\circ}$	$s_1\dfrac{15^\circ}{4^\circ}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	Name of the observer of the vapor pressure and density
0	0,7195	0,7195	1,0000	1,000	Raoult¹) $\left(\dfrac{p_1}{p_0}\right)$
4,8	0,7334	0,6982	0,9700	0,960
9,5	0,7476	0,6766	0,9403	0,919	Mikhailenko²)
18,1	0,7721	0,6323	0,8789	0,846
24,5	0,7909	0,5971	0,8289	0,803	$\left(S\dfrac{15^\circ}{4^\circ}\right)$.
55,3	0,8829	0,3947	0,5485	0,576
73,4	0,9382	0,2496	0,347	0,404

Nitrobenzene $C_6H_5NO_2$.

wt.%	$S\dfrac{15^\circ}{4^\circ}$	$s_1\dfrac{15^\circ}{4^\circ}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	Name of the observer of the vapor pressure and density
0	0,71948	0,71948	1,0000	1,0000	Mikhailenko²) and Deltmer
1,718	0,72539	0,71293	0,9908	—	$\left(\dfrac{p_1}{p_0}\right);$
9,701	0,75361	0,68050	0,9458	0,943
17,064	0,78077	0,64754	0,8999	0,902
22,33	0,80136	0,62240	0,8652	0,874
25,14	0,80991	0,61093	0,8489	0,859
49,82	0,91908	0,46117	0,6410	0,719	Mikhailenko²)
69,13	1,01806	0,31422	0,4366	0,571
74,12	1,04546	0,27058	0,3761	0,517	$\left(S\dfrac{15^\circ}{4^\circ}\right)$
90,75	1,14602	0,10600	0,1473	0,268
98,89	1,20060	0,01371	0,0190	—
100,00	1,20851	0,0000	—	—

¹) Raoult, Zeitschr. phys. Chem. 2, 353. 1888. ²) Chapters III and IV.

Iodine.

$n^0/\!_0$	$S\dfrac{25^0}{4^0}$	$s_1\dfrac{25^0}{4^0}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	Names of the observers of vapor pressure and density
0	0,70811	0,70811	1,0000	1,0000	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
0,70	9,71217	0,70719	0,9986	0,9978	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
1,83	0,71988	0,70670	0,9979	0,9945	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
3,10	0,72757	0,70498	0,9956	0,9905	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
3,65	0,73090	0,70421	0,9945	0,9887	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
4,82	0,73848	0,70288	—	0,9850	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
4,915	0,73912	0,70281	0,9924	0,9847	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
6,13	0,74733	0,70154	0,9906	0,9808	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
7,37	0,75504	0,69941	0,9876	0,9770	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$
8,03	0,76184	0,70069	0,9895	0,9748	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$

Table IX.

Solutions of iodine in carbon disulfide $(CS_2)$.

$n^0/\!_0$	$S\dfrac{25^0}{4^0}$	$s_1\dfrac{25^0}{4^0}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	$V_{sp}$	Name of the observer of vapor pressure and density
0	1,25589	1,25589	1,0000	1,0000	—	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
0,60	1,26112	1,25361	0,9982	0,9985	0,1	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
1,13	1,26574	1,25142	0,9964	0,9974	0,06	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
2,02	1,27297	1,24719	0,9930	0,9948	0,07	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
2,82	1,28096	1,24487	1,9912	0,9926	0,05	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
3,34	1,28571	1,24272	0,9895	0,9912	0,05	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
4,83	1,30003	1,23727	0,9852	0,9870	0,03	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
5,85	1,30934	1,23256	0,98145	0,9840	0,04	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
6,12	1,31199	1,23166	0,9807	0,9832	0,03	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
6,48	1,31526	1,23001	0,9794	0,9821	0,04	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
9,07	1,34088	1,21920	0,9708	0,9742	0,03	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.
11,85	1,36913	1,20695	0,9610	0,9652	0,03.	Mikhailenko and Zeltner ^1) $\left(\dfrac{p_1}{p_0}\ \text{and}\ S\dfrac{25^0}{4^0}\right)$.

^1) Chapters III and IV.

Table X.

Solutions of iodine in chloroform \((CHCl_3)\).

\(n^\circ/\%\)	\(S^{25^\circ}_{4^\circ}\)	\(s_1^{25^\circ}_{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	\(V_{sp}\)	Name of the observer of the vapor pressure and density
0	1.47896	1.47896	1.0000	1.000	—	Mikhailenko and Yavorskii1 \(\left(S^{25^\circ}_{4^\circ}\right)\); Mikhailenko and Deltnevr1 \(\left(\dfrac{p_1}{p_0}\right)\).
0.782	1.48654	1.47492	0.9988	0.9980	0.04	Mikhailenko and Yavorskii1 \(\left(S^{25^\circ}_{4^\circ}\right)\); Mikhailenko and Deltnevr1 \(\left(\dfrac{p_1}{p_0}\right)\).
1.748	1.49536	1.46922	0.9931	0.9955	0.06	Mikhailenko and Yavorskii1 \(\left(S^{25^\circ}_{4^\circ}\right)\); Mikhailenko and Deltnevr1 \(\left(\dfrac{p_1}{p_0}\right)\).
2.792	1.50503	1.46301	0.9890	0.9927	0.05	Mikhailenko and Yavorskii1 \(\left(S^{25^\circ}_{4^\circ}\right)\); Mikhailenko and Deltnevr1 \(\left(\dfrac{p_1}{p_0}\right)\).

From the data presented in Tables VIII–X it follows that, for solutions of nonvolatile substances in nonassociated solvents, the relation between the densities of the solvent in the liquid and gaseous phases is expressed, apparently, in the simplest form, namely, by the equality

\[ \frac{s_1}{s_0} = \frac{p_1}{p_0}. \tag{6} \]

Deviations from equality (6) seem to be the greater, the more concentrated the solution; for dilute solutions the difference lies within the limits of observational errors; at infinite dilution it is probably equal to zero.

Thus, the law expressed approximately by equality (6) appears to belong to the class of such laws as those to which a substance obeys in a state of great rarefaction or dilution (the Mariotte–Boyle, Gay-Lussac, and Avogadro laws); namely, it is strictly exact only in the limiting, ideal case; in every actual, real case, greater or lesser deviations are observed, depending on the nature of the substances with which the experiment is performed.

If one examines more closely, in the material presented in Tables VIII–X, the ratios of the quantities \(\dfrac{s_1}{s_0}\) and \(\dfrac{p_1}{p_0}\), it is easy to notice that in all cases, with one exception (solutions of iodine in ether), \(\dfrac{p_1}{p_0}\) is greater than \(\dfrac{s_1}{s_0}\). Such a phenomenon, and moreover in a very sharply expressed form, has already been observed once, namely, in aqueous solutions of nonelectrolytes and colloids. There it was shown that this deviation from equality (6) can be taken into account with the aid of a certain constant, which was conjecturally compared with the true molecular volume of the dissolved substance and denoted \(V_{sp}\). An analogous calculation was also carried out here for solutions of iodine in carbon disulfide and chloroform, and an interesting

result. The quantity \(V_{sp}\) was calculated by formula (17) and is given in Tables IX and X alongside the quantities \(\frac{p_1}{p_0}\). As can be seen, it is very small and fluctuates within the same limits both for solutions of iodine in chloroform and for solutions of iodine in carbon disulfide. Undoubtedly, here too it must be recognized as independent of the concentration, although, owing to the insignificance of the quantity itself, experimental errors are reflected in a large percentage fluctuation of it. If one assumes that the quantity \(V_{sp}\) is on average equal to 0.05, then the true molecular volume of an iodine molecule is calculated to be 12.70 c.c. This value is surprisingly close to the atomic volume of iodine in compounds, for which Traube gives the number 13.45 c.c.

The same calculations were made for solutions in ether of naphthalene, azobenzene, benzophenone, and diphenylamine. For benzophenone the true molecular volume obtained is 45.5, for azobenzene—54.6, for diphenylamine—25.35; for naphthalene no constant value of the specific volume was obtained.¹) The numbers obtained for the true molecular volume in two cases agree very well with the numbers calculated for the true molecular volume by Kanonnikov’s method.²) Namely, for azobenzene, according to Kanonnikov, the true molecular volume is calculated as 55.6; for benzophenone—40.02. The true molecular volume of diphenylamine, calculated by Kanonnikov’s method (52.92), however, proved to be almost twice as large as that calculated here (25.35).

For solutions of iodine in ether the ratio \(\frac{s_1}{s_0} > \frac{p_1}{p_0}\). This may serve as an indication that part of the solvent forms a chemical compound with the solution. On p. 18 a method was given for calculating the amount of this chemically bound solvent if the specific gravity and the relative vapor pressure of the solution are known. These calculations were also carried out here, and the results obtained are collected in Table XI.

The part of the solvent bound to the dissolved substance in the manner of a chemical compound \((x)\) was calculated by the formula:

\[ x = (100-\pi) - \frac{p_1}{p_0}\cdot\frac{s_0}{S}\times 100,\qquad \text{where} \tag{20} \]

\(\pi\) denotes the concentration of the solution in weight percent;

\(S\)—the density of the solution;

\(s_0\)—the density of the pure solvent;

\[ \frac{p_1}{p_0} \]
—the relative vapor pressure of the solution.

¹) Perhaps this is due to experimental errors, or perhaps to other, still unknown causes. The latter thought was expressed by the authors themselves (Goodwin and Burgers), from whom the vapor-pressure data for ethereal solutions of naphthalene were taken; they noted that, when the vapor-pressure measurement experiments are repeated, identical numbers are not always obtained.

²) Kanonnikov, loco cit.

The amount of dissolved substance associated with a molecule of the solvent \((Y_{mol})\) was calculated by the formula:

\[ Y_{mol}=\frac{\pi}{x}\times 74. \tag{21} \]

Table XI.

\(\pi\%\)	\(\dfrac{S^{25^\circ}}{4^\circ}\)	\(\dfrac{p_1}{p_n}\)	\(x\)	\(Y_{mol}\)	Observers of vapor pressure and density
0,70	0,71217	0,9978	0,100	518	Mikhailenko and Deltner.¹)
1,83	0,71988	0,9945	0,36	376	Mikhailenko and Deltner.¹)
3,10	0,72757	0,9905	0,52	370	Mikhailenko and Deltner.¹)
3,65	0,73090	0,9887	0,54	500	Mikhailenko and Deltner.¹)
4,82	0,73848	0,9850	0,73	488	Mikhailenko and Deltner.¹)
4,91	0,73912	0,9847	0,75	484	Mikhailenko and Deltner.¹)
6,13	0,74733	0,9808	0,93	488	Mikhailenko and Deltner.¹)
7,37	0,75504	0,9770	0,97	562	Mikhailenko and Deltner.¹)
8,03	0,76184	0,9748	1,36	437	Mikhailenko and Deltner.¹)

Of special interest for the investigator of the relation between the partial density of the solvent in a solution and the vapor pressure of the solution were mixtures of ether with aniline and nitrobenzene. Precisely in the case of these solutions it was possible to trace the form of this relation over an infinitely wide interval of concentrations. For greater clarity I used the graphical method (Fig. 1). Along the axis of abscissae are plotted the values of the partial density of ether in the liquid phase \(\left(\dfrac{s_1}{s_0}\right)\); along the axes of ordinates are plotted the values of the relative vapor pressure of ether \(\left(\dfrac{p_1}{p_0}\right)\).²) If the relation

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0} \]

were strictly satisfied, all points of the quantities \(\dfrac{p_1}{p_0}\) would lie on the diagonal; otherwise they are situated at a greater or lesser distance from the diagonal.

¹) Chapters III and IV.
²) All the curves placed here were, where possible, carefully drawn at first on a large scale; afterward they were photographically reduced to the scale of the text.

As is shown by (Fig. 1), the curve of relative elasticities of ether vapor, both in mixtures of ether with aniline and in mixtures of ether with nitrobenzene, at first runs along one side of the diagonal, and then, crossing the diagonal, passes to the other side. Thus, for both mixtures there exists one, and only one, concentration at which the ratio \(\frac{s_1}{s_0} = \frac{p_1}{p_0}\) is strictly exact. For all other concentrations the curve of specific elasticities departs from the diagonal. The curve of the specific elasticities of ether vapor for mixtures of ether and aniline, over almost its entire

Fig. 1.

extent, runs much closer to the diagonal than does the corresponding curve for mixtures of ether and nitrobenzene. The exception is dilute solutions: for dilute solutions of mixtures of ether and nitrobenzene, the curve of the specific elasticities of ether lies very close to the diagonal (in the drawing it coincides with the diagonal). How the points of intersection of the curves with the diagonal are connected with other properties of the liquids forming the mixture—this, for lack of experimental material, remains for the present an open question.

2. Mixtures of volatile non-associated liquids.

It proved possible to investigate the following pairs of mixtures of volatile non-associated liquids; namely, mixtures of benzene and chlorobenzene, mixtures of benzene and bromobenzene, and mixtures of benzene and chloroform. The partial vapor pressures of the components of the mixtures were measured by Linebarger¹ by the method described by me in my review of methods for measuring the vapor pressure of solutions under the name of the “density” method, or the method of “isothermal distillation in a stream of gas”; the partial vapor pressure of one and the other component was calculated by Linebarger on the basis of analysis of the distillate. The specific gravities of the mixtures were measured by me (Chapter III).

The measurements of vapor pressure were made at a temperature of 34.8°; the measurements of specific gravity at temp. 25°. A comparison of the relative vapor pressures with the specific partial densities proved, however, to be possible, since here also, as Linebarger asserts on the basis of direct experiments, the relative partial vapor pressure of the components of a mixture may be regarded as independent of temperature.

The results of the comparison are collected in Table XII. The values of the relative vapor pressure $\frac{p_1}{p_0}$ given in this table are the original numbers; the relative partial densities $\frac{s_1}{s_0}$ were found by graphical interpolation of the numerical data of my measurements.

Table XII.

Benzene $C_6H_6$ and chlorobenzene $C_6H_5Cl$.

% mol $C_6H_5Cl$	$\frac{p_1}{p_0}$ benz.	$\frac{s_1}{s_0}$ benz.	$\frac{p_1}{p_0}$ chlorobenz.	$\frac{s_1}{s_0}$ chlorobenz.	Name of observers of vapor pressure and density
0	1.0000	1.0000	0	0
15.18	0.8568	0.828	0.0837	0.172	Linebarger
29.08	0.6966	0.678	0.3251	0.322	$p_1$ benz. $p_1$ chlorobenz. } at 34.8°
65.06	0.3528	0.318	0.6059	0.682
79.21	0.1919	0.186	0.9408	0.814
100.0	0	0	1.0000	1.000	Mikhailenko2 $S \dfrac{25^\circ}{4^\circ}$

Benzene \(C_6H_6\) and bromobenzene \(C_6H_5Br\).

\(\%_{\mathrm{mol}\ C_6H_5Br}\)	\(\dfrac{p_1}{p_0}\) benz.	\(\dfrac{s_1}{s_0}\) benz.	\(\dfrac{p_1}{p_0}\) bromobenz.	\(\dfrac{s_1}{s_0}\) bromobenz.	Names of the observers of vapor pressure and density
30,33	0,8141	0,659	0,3250	0,341	the same

Benzene \(C_6H_6\) and chloroform \(CHCl_3\).

\(\%_{\mathrm{mol}\ CHCl_3}\)	\(\dfrac{p_1}{p_0}\) benz.	\(\dfrac{s_1}{s_0}\) benz.	\(\dfrac{p_1}{p_0}\) chloroform	\(\dfrac{s_1}{s_0}\) chloroform	Names of the observers of vapor pressure and density
0	1,0000	1,000	0	0
16,97	0,8494	0,843	0,1369	0,157	the same
50,53	0,5110	0,519	0,4520	0,481
59,47	0,4071	0,421	0,5609	0,579
100,00	0	0	1,000	1,000

From the data presented in Table XII it follows that, for the case of mixtures of volatile liquids, the relation between the partial densities of both components in the liquid and gaseous phases is apparently not always expressed in the simple form that was observed earlier for the case of solutions when one of the components of the mixture is nonvolatile.

In order to represent visually the law governing the change in the partial vapor pressure of each component of the mixture with the change in the partial density of that component in the liquid phase, curves were also drawn here (Fig. 2). On the abscissa axis are plotted quantities proportional to the partial densities of the component in the liquid phase; on the ordinate axes are plotted quantities proportional to the partial vapor pressures of this same component.

If the equality \(\dfrac{s_1}{s_0} = \dfrac{p_1}{p_0}\) were exactly satisfied, then all points of intersection would lie on the diagonals of the rectangle (indicated in the drawing by a dotted line). Approximately this holds only for the partial vapor pressures of benzene over mixtures of benzene and chloroform. The curve of the partial vapor pressures of chloroform no longer coincides with the diagonal; it does, however, pass very close to it.

The relations are more complex for mixtures of benzene with chlorobenzene; namely, the curve of the partial vapor pressures of chlorobenzene crosses the diagonal twice. It is very regrettable that the insufficiency of observations does not allow this extremely curious fact to be established firmly. At the same time, the curve of par-

partial vapor pressures of benzene for these same mixtures will all the time run on one side of the diagonal and, moreover, very close to it.

Thus, if not simple, then in any case very nearly simple relations are nevertheless observed for one of the three cases investigated, namely, for mixtures of benzene with chloroform.

It may be thought that for those pairs of liquids for which the partial vapor pressure is a linear function of the molecular concentration of their mixtures, such as mixtures of ethylene bromide and propylene bromide (Zawidzki¹) and methyl chloride and carbonic anhydride (Hartmann²), the equation

$$ \frac{s_1}{s_0} = \frac{p_1}{p_0} $$

will be exactly satisfied for both components of the mixture.³

Fig. 2.

3. Mixtures of Associated Liquids

Among mixtures of such liquids, mixtures of benzene with acetic acid were investigated. Benzene belongs to the class of non-associated liquids, or, rather, only slightly associated ones (Traube determines the association factor of benzene as the number 1.18). Acetic acid, on the contrary, is strongly associated both in the liquid and in the gaseous state.

For acetic acid in the liquid state Ramsay and Shields¹, by the “surface-tension” method, determined the association factor to be 2.06 at a temperature of 20°. Traube², measuring the degree of association of liquids by the method of “molecular volumes,” gives an association factor of 1.56 for liquid acetic acid. With the aid of the van der Waals theory the same association factor for liquid acetic acid is calculated as 3.36—3.49. Finally, Linebarger³ determines the molecular weight of liquid acetic acid as between 240—244, etc. Thus, different methods determine the degree of association of liquid acetic acid very differently; but they all agree that acetic acid is associated in the liquid state.

In the dissolved state, at least in solutions in benzene, acetic acid is also associated; namely, the data of the measurement of the freezing temperature of benzene solutions of acetic acid by Raoult⁴, Hentschel⁵, and Beckmann⁶, consistently show that acetic acid, even at very high dilution, is present in solution as double molecules. The fact that acetic acid in the vapor state is also associated is a long and well-known fact.

According to Beckmann⁷, benzene in solutions in acetic acid is not associated.

The partial vapor pressures of benzene and acetic acid over mixtures of benzene with acetic acid were measured by Zawidzki⁸ at a temperature of 49.99°. The partial vapor pressure of acetic acid given by him corresponds to the total pressure—that is, to the sum of the pressures of double and simple molecules present in the gaseous phase. In addition, the same partial vapor pressures of benzene and acetic acid were measured by Linebarger⁹ at temperatures of 35° and 20°. In his data, too, the partial vapor pressure of acetic acid corresponds to the total pressure.

Measurements of the density of liquid mixtures of benzene with acetic acid were made by me at temp. 25° (Chapter III).

In Table XIII the concentration of the solution is given in weight percent (wt. %), i.e., by the content of the number of grams of acid in 100 grams of solution;

the relative partial elasticities of the vapor of both components of the mixture
\(\left(\dfrac{p_1}{p_0}\right.\) benzene and \(\left.\dfrac{p_1}{p_0}\right.\) acid) are the original numbers; the relative partial densities
\(\left(\dfrac{s_1}{s_0}\right.\) benzene and \(\left.\dfrac{s_1}{s_0}\right.\) acid) were obtained by graphical interpolation of the values of specific gravity found by me.

Table XIII.

Mixtures of benzene with acetic acid. (1)

\(x^\circ\) acid	\(\dfrac{p_1}{p_0}\) benz.	\(\dfrac{s_1}{s_0}\) benz.	\(\dfrac{p_1}{p_0}\) acid	\(\dfrac{s_1}{s_0}\) acid	Name of observer of vapor elasticity and density
0	1,000	1,0000	0	0
1,7	0,9954	0,985	0,065	0,014
4,1	0,9685	0,964	0,1179	0,034
5,0	0,9629	0,9565	0,1309	0,0415
10,0	0,9343	0,912	0,2078	0,084	Zawidzky ¹)
13,77	0,9164	0,878	0,2563	0,117	\(p_1\) benz. \(\}\ 49,99^\circ\) \(p_1\) acid \(\}\ 49,99^\circ\)
20,9	0,8678	0,8135	0,3321	0,179	Mikhailenko ²)
25,35	0,8412	0,773	0,3701	0,218	\(S\ \dfrac{25^\circ}{4^\circ}\)
35,7	0,7907	0,676	0,4477	0,313
41,36	0,7521	0,622	0,4892	0,3665
43,6	0,7323	0,601	0,5181	0,3875
65,30	0,5736	0,3845	0,6552	0,605
68,0	0,6642	0,3565	0,6642	0,634
72,42	0,5058	0,310	0,7256	0,681
88,10	0,2819	0,138	0,9152	0,8575
98,5	0,0498	0,0175	0,9874	0,9815
100	0	0	1,0000	1,0000

1) Loco cit.
2) Chapter III.

Table XIV.

Mixtures of benzene with acetic acid. (2)

% acid	$\dfrac{p_1}{p_0}$ benz.	$\dfrac{s_1}{s_0}$ benz.	$\dfrac{p_1}{p_0}$ acid	$\dfrac{s_1}{s_0}$ acid	Name of observer of vapor pressure and density
0	1,0000	1,000	0	0	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
6,44	0,9587	0,944	0,1321	0,053	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
15,17	0,8896	0,866	0,2415	0,129	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
37,10	0,8013	0,663	0,3963	0,326	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
43,99	0,7293	0,597	0,4982	0,3915	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
49,86	0,7062	0,540	0,5283	0,449	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
53,24	0,6683	0,507	0,5623	0,481	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
54,65	0,6663	0,493	0,5774	0,495	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
56,60	0,6575	0,473	0,6189	0,515	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
73,87	0,4979	0,294	0,6944	0,697	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
80,0	0,4062	0,227	0,8416	0,764	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
100,0	0	0	1,0000	1,000	Linebarger¹); $p_1$ benz., $p_1$ acid, at 35°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$

Table XV.

Mixtures of benzene with acetic acid. (3)

% acid	$\dfrac{p_1}{p_0}$ benz.	$\dfrac{s_1}{s_0}$ benz.	$\dfrac{p_1}{p_0}$ acid	$\dfrac{s_1}{s_0}$ acid	Name of observer of vapor pressure and density
0	1,0000	1,0000	0	0	Linebarger¹); $p_1$ benz., $p_1$ acid, at 20°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
53,24	0,6422	0,507	0,5640	0,481	Linebarger¹); $p_1$ benz., $p_1$ acid, at 20°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
80.00	0,4365	0,227	0,7777	0,764	Linebarger¹); $p_1$ benz., $p_1$ acid, at 20°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
97,28	0,0820	0,032	0,9743	0,967	Linebarger¹); $p_1$ benz., $p_1$ acid, at 20°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$
100,00	0	0	1,0000	1,000	Linebarger¹); $p_1$ benz., $p_1$ acid, at 20°; Mikhailenko²), $S \dfrac{25^\circ}{4^\circ}$

¹) Loco cit.

²) Chapter III.

From the data given in Tables XIII–XV, and also from drawing (3), constructed in exactly the same way as the preceding ones, it is evident that the relation between the partial vapor pressure of both the associated and the non-associated component of the solution and its partial density in the liquid phase is expressed in a more complicated manner than in all the preceding cases.

Fig. 3.

Drawing (3), moreover, makes it possible to note that neither curve intersects the diagonal, and that the curve of the partial vapor pressures of benzene has a more regular form, although it lies farther from the diagonal than the corresponding curve of the partial vapor pressures of acetic-acid vapor.

Chapter II.

Relations between the partial density of the solvent in a solution and other quantities.

The relations between the magnitude of the partial density of the solvent in the liquid phase and other quantities of the solution may be investigated from two points of view: from the point of view of obtaining, by an indirect route, data for judging the form of the relation between the partial density and the vapor pressure, and from the point of view of establishing the connection between the partial density and other measurable properties of the solution. In treating the material collected in this chapter, both of these points of view were kept in mind.

Partial density and temperature.

As is known, the magnitude of the relative vapor pressure of solutions varies comparatively little with temperature. This circumstance was already noted by Babo¹ and formulated by him in the sense that the magnitude of the relative vapor pressure of solutions does not depend on temperature. This is Babo’s law, and it is usually expressed as follows:

\[ \frac{p_1}{p_0} = Const., \quad \text{where} \]

\(p_1\) is the vapor pressure of the solution,

\(p_0\) is the vapor pressure of the pure solvent.

Soon Kirchhoff², with the aid of the methods of thermodynamics, showed that between the magnitude of the relative vapor pressure of solutions and the heat of dilution of solutions there exists a causal connection, and that Babo’s law is strictly exact only for the case when the heat of dilution of the solution is equal to zero. If the heat of dilution of the solution has some magnitude, whether positive or negative, then greater or lesser deviations from Babo’s law must be observed.

Subsequently Babo’s law was subjected many times both to theoretical investigation and to experimental verification. Such, for example, are the works of Planck¹), Duhem²), Arons³), Tammann⁴), Dieterici⁵), Jüptner⁶), and others. All these investigations, while in general confirming Kirchhoff’s conclusions, at the same time showed that the magnitude of the heat of dilution of a solution is reflected numerically only slightly in the magnitude of the relative vapor pressure of solutions, and that, in order to notice this influence, the heat of dilution must attain large values. In cases where the heat of dilution has a small value, this influence either cannot be established at all, or, if it can, then only by employing very precise methods for measuring vapor pressure. Let us point, for example, to the work of Emden⁷), who investigated the vapor pressure of aqueous solutions of a series of salts within the range \(20^\circ\)—\(100^\circ\) and showed that the deviations from the mean value

\[ \frac{p_1}{p_0} \]

fluctuate irregularly in one direction and the other around a certain constant—and consequently lie within the limits of experimental error; let us also point to Raoult’s work⁸) on the vapor pressure of solutions of organic substances in ether, which gave the same results as Emden’s; to the works of Dieterici⁹), and others. My measurements of the vapor pressure of aqueous sugar solutions and of solutions in organic solvents (Chapter IV) gave the same results.

Thus, in the majority of cases (with the exception of those solutions whose heat of dilution is very large) the ratio \(\frac{p_1}{p_0}\) may be considered independent of temperature, at least within the average accuracy attained by our methods of measuring vapor pressure.

If we accept that the equality \(\frac{p_1}{p_0} = \frac{s_1}{s_0}\) is valid, it follows from this that:

\[ \frac{s_1}{s_0} = Const. \tag{22} \]

i.e. the magnitude of the relative partial density of the solvent in the solution does not depend (depends little) on temperature. This is Babo’s law as applied to the solvent in the liquid phase.

The investigation of the influence of temperature on the specific partial density of the solvent thus acquires new interest. Namely, apart from the fact that it may serve to verify the equality \(\frac{p_1}{p_0} = \frac{s_1}{s_0}\) in those

¹) Planck, Wied. Ann. 30, 562. 1887.
²) Duhem, Compt. rend. 104, 683. 1887.
³) Arons, Wied. Ann. 25, 408. 1885.
⁴) Tammann, Wied. Ann. 36, 693. 1889.
⁵) Dieterici, Wied. Ann. 45, 207. 1892.
⁶) Jüptner, Zeitschr. phys. Chem. 38, 76.
⁷) Emden, Wied. Ann. 38, 447. 1889.
⁸) Raoult, Ann. de chim. et phys. [6]. 15, 375. 1888.
⁹) Dieterici, Wied. Ann. 50, 47. 1893.

in cases where the vapor pressure of solutions is unknown, it is also of independent interest—an interest in determining whether the specific partial density of the solvent in the solution is causally connected with the heat of dilution of the solution or not.

The results of calculating the partial densities of the solvent in the solution at different temperatures are brought together in Tables XVI, XVII, and XVIII.

In Table XVI the specific gravities of aqueous solutions of sodium chloride and the specific gravities of pure water are taken from the work of Gerlach¹. In Tables XVII and XVIII the experimental data are taken from the work of Tammann and Hirschberg, Zeitschr. phys. chem., 13, 543, 1894.

The specific gravities of aqueous solutions of lithium chloride are taken from Mendeleev’s book, Investigation of Aqueous Solutions by Specific Gravity. 1887

The composition of the solution is expressed in weight percent \((\pi\%)\), or by the ratio between the mass of the salt and the mass of the solvent, taken as \(100\) \((c)\).

For comparison there is given a table of vapor pressures of the aqueous solution of sodium chloride, taken from the above-cited work of Emden (Table XIX).

Table XVI.

Sodium chloride \(NaCl\).

| Temp. | \multicolumn{3}{c}{\(\pi=1\%\)} | Temp. | \multicolumn{3}{c}{\(\pi=5\%\)} |
|---:|---:|---:|---:|---:|---:|---:|---:|
| | \(S\frac{t^0}{15^0}\) | \(s_1\frac{t^0}{15^0}\) | \(\frac{s_1}{s_0}\) | | \(S\frac{t^0}{15^0}\) | \(s_1\frac{t^0}{15^0}\) | \(\frac{s_1}{s_0}\) |
| \(0^\circ\) | 1,0083 | 0,9979 | 0,9972 | \(0^\circ\) | 1,03877 | 0,9868 | 0,9861 |
| \(10^\circ\) | 1,0079 | 0,9978 | 0,9972 | \(10^\circ\) | 1,03737 | 0,9855 | 0,9849 |
| \(20^\circ\) | 1,0065 | 0,9964 | 0,9970 | \(20^\circ\) | 1,03495 | 0,9832 | 0,9838 |
| \(30^\circ\) | 1,0036 | 0,9936 | 0,9970 | \(30^\circ\) | 1,03166 | 0,9800 | 0,9834 |
| \(40^\circ\) | 1,0001 | 0,9901 | 0,9969 | \(40^\circ\) | 1,02788 | 0,9765 | 0,9832 |
| 50 | 0,9960 | 0,9861 | 0,9969 | \(50^\circ\) | 1,02342 | 0,9722 | 0,9830 |
| \(60^\circ\) | 0,9908 | 0,9809 | 0,9941 | 80 | 1,00632 | 0,9560 | 0,9831 |
| \(70^\circ\) | 0,9851 | 0,9753 | 0,9969 | \(90^\circ\) | 0,99997 | 0,9500 | 0,9835 |
| \(80^\circ\) | 0,9789 | 0,9690 | 0,9967 | \(100^\circ\) | 0,99385 | 0,9441 | 0,9841 |
| \(90^\circ\) | 0,9727 | 0,9630 | 0,9970 | | | | |
| \(100^\circ\) | 0,9663 | 0,9566 | 0,9970 | | | | |

| Temp. | \multicolumn{3}{c}{\(\pi=10\%\)} | Temp. | \multicolumn{3}{c}{\(\pi=25\%\)} |
|---:|---:|---:|---:|---:|---:|---:|---:|
| | \(S\frac{t^0}{15^0}\) | \(s_1\frac{t^0}{15^0}\) | \(\frac{s_1}{s_0}\) | | \(S\frac{t^0}{15^0}\) | \(s_1\frac{t^0}{15^0}\) | \(\frac{s_1}{s_0}\) |
| \(0^\circ\) | 1,07764 | 0,9699 | 0,9692 | \(0^\circ\) | 1,19897 | 0,8992 | 0,8986 |
| \(30^\circ\) | 1,06824 | 0,9614 | 0,9647 | \(30^\circ\) | 1,18439 | 0,8883 | 0,8913 |
| \(70^\circ\) | 1,04779 | 0,9430 | 0,9639 | \(70^\circ\) | 1,16144 | 0,8711 | 0,8904 |
| \(100^\circ\) | 1,02947 | 0,9054 | 0,9657 | \(100^\circ\) | 1,14338 | 0,8575 | 0,8938 |

Lithium chloride \(LiCl\).

\(\pi = 4{,}21.\)

Temp.	\(S \dfrac{t^0}{4^0}\)	\(s_1 \dfrac{t^0}{4^0}\)	\(\dfrac{s_1}{s_0}\)
\(0^0\)	1,0258	0,9825	0,9827
\(20^0\)	1,0230	0,9799	0,9817
\(40^0\)	1,0169	0,9741	0,9788
\(60^0\)	1,0082	0,9657	0,9820
\(80^0\)	0,9976	0,9556	0,9832
\(100^0\)	0,9850	0,9436	0,9843

\(\pi = 11{,}90.\)

Temp.	\(S \dfrac{t^0}{4^0}\)	\(s_1 \dfrac{t^0}{4^0}\)	\(\dfrac{s_1}{s_0}\)
\(0^0\)	1,0711	0,9436	0,9438
\(20^0\)	1,0670	0,9400	0,9417
\(40^0\)	1,0607	0,9345	0,9390
\(60^0\)	1,0527	0,9274	0,9431
\(80^0\)	1,0430	0,9189	0,9454
\(100^0\)	1,0322	0,9094	0,9486

\(\pi = 35{,}84.\)

Temp.	\(s \dfrac{t^0}{4^0}\)	\(s_1 \dfrac{t^0}{4^0}\)	\(\dfrac{s_1}{s_0}\)
\(20^0\)	1,2212	0,7837	0,7851
\(40^0\)	1,2144	0,7794	0,7831
\(60^0\)	1,2070	0,7746	0,7877
\(80^0\)	1,1991	0,7696	0,7918
\(100^0\)	1,1907	0,7642	0,7971

Table XVII.

Alcohol solutions.

\(c\)	\(S \dfrac{10^0}{10^0}\)	\(\dfrac{s_1}{s_0}\)	\(S \dfrac{20^0}{20^0}\)	\(\dfrac{s_1}{s_0}\)	\(S \dfrac{30^0}{30^0}\)	\(\dfrac{s_1}{s_0}\)
Potassium acetate.	Potassium acetate.	Potassium acetate.	Potassium acetate.	Potassium acetate.	Potassium acetate.	Potassium acetate.
0	0,9894	1,0000	0,9788	1,0000	0,9680	1,0000
4,61	0,9897	0,9562	0,9793	0,9564	0,9689	0,9568
8,03	0,9899	0,9261	0,9797	0,9267	0,9695	0,9273
12,26	0,9902	0,8915	0,9799	0,8918	0,9701	0,8927
Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.
5,90	0,9897	0,9446	0,9792	0,9447	0,9687	0,9450
15,90	0,9901	0,8634	0,9799	0,8638	0,9697	0,8644
33,30	0,9904	0,7509	0,9809	0,7519	0,9710	0,7524

Sublimate.

12,0	0,9894	0,8929	0,9790	0,8930	0,9684	0,8932
25,09	0,9895	0,7995	0,9793	0,8003	0,9689	0,8006
35,70	0,9897	0,7371	0,9795	0,7374	0,9691	0,7377

Table XVIII.

Ether solutions.

\(c\)	\(S\dfrac{10^0}{10^0}\)	\(\dfrac{s_1}{s_0}\)	\(S\dfrac{20^0}{20^0}\)	\(\dfrac{s_1}{s_0}\)	\(S\dfrac{30^0}{30^0}\)	\(\dfrac{s_1}{s_0}\)
Benzoic acid.	Benzoic acid.	Benzoic acid.	Benzoic acid.	Benzoic acid.	Benzoic acid.	Benzoic acid.
0	0,9849	1,0000	0,9695	1,0000	0,9537	1,0000
10,14	0,9859	0,9088	0,9712	0,9096	0,9565	0,9109
20,28	0,9868	0,8330	0,9728	0,8342	0,9594	0,8364
Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.	Salicylic acid.
33,19	0,9876	0,7528	0,9749	0,7550	0,96190	0,7573
Naphthalene.	Naphthalene.	Naphthalene.	Naphthalene.	Naphthalene.	Naphthalene.	Naphthalene.
15,54	0,9863	0,8666	0,9722	0,8682	0,9580	0,8695
28,80	0,9867	0,7778	0,9734	0,7795	0,9597	0,7814
Sublimate.	Sublimate.	Sublimate.	Sublimate.	Sublimate.	Sublimate.	Sublimate.
5,70	0,9851	0,9463	0,9697	0,9463	0,9539	0,9463

Table XIX.

Sodium chloride \(NaCl\).
\(c = 5,067\) (Emden).

\(t^0\)	\(p_0\)	\(p_1\)	\(\dfrac{p_1}{p_0}\)
18,92	16,32	15,8	0,938
25,44	24,28	23,4	0,963
30,13	31,91	31,8	0,965
35,56	45,71	44,3	0,969
40,88	57,67	55,55	0,963
44,92	71,19	69,5	0,976

\(t^\circ\)	\(p_0\)	\(p_1\)	\(\dfrac{p_1}{p'_0}\)
44,69	90,61	87,3	0,963
55,09	117,91	113,6	0,963
60,09	149,21	144,7	0,969
64,48	183,10	177,9	0,971
70,85	241,26	234,3	0,971
75,86	298,37	289,7	0,971
82,33	388,71	262,7	0,967
85,99	449,34	434,41	0,966
91,36	525,55	534,2	0,966

From the numerical data of Tables XVI, XVII, and XVIII it follows that, while the temperature changes from \(0^\circ\) to \(100^\circ\), and the specific gravities and partial densities change by 5% of their initial value, the relative partial density fluctuates within comparatively very small limits. In general, the picture is the same as in the calculation of the value of the relative elasticity of vapor.

Thus, Babo’s law, apparently, can also be transferred to the partial densities of the solvent in the liquid phase.

Examining more closely the numerical values of the relative partial density given in Table XVI, we do not, however, have the right to consider the ratio \(\dfrac{s_1}{s_0}\) constant.

Indeed, the specific gravities are given with an accuracy of \(\pm 0{,}0002\). Consequently, the experimental error can affect only the fourth decimal place of the ratio \(\dfrac{s_1}{s_0}\); but we see that with temperature the third decimal place changes, and moreover regularly, so that between \(60^\circ\) and \(70^\circ\) there is a minimum.

I drew attention to this circumstance already in my first article¹) and then pointed out that this “curious minimum of the ratio \(\dfrac{s_1}{s_0}\) deserves special investigation.”

Such investigations were not long in coming, and here I wish to show that their result should be regarded as new evidence of the correctness of the conclusion that Babo’s law is applicable to the partial densities of the solvent in the liquid phase.

It was already indicated above that Babo’s law, as applied to the elasticity of the vapor of solutions, is strictly exact only in the case when the heat of dilution of the solution is equal to zero, and that in the case when it is not equal to zero, between the heat of dilution and the relative magnitude of the lowering of the elasticity

¹) Ya. I. Mikhailenko. On the relation between vapor elasticity and density. Univ. Izv. Kiev. 1898.

there exists a certain relation between the vapor pressure of the solution and the heat of dilution of the solution, which was formulated by Kirchhoff in the following form¹:

\[ \frac{dQ(x)}{dx}=-RT^2 \frac{d\ln \frac{p_0}{p_1}}{dT}, \tag{23} \]

where

\(dQ(x)\) is the heat of solution of a molecule of the substance up to “dilution” \(x\)²;
\(T\) — absolute temperature;
\(R\) — gas constant;
\(p_0\) — vapor pressure of the solution;
\(p_1\) — vapor pressure of the solvent.

It follows from equation (23) that, when the quantity \(\ln \frac{p_0}{p_1}\), which may, without great error, be taken as equal to \(\frac{p_0-p_1}{p_0}\), i.e. to the relative lowering of the vapor pressure of the solution, increases with temperature, the heat of dilution must be negative; when the quantity \(\ln \frac{p_0}{p_1}\) decreases with temperature, the heat of dilution must be positive. If the content of Babo’s law can be transferred to the solvent in the liquid phase, then, evidently, the magnitude of the relative lowering of the partial density of the solvent will be connected in the same way with the heat of dilution of the solution. And from this it follows that the minimum of the relative partial density observed for solutions of \(NaCl\) must correspond to a zero heat of dilution of the solution; further, for temperatures at which the relative partial densities increase with temperature, the heat of dilution of the solution must be negative; for those temperatures at which the partial densities decrease with temperature, the heat of dilution of the solution must be positive.

These predictions have found full and not only qualitative, but apparently also quantitative, confirmation in the recently performed interesting experiments of Colson³. Namely, he found that the heat of dilution of aqueous solutions of the salts \(NaCl\), \(KCl\), \(NaNO_3\), and \(KNO_3\) changes its sign with temperature; for each solution there is one temperature at which this heat of dilution is zero. For solutions of \(NaCl\), according to Colson’s experiments, this temperature lies at \(52^\circ\); for aqueous solutions of \(KCl\) it lies at \(64.5^\circ\); for solutions of \(NaNO_3\) — at \(116^\circ\); finally, for solutions of \(KNO_3\) — at \(122^\circ\) (the last two numbers were found by extrapolation). Comparing the results of Colson’s experiments with the course of the change in the magnitude of the partial lowering of density, we find complete agreement in the sense of Babo’s law.

In Table XX are combined the thermal effects of dilution of solutions of the salts investigated by Colson at different temperatures, where \(\Delta\) denotes the decrease or increase of temperature upon dilution of \(100\) c. cm. of a saturated salt solution with \(400\) c. cm. of water.

In Table XXI is given the course with temperature of the values of the relative partial density

\[ \frac{s_0-s_1}{s_0} \]

for solutions of the same salts.

Partial densities were calculated from data taken from the book by D. Mendeleev, Investigation of Aqueous Solutions by Specific Gravity. 1887.

Table XX.

NaCl	NaCl	KCl	KCl	NaNO₃	NaNO₃	KNO₃	KNO₃
Temp.	A	Temp.	A	Temp.	A
15.0°	−0.715°	13.4°	−0.465°	14.4°	−2.33°	41.5°	−0.39°
36.7	−0.25	29.0	−0.31	18.0	−2.22	49.3	−0.35
43.8	−0.15	40.3	−0.21	29.3	−1.94	57.2	−0.31
46.6	−0.085	41.5	−0.20	42.0	−1.62	88.0	−0.16
53.5	+0.03	46.3	−0.145	89.7	−0.63	92.0	−0.145
54.2	+0.03	56.3	−0.07	92.7	−0.59
		92.8	+0.18

Table XXI.

NaCl, π = 5.0%	NaCl, π = 5.0%	KCl, π =	KCl, π =	NaNO₃, π = 14.9%	NaNO₃, π = 14.9%	KNO₃, π = 10.8%	KNO₃, π = 10.8%
t°	$\dfrac{s_0 - s_1}{s_0}$	t°	$\dfrac{s_0 - s_1}{s_0}$	t°	$\dfrac{s_0 - s_1}{s_0}$	t°	$\dfrac{s_0 - s_1}{s_0}$
0°	0.0139	—	—	0°	0.0532	—	—
10	0.0151	10°	0.0192	19.5	0.0586	19.5°	0.0461
20	0.0162	19.5	0.0198	40	0.0619	40	0.0481
30	0.0166	40	0.0205	60	0.0637	60	0.0488
40	0.0168	60	0.0205	80	0.0643	80	0.0491
50	0.0170	80	0.0201	100	0.0644	100	0.0492
80	0.0169	100	0.0198
90	0.0165
100	0.0169

As the data of Tables XX and XXI show, the relative decreases in vapor pressure do indeed follow the heats of dilution in the sense of Kirchhoff’s rule. In solutions of \(NaCl\) and \(KCl\), the maxima of the magnitudes of the relative partial density lie within the same temperature limits as does the zero heat of dilution. For solutions of \(NaNO_3\) and \(KNO_3\), the relative magnitudes of the decrease in the partial density of the solvent increase continuously; their maximum lies beyond \(100^\circ\). In complete agreement with this, the zero heat of dilution also lies beyond \(100^\circ\).

The attempt to transfer the content of Babo’s law to the partial densities of the solvent in the liquid phase is being made here, as far as I know, for the first time. The results obtained give grounds to hope that more extensive and more detailed investigations into the application of Babo’s law to the liquid phase of a solution will bring new life to the study of the complex and difficult questions concerning the relation between the temperature and the volume of solutions, and will serve as an encouraging stimulus for practical work on measuring the coefficients of thermal expansion of solutions of substances in organic solvents—measurements which at present are almost nonexistent. One may also hope that Babo’s law, in investigations in this field, will prove useful as a guiding principle.

For the time being, Babo’s law, in its application to the liquid phase, may be used for an approximate calculation of the specific gravities of solutions at various temperatures, and hence of their coefficients of thermal expansion. Namely, let there be given a solution whose concentration, expressed in weight percent, is \(x\%\); the specific gravity of this solution at some temperature is \(S \dfrac{t^0}{4^0}\).

The partial density of this solution \(s_1 \dfrac{t^0}{4^0}\) will then be:

\[ s_1 \frac{t^0}{4^0} = S \frac{t^0}{4^0} \times \frac{100-x}{100}. \]

If it is assumed that \(\dfrac{s_1}{s_0}\) does not change with temperature, then the specific gravity of this same solution at some other temperature \(t_1\) is calculated from the equation:

\[ S \frac{t_1}{4^0} = K \times \frac{100}{100-x} \times s_0 \frac{t_1}{4^0}, \quad \text{where} \tag{24} \]

\(K\) is a constant equal to \(\dfrac{s_1}{s_0}\) for this solution.

With the aid of equations (22) and (24) it is also easy to show that, if Babo’s law holds for some solution, then this solution must expand with heat according to the same law as the solvent.

Partial Density and Osmotic Pressure.

Definition and classification of osmotic pressure. If in a vessel \(AB\) (Fig. 4), closed at both ends by pistons moving without friction and divided into two halves by a partition permeable to the given liquid, this liquid is present, then, in the case of equilibrium, equal forces \((P=P')\), of any magnitude but not less than the elasticity of the saturated vapor of this liquid at the temperature of the experiment, must be applied to both pistons.

Fig. 4.

If in one compartment of the vessel there is one solution, and in the other compartment another solution of the same solutes but of a different concentration, or, in general, a solution of any other solute in the same solvent, or the pure solvent, and if the membrane is permeable to the solvent but impermeable to the dissolved solute, then, in the case of equilibrium, generally different forces must be applied to the pistons

\[ (P \gtrless P'). \]

The equilibrium of two solutions separated by a partition permeable to the solvent but impermeable to the dissolved solutes is called osmotic equilibrium.

The difference of the applied forces is called osmotic pressure.

Osmotic equilibrium is, obviously, a special case of the equilibrium of two phases under different pressures. The semipermeable partition, on the one hand, makes it possible to realize this difference of pressures; on the other hand, it gives the solvent the possibility of passing from one phase into the other. If the pressure on some phase changes, then a transition of the solvent from one phase into the other begins—a diffusion or, otherwise, osmotic current of the solvent from one compartment of the vessel into the other, which ceases only when, as a consequence of the resulting change in the concentrations of the one and the other solution, a new equilibrium is established at a new difference of pressures.

We distinguish the following cases of osmotic equilibria.

1) In one compartment of the vessel \(AB\) there is a solution \((B)\), in the other compartment—a pure solvent \((A)\). The applied forces in the state of equilibrium are \(P\) and \(P'\).

a) Let the solvent be under the pressure of its own vapor, i.e. \(P'=p_0\); then, as experiment shows, \(P\) is always a positive quantity and always \(P>p_0\); consequently, \(P-p_0=Q_1\) is also a positive quantity; i.e., in order to maintain the solution in osmotic equilibrium with the pure solvent, which is under the pressure of its own vapor, some additional positive …

positive pressure; otherwise, the solution must be compressed; we shall call the osmotic pressure \(Q_1\) a positive osmotic pressure on the solution;

b) let the solution be under the pressure of its own vapor, i.e. \(P=p_1\); then, as experiment shows, \(P'\) is always a negative quantity; \(P'-p_1=Q_2\) is also a negative quantity; i.e., in order that a solution, being under the pressure of its own vapor, may be in osmotic equilibrium with the pure solvent, a certain negative pressure must be applied to the solvent—otherwise, the solvent must be stretched; the osmotic pressure \(P'-p_1=Q_2\) we shall call the negative osmotic pressure on the solvent;

c) in the general case, if \(P'\), the pressure on the solvent, is positive, i.e., if the solvent is compressed, then \(P-P'=Q_1\), i.e. the osmotic pressure is always positive; if \(P'\) is a negative quantity, i.e. if the solvent is stretched, then \(P'-P=Q_2\), i.e. the osmotic pressure is always negative; the magnitude \(P\) in this case may be positive or negative, but \(Q_2\) is always a negative quantity.

2) In both compartments of the vessel there are solutions \(A\) and \(B\). The applied forces in the state of osmotic equilibrium are \(P'\) and \(P\). If both applied forces \(P\) and \(P'\) are positive, then the greater pressure falls on that solution whose vapor elasticity in the void is smaller.¹)

Relation between the osmotic pressure and the partial density of the solvent in the solution. Between the osmotic pressure and other quantities of the solution, by means of the methods of thermodynamics, a certain relation may be derived, which in its most exact form, in general form, is expressed by the following equality:

\[ \left(\frac{1}{s_{P_0}}+\frac{1}{s^2_{P_0}}\pi\frac{\partial s_{P_0}}{\partial \pi}\right)(P-p_1) \left(1-\frac{P+p_1-2P_0}{2}k\right)+ \]

\[ +\frac{1}{s_{P_0}}\pi\frac{\partial k}{\partial \pi} \frac{P^2-p_1^2-2P_0(P-p_1)}{2} \]

\[ -\left(\frac{1}{s'_{P_0}}+\frac{1}{s'^2_{P_0}}\pi'\frac{\partial s'_{P_0}}{\partial \pi'}\right)(P'-p'_1) \left(1-\frac{P'+p'_1-2P_0}{2}k'\right)- \]

\[ -\frac{1}{s'_{P_0}}\pi'\frac{\partial k'}{\partial \pi'} \frac{P'^2-p_1'^2-2P_0(P'-p'_1)}{2} = \int_{p}^{p'} v\,dp. \tag{25} \]

In this formula \(P\) and \(P'\) are the pressures that must be applied to the solutions so that they are in osmotic equilibrium with one another, under the indispensable condition that the concentration of the solutions can change only as a result of the addition or removal of some one constituent part of the solution.

¹) A more detailed justification of this classification and of the concept of negative osmotic pressure is given in my article: Ya. I. Mikhailenko. The Relation between the Elasticity of the Vapor of a Solution and Its Osmotic Pressure. Kiev. 1902.

²) This expression was derived by me, by different methods, in the above-cited article.

\(s_{P_0}\) and \(s'_{P_0}\) are the specific weights of both solutions, measured at some arbitrarily chosen pressure \(P_0\); \(k\) and \(k'\) are the coefficients of compression of the solutions; \(p_1\) and \(p'_1\) are the vapor pressures of both solutions in the case when no external forces are applied to the surface of separation.

\(\pi\) and \(\pi'\) are the contents of dissolved substances in 100 parts by weight of the solution.

\(P-P'=Q\) is the osmotic pressure.

If it is admitted that saturated vapors obey the Boyle–Mariotte and Gay-Lussac laws and, in addition, if it is assumed that the specific weights \(s\) and \(s'\) are measured at pressures equal to the vapor pressure of the saturated vapor of the solutions, then equation (25) takes the following, simpler form:

\[ \begin{gathered} \left(\frac{1}{s}+\frac{1}{s^2}\pi\frac{\partial s}{\partial \pi}\right)(P-p_1) \left(1-\frac{P-p_1}{2}k\right) +\frac{1}{s}\pi\frac{\partial k}{\partial \pi}\frac{(P-p_1)^2}{2} \\ -\left(\frac{1}{s'}+\frac{1}{s'^2}\pi'\frac{\partial s'}{\partial \pi'}\right)(P'-p'_1) \left(1-\frac{P'-p'_1}{2}k'\right) -\frac{1}{s'}\pi'\frac{\partial k'}{\partial \pi'}\frac{(P'-p'_1)^2}{2} \\ =RT\ln\frac{p'_1}{p_1}. \end{gathered} \tag{26} \]

In certain particular cases formula (26) is simplified still further. Namely:

1) Let the solution whose vapor pressure is \(p_1\) be in osmotic equilibrium with the pure solvent under the pressure of its own vapor. Then, in equation (26), the terms containing the multipliers \(\frac{\partial s'}{\partial \pi'}\) and \(\frac{\partial k'}{\partial \pi'}\) become equal to 0, the term \(\frac{1}{s'}\) becomes equal to \(V_0\), i.e. to the specific volume of the pure solvent, \(P'\) will be equal to \(p'_1=p_0\), and equation (26) takes the form:

\[ \left(\frac{1}{s}+\frac{1}{s^2}\pi\frac{\partial s}{\partial \pi}\right)(P-p_1) \left(1-\frac{P-p_1}{2}k\right) +\frac{1}{s}\pi\frac{\partial k}{\partial \pi}\frac{(P-p_1)^2}{2} =RT\ln\frac{p_0}{p_1}. \tag{27} \]

2) Let the solvent be in equilibrium with a solution which is under the pressure of its own vapor \(p_1\).

In this case, in equation (26) one must put: \(P=p_1\), \(p'_1=p_0\); \(\frac{\partial s'}{\partial \pi'}\) and \(\frac{\partial k'}{\partial \pi'}\) become equal to 0; finally \(\frac{1}{s'}=V_0\); equation (26) then takes the form:

\[ -\,V_0(P'-p_0)\left(1-\frac{P'-p_0}{2}k_0\right) =RT\ln\frac{p_0}{p_1}. \tag{28} \]

If in equations (25), (26), (27), and (28) we replace the quantity \(\dfrac{p_0}{p_1}\) by the equal quantity \(\dfrac{s_0}{s_1}\), then the same equations give us relations between the osmotic pressure and the partial density of the solvent in the solution.

In the case of dilute solutions, equations (27) and (28) take an even simpler form. Namely, if the compression of the solutions is neglected and the specific gravity of the solution is taken to be equal to the specific gravity of the pure solvent, then the term \(\dfrac{1}{s^2}\tau\dfrac{\partial s}{\partial \pi}\) becomes equal to \(0\), \(\dfrac{1}{s}\) will be equal to the specific volume of the pure solvent \(V_0\), and the terms containing the factor \(k\) vanish.

It may also be assumed without great error that

\[ P-p_1=p_0-P'=\pm Q \]

(osmotic pressure); then both equations (27) and (28) are transformed into the equation:

\[ \pm V_0 Q = RT \ln \frac{p_0}{p_1}, \tag{29} \]

i.e. into the well-known van’t Hoff equation.

Taking \(\dfrac{p_1}{p_0}=\dfrac{s_1}{s_0}\), from equation (29) we obtain:

\[ \pm V_0 Q = RT \ln \frac{s_0}{s_1}, \tag{30} \]

whence

\[ \pm Q=\frac{0.0821\cdot T\cdot 1000\cdot s_0}{M_0}\cdot\frac{s_0-s_1}{s_0}\ \text{Atm.} \tag{31} \]

In this last equation, \(0.0821\) is the gas constant for the case when the pressure is expressed in atmospheres and the volume in liters; \(M\) is the molecular weight of the solvent, and \(s_0\) is the density of the solvent in the liquid state; the term \(\ln\dfrac{s_0}{s_1}\) is taken to be equal to \(\dfrac{s_0-s_1}{s_0}\).

Calculation of osmotic pressure from the lowering of the partial density of the solvent. Table XXII gives calculations of the osmotic pressure by formula (31). For comparison, alongside are given the values of the osmotic pressure of the same solutions calculated by the formula:

\[ Q=\frac{0.0821\cdot T\cdot 1000\cdot s_0}{M_0}\times\frac{p_0-p_1}{p_0} \tag{32} \]

Table XXII.

\(x^\circ/\!_0\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	\(Q\) atm. from the lowering of partial density	\(Q\) atm. from the lowering of vapor pressure	Name of the observer of vapor pressure and density
Solutions of naphthalene in ether, \(C_{10}H_8; M=128.\)¹)	Solutions of naphthalene in ether, \(C_{10}H_8; M=128.\)¹)	Solutions of naphthalene in ether, \(C_{10}H_8; M=128.\)¹)	Solutions of naphthalene in ether, \(C_{10}H_8; M=128.\)¹)	Solutions of naphthalene in ether, \(C_{10}H_8; M=128.\)¹)	Solutions of naphthalene in ether, \(C_{10}H_8; M=128.\)¹)
0,99	0,9943	0,993	1,308	1,574	Noyes und Abbot
4,76	0,9688	0,970	7,367	6,978	(loco cit.)
9,09	0,9390	0,945	14,87	13,23
16,66	0,8862	0,901	27,61	24,01
Solutions of iodine in chloroform.	Solutions of iodine in chloroform.	Solutions of iodine in chloroform.	Solutions of iodine in chloroform.	Solutions of iodine in chloroform.	Mikhailenko and Zel’tner \(\left(\dfrac{p_1}{p_0}\right)\)
0,782	0,9988	0,9980	0,3640	0,6066	Mikhailenko and Yavorsky \(\left(\dfrac{s_1}{s_0}\right)\)
1,748	0,9931	0,9955	2,0928	1,3649	(Chapters III and IV).
2,792	0,9890	0,9927	3,3364	2,2142
Solutions of iodine in carbon disulfide.	Solutions of iodine in carbon disulfide.	Solutions of iodine in carbon disulfide.	Solutions of iodine in carbon disulfide.	Solutions of iodine in carbon disulfide.	Solutions of iodine in carbon disulfide.
0,60	0,9982	0,9985	0,7277	0,6064
1,13	0,9964	0,9974	1,4555	1,0512	Mikhailenko and Zel’tner
2,02	0,9931	0,9948	2,7897	2,102	(Chapters III and IV).
2,82	0,9912	0,9926	3,5578	2,9918
3,34	0,9895	0,9912	4,2451	3,5578
4,83	0,9851	0,9870	6,0241	5,2558
5,85	0,9814	0,9840	7,5198	6,4687
6,12	0,9807	0,9832	7,8030	6,7922
6,48	0,9794	0,9821	8,3286	7,2368
9,07	0,9708	0,9742	11,8054	10,4310
11,85	0,9610	0,9652	15,7674	14,0697

¹) For solutions of naphthalene in ether the osmotic pressure was calculated by the formulas:

\[ Q'=\frac{0{,}0821\cdot T\cdot 1000\cdot s_0}{M_0}\times \frac{s_0-s_1}{s_1},\qquad Q'=\frac{0{,}0821\cdot T\cdot 1000\cdot s_0}{M_0}\times \frac{p_0-p_1}{p_1}. \]

I find it superfluous to present a large number of comparative calculations. Obviously, the closer the ratios $\frac{s_1}{s_0}$ and $\frac{p_1}{p_0}$ are to one another, the closer will be the values of the osmotic pressure calculated from the lowering of the partial density and from the lowering of the vapor elasticity. For those cases in which $\frac{s_1}{s_0}=\frac{p_1}{p_0}$, both methods will, of course, give identical results.

With regard to these calculations I shall point out only one feature of the construction of formulas (31) and (32). Namely, in calculating the osmotic pressure by these formulas one has to multiply the very large quantity

\[ \frac{0.0821 \cdot T \cdot 1000 \cdot s_0}{M_0} \]

by the very small quantity $\frac{p_0-p_1}{p_0}$ or $\frac{s_0-s_1}{s_0}$. The consequence of this is that comparatively very small errors in the measurement of the vapor elasticity and of the density are strongly reflected in the value of the osmotic pressure being calculated. Undoubtedly, this circumstance should partly be blamed for the fact that the difference between the values of the osmotic pressure calculated by the two methods in some cases considerably exceeds 10%.

Another feature of formulas (31) and (32) consists in the fact that the term $\frac{0.0821 \cdot T_0 \cdot 1000 \cdot s_0}{M_0}$ is nothing other than the hypothetical gas pressure of the solvent under the assumption that the latter obeys the laws of ideal gases and is compressed to the specific volume of its liquid state. The terms $\frac{s_0-s_1}{s_0}$ and $\frac{p_0-p_1}{p_0}$ determine what part of this pressure is represented by the osmotic pressure of the dissolved substance. Consequently, by formulas (31) and (32), the osmotic pressure of the dissolved substance is represented as a part of the gas pressure of the solvent at the temperature of the experiment, compressed to the volume which it has in the liquid state and under the assumption that it obeys the laws of ideal gases. The more concentrated the solution, the closer the osmotic pressure will be to the ideal gas pressure of the solvent; and for solutions which, in their concentration, differ infinitely little from the concentration of the pure dissolved substance, the osmotic pressure of the dissolved substance will differ infinitely little from the ideal gas pressure of the solvent. In other words, if there are solutions whose osmotic pressure can be calculated by formulas (31) and (32) within the limits of all possible concentrations, then the ideal gas pressures of the dissolved substance and of the solvent in the liquid state will be equal, and, consequently, their densities will be related as their molecular weights. Such solutions will, at all possible concentrations, behave as infinitely dilute solutions and, together with Nernst, they may be called ideal solutions.

In order to form some judgment as to whether such solutions exist, and to what extent existing solutions deviate from the laws—

of ideal solutions; in Table XXIII the osmotic pressures have been calculated by formula (32) for mixtures of those pairs of liquids whose specific gravities were measured by me (Chapter III).

In Table XXIII the osmotic pressures of solutions of nitrobenzene in ether, calculated by formulas (31) and (32), are compared, and alongside them is given the gas pressure, calculated for an ideal gas with molecular weight 123, at temp. \(15^\circ\) and a density equal to the partial density of nitrobenzene in the solution. The ratio between the densities of ether and nitrobenzene at \(15^\circ\) is \(\frac{0{,}7196}{1{,}2085}=0{,}5957\); the ratio between the molecular weights is—

\[ \frac{74}{123}=0{,}6016. \]

The numerical values of the specific gravity and of the vapor pressure were determined by me (Chapters III and IV).

Table XXIII.

Ether and nitrobenzene. \((C_2H_5)_2O — 74;\ C_6H_5.NO_2 — 123.\)

\(\pi^\circ/\!_0\) \(C_6H_5.NO_2\)	\(S\ \frac{15^\circ}{4^\circ}\)	\(\frac{s_1}{s_0}\) ether	\(\frac{p_1}{p_0}\) ether	\(Q\) by lowering of the partial density of ether.	\(Q'\) by lowering of the vapor pressure of ether.	\(Q''\) gas pressure of nitrobenzene.
0	0,7195	1,0000	1,0000	—	—	—
1,71	0,7254	0,9908	—	2.115	—	2,39
9,70	0 7536	0,9458	0,951	12,46	11,26	14,04
17,06	0 7808	0,8999	0,913	23,01	20,69	25,58
22,33	0,8014	0,8652	0,886	30,99	26,21	34,37
25,14	0,8099	0,8489	0,871	34,74	29,65	38,22
49,82	0,9191	0,6410	0,734	82,53	61,15	87,97
69,13	1,0181	0,4366	0,584	129,52	95,63	135,21
74,12	1,0455	0,3761	0,532	143,43	107,59	148,89
90,75	1,1460	0,1473	0,268	196,32	168,28	199,79
98,86	1,2006	0,0190	—	225,53	—	228,01
100	1,2085	0	0	—	—	232,16

In Tables XXIV–XXVIII are compared the values of the osmotic pressure calculated from the decrease in the density of one and the other component in the solution. In the column under the sign \(Q\) are given the values of the osmotic pressure of the solution with respect to the first component of the mixture; under the sign \(Q'\) are given the values of the osmotic pressure of the same solution, but with respect to the second component of the mixture. Beside them are placed the elasticities of an ideal gas of the same molecular weight as one or the other component of the mixture, at the temperature of the solution, and with the spatial concentration which the given component has in the solution.

Table XXIV.

Benzene and ethylene bromide. \(C_6H_6\)—78; \(C_2H_4Br_2\)—188.

\(x\%\) \(C_2H_4Br_2\)	\(\dfrac{s_1}{s_0}\) benzene	\(Q\) from the decrease in density of benzene	\(Q\), gas pressure of ethylene bromide	\(\dfrac{s_1}{s_0}\) ethylene bromide	\(Q'\) from the decrease in density of ethylene bromide	\(Q'\), gas pressure of benzene
		Atm.	Atm.		Atm.	Atm.
0	1,0000	0	0	0	282,18	274,07
0,98	0,9954	1,261	1,12	0,0040	281,04	272,91
4,77	0,9793	5,675	5,58	0,0198	276,58	268,52
8,33	0,9634	10,35	9,97	0,0353	272,26	264,17
8,02	0,9649	9,62	9,58	0,0339	272,60	264,59
19,51	0,9082	24,59	25,06	0,0888	257,11	249,05
29,51	0,8537	40,11	40,64	0,1440	241,53	234,09
36,81	0,8078	52,69	53,53	0,1898	228,61	221,51
35,39	0,8171	50,15	50,91	—	—	224,05
47,23	0,7355	72,52	74,37	0,2645	207,53	201,68
56,63	0,6531	95,11	97,01	0,3535	182,42	179,10
69,56	0,5186	131,99	134,97	0,4783	147,21	142,19
81,70	0,3564	176,46	180,98	0,6415	101,15	97,71
88,99	0,2344	209,91	215,51	0,7638	66,64	64,27
98,97	0,0250	267,30	274,94	0,9745	7,19	6,89
100	0	274,09	282,18	1,0000	0	0

Table XXV.

Benzene and chloroform; \(C_6H_6—78;\ CHCl_3—119\).

\(\pi^\circ/\%\) \(CHCl_3\)	\(\dfrac{s_1}{s_0}\) benz.	\(Q\) from the lowering of the density of benzene	\(Q\) vapor pressure of \(CHCl_3\)	\(\dfrac{s_1}{s_0}\) chloroform	\(Q'\) from the lowering of the density of chloroform	\(Q'\) vapor pressure of \(C_6H_6\)
0	1,0000	Athm. 0	Athm. 0	0	Athm. 303,33	Athm. 274,07
1,45	0,9911	2,45	2,61	0,0086	300,81	271,70
7,07	0,9563	11,98	13,03	0,0430	290,39	262,21
12,36	0,9223	21,29	23,29	0,0767	273,77	252,88
20,31	0,8672	36,39	39,60	0,1305	263,83	237,73
43,11	0,6898	85,01	93,62	0,3085	209,82	189,07
61,60	0,5125	133,60	147,30	0,4854	156,14	140,49
79,06	0,3090	189,39	209,07	0,6891	94,33	84,72
88,65	0,1780	225,29	249,10	0,8209	54,34	48,79
94,85	0,0841	245,31	277,62	0,9147	25,88	23,06
98,04	0,0327	265,11	293,37	0,9667	10,10	8,97
98,90	0,0185	269,06	297,70	0,9811	5,73	5,06
100	0	274,07	303,33	1,0000	0	0

Table XXVI.

Benzene and chlorobenzene; \(C_6H_6—78;\ C_6H_5Cl—112{,}5\).

\(\pi^\circ/\%\) \(C_6H_5Cl\)	\(\dfrac{s_1}{s_0}\) benz.	\(Q\) from the lowering of the density of benzene	\(Q\) vapor pressure of chlorobenzene	\(\dfrac{s_1}{s_0}\) chlorobenz.	\(Q'\) from the lowering of the density of chlorobenzene	\(Q'\) vapor pressure of benzene
0	1,0000	Athm. 0	Athm. 0	0	Athm. 239,44	Athm. 274,07
2,33	0,9813	5,12	4,449	0,0186	234,98	268,95
4,90	0,9605	10,82	9,408	0,0393	230,03	263,26
7,98	0,9354	17,70	15,41	0,0644	224,02	256,38
24,12	0,7984	55,25	48,22	0,2015	191,19	218,81
29,67	0,7471	69,32	59,89	0,2501	179,55	204,79
36,83	0,6833	86,80	75,71	0,3169	163,56	187,29
47,36	0,5832	114,23	99,72	0,4164	139,73	159,84

\(\pi^\circ/\%\) \(C_6H_5Cl\)	\(\dfrac{s_1}{s_0}\) benz.	\(Q\) from the decrease in the density of benzene	\(Q\) gas pressure of chlorobenzene	\(\dfrac{s_1}{s_0}\) chlorobenz.	\(Q'\) from the decrease in the density of chlorobenzene	\(Q'\) gas pressure of benzene
60,48	0,4513	150,40	131,28	0,5482	108,18	123,70
70,86	0,3412	180,55	157,66	0,6584	81,79	93,51
80,0	0,2396	208,4	182,02	0,7602	57,42	64,14
89,01,	0,1346	237,18	207,17	0,8652	32,28	36,87
95,22	0,0594	257,79	225,16	0,9399	14,39	16,28
98,66	0,0167	269,49	235,38	0,9827	4,14	4,59
100	0	274,07	239,46	1,0000	0	0

Table XXVII.

Benzene and bromobenzene; \(C_6H_6\)—78; \(C_6H_5Br\)—157.

\(\pi^\circ/\%\) \(C_6H_5Br\)	\(\dfrac{s_1}{s_0}\) benz.	\(Q\) from the decrease in the density of benzene	\(Q\) gas pressure of bromobenzene	\(\dfrac{s_1}{s_0}\) bromobenz.	\(Q'\) from the decrease in the density of bromobenzene	\(Q'\) gas pressure of benzene
0	1,0000	Athm. 0	Athm. 0	0	Athm. 231,69	Athm. 274,07
1,53	0,9911	2,44	2,07	0,0084	229,63	271,63
4,29	0,9743	7,04	5,94	0,0257	225,74	267,06
12,98	0,9194	22,09	18,68	0,0806	208,17	251,97
18,32	0,8835	31,93	26,99	0,1165	204,70	242,15
30,37	0,7960	55,91	47,27	0,2040	184,42	218,15
41,09	0,7091	79,73	67,36	0,2907	164,34	194,35
54,56	0,5826	114,39	95,26	0,4111	136,44	159,68
63,70	0,4923	139,15	117,65	0,5077	114,08	134,91
79,44	0,3057	190,29	160,86	0,6941	70,87	83,77
88,95	0,1742	226,33	191,39	0,8258	40,36	47,74
95,22	0,0786	246,78	213,47	0,9213	18,23	21,55
99,01	0,0168	269,47	227,88	0,9831	3,91	4,60
100	0	274,07	231,69	1,0000	0	0

Table XXVIII.

Carbon tetrachloride and aniline; \(CCl_4\)—153.8; \(C_6H_5.NH_2\)—93.

wt. % \(C_6H_5.NH_2\)	\(\dfrac{s_1}{s_0}\) \(CCl_4\)	\(Q\) by density lowering of \(CCl_4\)	\(Q\) vapor pressure of aniline	\(\dfrac{s_1}{s_0}\) aniline	\(Q'\) by density lowering of aniline	\(Q''\) vapor pressure of \(CCl_4\)
		Atm.	Atm.		Atm.	Atm.
0	1,0000	0	0	0	266,87	252,05
1,48	0,9768	5,83	6,11	0,0229	261,38	246,82
5,80	0,9131	21,90	23,41	0,0875	244,08	230,15
11,57	0,8316	42,44	45,37	0,1696	222,14	209,69
20,24	0,7186	70,92	75,91	0,2838	191,58	181,15
31,26	0,5871	104,07	111,25	0,4159	156,25	144,63
37,46	0,5188	121,29	129,56	0,4844	137,92	130,81
51,37	0,3791	156,50	166,91	0,6240	100,58	95,55
56,46	0,3320	168,37	179,47	0,6710	88,01	83,69
68,72	0,2265	194,96	207,49	0,7757	60,00	57,10
83,29	0,1142	223,27	237,73	0,8872	30,17	28,78
94,52	0,0359	243,00	257,98	0,9645	9,49	9,26
88,91	0,0741	228,05	247,91	0,9268	19,58	18,69
98,96	0,0128	248,83	265,6	0,9931	1,84	1,68
100	0	252,05	266,87	1,0000	0	0

Clarification of the connection between osmotic pressure and the partial density of the solvent. In order to clarify more closely why the partial density of one or another component in a solution can serve as a measure of osmotic pressure, let us carry out the following series of considerations.

1. Let there be in a vessel, closed by two pistons moving without friction (Fig. 4), and divided by a partition into two halves, a strongly compressed gas (to a density of the order of the densities of liquids).

Let the partition be permeable to this gas. Then, in the case of equilibrium, equal forces acting in opposite directions must be applied to both pistons, \(P=P'\).

The magnitude of these forces is determined by the temperature and the spatial concentration of the gas, in other words, by the magnitude of its density. Assuming that the gas obeys the laws of ideal gases, we obtain:

Fig. 4.

\[ P = P' = \frac{RT}{M_0}\,s_0 \]

or

\[ P = P' = \frac{0.0821 \cdot T \cdot 1000 \cdot s_0}{M_0}\ \text{Atm.}, \quad \text{where} \tag{33} \]

\(T\) is the absolute temperature;
\(M_0\)—the molecular weight of the gas;
\(s_0\)—the density of the gas at pressure \(P\) and temperature \(T\).

Let us introduce into compartment \(B\) some weight quantity \((g)\) of a new gas, which does not enter into chemical interaction with the first, but forms a solution with it. Let the partition be impermeable to this gas. Then the equilibrium will be disturbed. At the first moment, before the osmotic flow has begun, the pressure in compartment \(B\) will increase, and the piston to which the force \(P\) is applied will move until the sum of the partial elasticities of both gases filling compartment \(B\) balances the force \(P\). During this time the partial density of the gas serving as solvent will decrease to the value \(s_1\), and its partial pressure will decrease to the value \(P_1\):

\[ P_1 = \frac{0.0821 \cdot T \cdot 1000 \cdot s_1}{M_0} \tag{34} \]

At the next moment an osmotic flow will begin from compartment \(A\) into compartment \(B\). To prevent this flow, we must, as experiment shows, do one of two things: either apply to piston \(B\) a certain force \(Q\), acting in the same direction as the force \(P\), or else apply to piston \(A\) a certain force \(q_1\), acting in the direction opposite to the action of the force \(P'\). That is, in order to restore the equilibrium disturbed by adding a foreign gas to compartment \(B\), we must either compress the gas solution in compartment \(B\), or stretch the solvent gas in compartment \(A\).

Let us suppose that the magnitude of the force \(q_1\) is such that piston \(A\) moves to the left enough that the partial density of the gas in compartment \(A\) becomes equal to \(s_1\), i.e., to the partial density of the solvent gas in compartment \(B\). The forces applied to the two pistons will now be as follows: to piston \(A\) there will be applied a force \(P' - q_1 = P_1\), to piston \(B\)—the force \(P\). The osmotic pressure will be equal to:

\[ P - (P' - q_1) = P - P_1 = q_1. \tag{35} \]

Substituting into equality (35) the values of the quantities \(P\) and \(P_1\) from equations (33) and (34), we obtain:

\[ q_1=\frac{0.0821\cdot T\cdot 1000}{M_0}\times(s_0-s_1) \tag{36} \]

This equation is identical with equation (31).

Let us also suppose that the magnitude of the force \(q\), which must be applied to piston \(B\) in order to restore equilibrium when a foreign gas is added to compartment \(B\), is such that piston \(B\) will move to its former position and the partial density of the solvent gas will assume its original value. Then forces \(P+q\) will be applied to piston \(B\), and a force \(P'\) to piston \(A\). (The osmotic pressure is equal to \(P+q-P'=q\).)

The magnitude of the force \(q\) is equal to the elasticity of the added gas in the case when its mass (\(g\)) occupies a volume equal to the volume of compartment \(B\) at the position of the piston at which the specific partial density of the solvent gas has the value \(s_0\).

At that position of the piston at which the solvent gas has the partial density \(s_1\), the pressure of the added gas will have the value \(q\dfrac{s_1}{s_0}\). But the magnitude

\[ q\,\frac{s_1}{s_0}=q_1 \tag{37} \]

Substituting into equation (36) the value of \(q_1\) from equation (37), we obtain:

\[ q=\frac{0.0821\cdot T\cdot 1000}{M_0}(s_0-s_1)\frac{s_0}{s_1} \tag{38} \]

In the case of dilute solutions, the term \(\dfrac{s_0}{s_1}\) may be taken as equal to unity; then equality (38) also turns into equality (31).

Thus, if we accept that solutions may be compared with strongly compressed gases, and that osmotic pressure may be identified with the forces acting on the solvent or the solution and changing the partial density of the solvent by the same magnitude on one and the other side of the semipermeable partition, then for osmotic pressure there is obtained the same expression as that obtained with the aid of the equality

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0} \]

from the well-known van ’t Hoff formula, which gives the relation between osmotic pressure and the magnitude of the lowering of the vapor pressure of the solution.

1. Let, in the well-known Arrhenius scheme (Fig. 5), the semipermeable partition \((a)\) be placed in the upper part of the tube and a very thin layer of solution be poured onto it. The tube itself is filled with pure solvent and is inverted, with its open end, into the solvent. In the case of equilibrium, the osmotic pressure is evidently equal to the weight of a column of pure solvent of height \(h\) plus the difference of the vapor pressures at the upper and lower ends of the tube. Since the magnitude of the vapor pressure at the lower end of the tube, at the level \((b)\), is equal to \(p_0\), i.e. to the vapor pressure of the pure solvent, and the magnitude of the vapor pressure at the upper end of the tube, at the level \((a)\), is equal to \(p_1\),

i.e., the elasticity of the vapor of the solution, then the height \(h\) can be calculated, and consequently the weight of a column of liquid of height \(h\), i.e., the osmotic pressure, can also be calculated.

Fig. 5.

If these calculations are carried out, then for the osmotic pressure we obtain an expression¹ identical with the expression obtained from equality (28). This osmotic pressure was defined above as negative osmotic pressure, i.e., as the pressure that must be applied to the solvent, namely, by which the solvent must be stretched, so that this latter may be in osmotic equilibrium with the solution.

If, in calculating the weight of the column of liquid, the compression of the liquid is neglected, then for the osmotic pressure an expression is obtained that is identical with expression (29), i.e., in this case the negative osmotic pressure (the pressure on the solvent) is calculated as equal to the positive osmotic pressure (the pressure on the solution).

Let us attempt to calculate the osmotic pressure of the scheme in another way.

The column of liquid filling the tube must be regarded as if attached by its upper end to the semipermeable partition and freely suspended in the tube. This suspended column of liquid does not break apart as a result of the forces of cohesion between the particles of the liquid. And, since the liquid is a heavy liquid, it is obvious that the weight of the lower column of liquid must act upon the overlying layers in a stretching manner, as a result of which the density of the liquid must gradually increase from top to bottom. Namely, at the horizon \((a)\) it must have a minimal value; at the horizon \((b)\) its density must be normal, i.e., equal to the density of the liquid under the pressure of its own vapor.

The force that acts on an infinitely thin layer of liquid adjacent directly to the semipermeable partition is equal to the weight of the column of liquid \(h\) minus the vapor pressure at the horizon of the lower end of the tube. Let us denote this force by \(P'\). Let us denote the specific weight of the liquid under pressure \(p_0\), equal to the elasticity of the vapor of the liquid at the temperature of the experiment, by \(s_0\), and the coefficient of elasticity under its stretching by \(\frac{1}{k}\). Then, adopting the simplest dependence between the volume of the stretched liquid and the stretching forces, the density of the layer adjacent directly to the semipermeable partition \((s'_1)\) is calculated as follows:

\[ s'_1=\frac{s_0}{1-k(P'-p_0)} \tag{39} \]

Let us make the assumption that the density of the layer adjacent directly to the partition \((s'_1)\) is equal to the partial density of the solvent:

in the solution \((s_1)\). Then the pressure by which the layer of liquid at the partition is stretched, using formula (39), is calculated as follows:

\[ P'=\frac{s_1-s_0}{s_1 k}+p_0 \tag{40} \]

And the osmotic pressure \((q)\) will be expressed as follows:

\[ q=-\frac{s_0-s_1}{s_1 k}+p_0-p_1 \tag{41} \]

We shall neglect the term \(p_0-p_1\). Then equation (41) assumes the form:

\[ q=-\frac{s_0-s_1}{s_1 k} \tag{42} \]

where \(q\) is the pressure stretching the solvent.

Let us compare equation (42) with equation (31), for which purpose we shall carry out the following reasoning. Suppose that liquids may be regarded as strongly compressed gases; then the following equations may be written:

\[ Q_0 \frac{1}{s_0}=RT \]

\[ Q_1 \frac{1}{s_1}=RT \]

where \(Q_0\) and \(Q_1\) are those pressures which must be applied to one gram of solvent in the gaseous state in order to compress it to the volume \(\frac{1}{s_0}\) and to the volume \(\frac{1}{s_1}\). And from this it follows that

\[ \frac{Q_0}{Q_1}=\frac{s_0}{s_1} \tag{43} \]

But the coefficient of extension of the liquid \(k\) we previously defined as follows:

\[ k=\frac{s_1-s_0}{s_1(Q_1-Q_0)} \tag{44} \]

Using equation (43) and expressing in equation (44) the quantities \(s_0\) and \(s_1\) through \(Q_0\) and \(Q_1\), we obtain

\[ k=\frac{1}{Q_1} \tag{45} \]

Finally, calculating the quantity \(Q_1\) from the well-known equation for gases and substituting it into equation (42), we obtain:

\[ q=-\frac{0.0821\cdot T\cdot 1000\cdot s_1}{M_0}\times\frac{s_0-s_1}{s_1} \tag{46} \]

And this equation is identical with equation (31).

Thus, using the modified Arrhenius scheme to find the relation between the osmotic pressure and the partial density of the solvent in the solution, we have shown that, if the solvent is in osmotic equilibrium with the solution, then forces are applied to it equal in magnitude to the osmotic pressure and acting on the solvent in a stretching manner. Further, by making the assumption that the solvent can be in osmotic equilibrium with the solution only in the case when its density, altered by the osmotic forces, will be equal to the partial density of the solvent in the solution, and that liquids may conventionally be regarded as strongly compressed gases, we have obtained for the osmotic pressure the very same expression that is obtained from the well-known van ’t Hoff formula, under the condition that

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0}. \]

But can one speak of the stretching of liquids, and do there exist liquids that are incompressible and unstretchable?

The phenomena of capillarity and a whole series of direct experiments prove that, within certain limits, liquids can indeed be stretched. Such are the observations of Berthelot ¹), Moser ²), Helmholtz ³), and others. Worthington ⁴) showed that negative pressure can be produced within limits even down to \(-17\) Atm. and that the coefficient of stretching can be measured with sufficient accuracy. It was found, moreover, that for alcohol, within the limits \(+12\) and \(-17\) Atm., its coefficient of elasticity, both under stretching and under compression, remains unchanged. That is, in magnitude the coefficient of stretching of alcohol is equal to its coefficient of compression.

It is very likely that there are no liquids that are absolutely non-elastic, i.e., incapable of either being compressed or being stretched, just as there are no bodies that are absolutely nonvolatile, absolutely insoluble, etc.

Fig. 6.

1. Let a solution and solvent be in osmotic equilibrium with one another in an annular vessel (Fig. 6). Osmotic equilibrium is effected by means of two partitions: one \((A)\), permeable to the liquid solvent, and the other \((B)\), permeable to the vapor of the solvent; the latter partition allows different forces \(P\) and \(P'\) to be applied to the liquid and to the solution.

We shall prove the following two propositions:

1) if the liquid is under the pressure of its own vapor, i.e., if \(P'=p_0\), then to the solution there must be applied a force \(P=q+p_0\), i.e., the elasticity of the vapor over the solution that is in equilibrium with the pure solvent is equal to the elasticity of the vapor of the pure solvent;

2) if the solution is under the pressure of its own vapor, i.e., if \(P=p_1\), then to the solvent there must be applied a force \(P'=p_1-q\), i.e.,

1) Berthelot, Ann. de chim. phys. 30. 1850.
2) Moser, Poggond. Ann. 160. 138. 1877.
3) Helmholtz, Gesammt. Abhandl. III. 264.
4) Worthington, Trans. of the Royal. Soc. 183; 355. 1893.

the elastic pressure of the vapor of the solvent in equilibrium with the uncompressed solution must be equal to the elastic pressure of the vapor of the solution, \(p_1\).

Both of these assertions follow as consequences of the second law of thermodynamics. Indeed, if, in the case of equilibrium between the solution and the liquid, the elastic pressure of the vapor in one compartment of the vessel were different from that in the other, then distillation would occur from one compartment of the vessel into the other, the result of which would be a so-called perpetuum mobile of the second kind. And this would contradict the second law of thermodynamics.

From the propositions just proved it follows that, if a force \(q\) is applied to a solution whose vapor pressure is \(p_1\) (namely, if the solution is compressed), then the elastic pressure of the vapor of the solution increases. If, in magnitude, the force \(q\) is equal to the osmotic pressure of the solution when the solution is in equilibrium with the pure solvent under the pressure of its own vapor, then the elastic pressure of the vapor of the solution increases to a value equal to the elastic pressure of the vapor of the pure solvent. If forces \(q\) acting on the liquid in a stretching manner are applied to the liquid, then the elastic pressure of the vapor of the liquid decreases; if, in magnitude, the force \(q\) is equal to the osmotic pressure in the case when the solvent is in osmotic equilibrium with the solution under the pressure of its own vapor, then the elastic pressure of the vapor of the liquid decreases to a value equal to the elastic pressure of the vapor of the solution. Consequently, osmotic pressure may also be defined as follows: osmotic pressure is that pressure which must be applied to a liquid (to the surface of separation between the liquid and the vapor) in order to raise or lower the elastic pressure of the vapor of the liquid or of the solution to a value equal to the elastic pressure of the vapor of that liquid or solution with which the given liquid is in osmotic equilibrium.

Since a relation is already known between the magnitude of the osmotic pressure and the magnitude of the elastic pressure of the vapor of the solution, it is evident that this relation can be used to establish the relation between the magnitude of the forces applied to the surface of the liquid and the increase or decrease of the elastic pressure of its vapor (Kistyakovsky)¹). That is, this relation can be used to calculate the increase in the elastic pressure of the vapor, for example, of a solution contained in an ordinary vessel, when certain forces are applied to the surface of separation between the liquid and the vapor, directed into the liquid or out of the liquid.

Obviously, this desired relation will have a form identical with the formulas giving the relation between the osmotic pressure and the lowering of the elastic pressure of the vapor of the solvent as a result of the dissolution in it of a foreign body, i.e., with formulas (25), (26), (27), and (28).

The fact that equilibrium between a liquid and its vapor is disturbed by external influences, for example by capillarity, was noticed long ago²). But only recently, when N. N. Schiller took up this question, may it be considered definitively established that all observations relating to this can be represented in a certain general form, namely as follows: equilibrium between a liquid and its vapor is disturbed by all external forces—for example, pressure, electrical forces, capillary forces, etc.—applied to the liquid, but not to the vapor. Expressions for the relation between the magnitude of the applied forces and the magnitude of the change in the elastic pressure of the saturated vapor of the liquid produced by them were derived by N. N. Schiller in various—

¹) Kistyakovsky. Zh. R. F. Kh. O. 29, 273, 1897.
²) Thomson, Phil. Mag. (4) 42, 448. 1871.

by different routes: all of them proved, indeed, to be identical with expressions (27) and (28). Conversely, I have shown that, using the law of variation of the elasticity of the saturated vapor of a liquid with the forces applied to the interface between the liquid and its vapor, for the magnitudes of osmotic pressure the same expressions are obtained as by other routes¹.

Thus, the lowering of the vapor elasticity of the liquid—the solvent—as a result of the dissolution in this liquid of a foreign body, we may identify with the action upon the liquid of certain forces directed outward from the liquid. In magnitude these forces, as direct experiment proves (at least for dilute solutions), are equal to the elasticity of the dissolved body in a vacuum in that state of dispersion in which this latter is found in the solution.

The considerations just set forth lead to the following scheme of the phenomenon of dissolution, of the osmotic current, and of the equilibrium of forces for solutions in the presence and absence of a semipermeable partition.

The phenomenon of dissolution. Let there be given some volume of a body \(A\), placed in the midst of another body \(B\). If the body \(B\) is permeable to the body \(A\)—can dissolve it—then masses of the body \(A\) will begin to move from places of greater spatial concentration of the body to places of lesser spatial concentration. At the same time the very same thing will also occur with the substance \(B\). If the substance \(A\) is permeable to the substance \(B\)—can mix with it—then there will begin a flow of masses of the substance \(B\) from places of greater spatial concentration of these masses to places of lesser spatial concentration. Both of these simultaneously proceeding processes will continue until both substances fill the space occupied by them quite uniformly, or until they separate, depending on the temperature, pressure, and other conditions of the experiment, into one or another number of physically quite homogeneous phases. Then equilibrium will set in.

This picture of the phenomena of dissolution is identical with the mechanism of disaggregation of bodies occurring in a vacuum or in an atmosphere of gas, and suggests the supposition that the phenomena of dissolution, too, are caused by the same reason as the phenomena of physical disaggregation in a vacuum and in gases, and, in essence, are probably identical with these latter. That is, the phenomena of dissolution are the same phenomena of physical disaggregation (change of state), but occurring in the medium of another body (the solvent). The circumstance that the phenomena of disaggregation in the medium of a solvent proceed much farther than in a vacuum, and in general depend on the nature of the solvent, may be explained by the fact that in the medium of a solvent the substance is under a very strong pressure, which, as was explained in more detail on p. 19, promotes the uniform distribution of the substance in the given volume and hinders the formation of phases.

Osmotic pressure. Let us imagine a certain volume of a mixture of the bodies \(A\) and \(B\), placed within a mass of the body \(A\) and separated on all sides from the mass of the body \(A\) by a membrane permeable to the body \(A\), but impermeable to the body \(B\). Since the membrane is impermeable to the body \(B\), it is evident that displacement of the masses of the body \(B\) to the other side of the membrane cannot take place. Since the membrane is permeable to the body \(A\), displacement of the masses of the body \(A\) is evidently possible; this displacement will occur, according to the general law, from places of greater spatial concentration of the masses \(A\) to places of lesser spatial concentration, and will continue until complete equalization of the spatial concentrations of the masses of the body \(A\) occurs, or until a certain number of phases is formed, in accordance with the conditions of the experiment. By the latter words I understand the onset of a phenomenon analogous to the phenomenon of distribution; i.e., it is admitted as possible that the body \(A\) (the solvent) may be distributed between the body \(B\) and the void, analogously to a strongly compressed gas dissolved in a nonvolatile solvent, and that between the spatial concentrations of the body \(A\) on one and the other side of the semipermeable partition there will be established a certain drop in concentration. Which of these alternatives will occur is as yet not entirely clear. We shall adopt the simpler one, i.e., we shall assume that the displacement of the masses of the body \(A\) will end when its spatial concentration, and also the elasticity of the vapor, on both sides of the partition have one and the same value. Since the displacement of masses has occurred into a volume surrounded by a semipermeable partition, in this volume the solvent is compressed—as if forces had been applied to it—raising its vapor elasticity from the value \(p_1\) (the elasticity of the vapor of the solution) to the value \(p_0\) (the elasticity of the vapor of the solvent), and its partial density from the value \(s_1\) to the value \(s_0\). Since the solvent is an elastic body, the pressure communicated to it is transmitted also to the semipermeable partition—this is the osmotic pressure.

Does the dissolved body exert pressure on the semipermeable partition?

One might think that the masses of the dissolved body, encountering on their way a partition impermeable to them, press upon it analogously to a gas encountering on its way impermeable walls. I think that this is not so, and the following may, in my opinion, serve as proof of this. In Duhem’s scheme (a modified Arrhenius scheme), which we used somewhat above (Fig. 5), the solution is in osmotic equilibrium with the solvent, to which forces are applied that stretch this solvent. Since in this scheme the column of solvent liquid is as it were suspended from the semipermeable partition, then, if one may speak of pressure on the partition, it is only of such a pressure as is opposite in sign to that pressure which would be produced on the partition by the dissolved body situated in a vessel on the other side of the partition, if only it were capable of producing such a pressure.

Thus, the dissolved body exerts pressure not on the partition, but on the solvent. The result of this pressure is a lowering of the vapor elasticity of the solvent and a lowering of its partial density. The pressure in a cell with semipermeable walls is again pressure on the solvent; in magnitude this pressure is equal to the pressure of the dissolved body on the solvent; this is why the vapor elasticity of the solvent and its partial density return to their initial value. In general one may say that osmotic pressure balances the pressure of the dissolved body. But one cannot say that osmotic pressure is the pressure of the dissolved body on the semipermeable partition.

Equilibrium of a solution in a vessel with impermeable walls. Let the phenomenon of dissolution take place in a medium of solvent enclosed in a vessel with ordinary walls. For simplicity, let us assume that the dissolved body is nonvolatile. When all mass displacements characterizing the act of dissolution have ended, both the solvent and the dissolved body fill uniformly the space occupied by the liquid. The spatial concentrations of both the solvent and the dissolved body have assumed their final values and no longer change. All the forces applied to the masses of the solvent and the dissolved body are in equilibrium. A force equal to the elasticity of the vapor of the solution \((p_1)\) is applied to the surface of the solvent. No other external forces are applied to the solution (for greater simplicity of consideration we exclude the action of gravity).

Since one of the fundamental properties of a substance, whatever physical state it may be in, consists in its tendency to increase its volume, and since, in order to keep a given mass of substance in an unchanged volume, it is necessary to apply to this mass some force not less than the elasticity of the given individual in the gaseous state, or its elasticity of evaporation, or the elasticity of its volatility, the question is—what forces are applied to the dissolved body which, previously, in the act of dissolution, increased its volume, but now, when dissolution has ended, has ceased to increase it; what are these forces in magnitude and where are they to be sought. From the fact that the elasticity of the vapor of the solvent, after a foreign body has been dissolved in it, has decreased, it follows, on the basis of the preceding, that forces are applied to the solvent. Since no other external forces, apart from the forces of elasticity of its own vapor, are applied to a solution under the pressure of its own vapor, the forces that have changed the elasticity of the solvent vapor are to be sought nowhere else than in the dissolved body. Namely, these are the forces by which the phenomenon of dissolution of this body was brought about—in general, the forces that bring about the phenomenon of rarefaction of a substance.

Thus, forces equal to the elasticity of the dissolved body at the temperature of the experiment and at that spatial concentration which it has in the solution are applied to the solvent. These forces have changed the density of the solvent, namely in the sense of lowering it, and also the elasticity of the vapor—in general, they have disturbed the equilibrium between the liquid and the vapor.

Since the solvent is an elastic body, the action of the forces on the solvent must call forth elastic forces in the solvent. These elastic forces also balance the forces of rarefaction of the dissolved body.

Thus, when the solution is in a vessel with ordinary walls under a pressure equal to the elasticity of its own vapor (or under atmospheric pressure), the pressure of rarefaction of the dissolved body (osmotic pressure) is balanced by the elastic forces of the solvent. The partial elasticity of the solvent vapor and the partial density of the solvent in the liquid phase are changed by the pressure of rarefaction (osmotic pressure) of the dissolved body.

We shall explain the scheme of the equilibrium of forces of a solution contained in a vessel with ordinary walls by the following comparison. Let a continuous elastic ball of rubber represent a pure solvent. Suppose that, in the thickness of such a ball, a series of strong springs is placed in different directions. These springs, striving to uncoil, will stretch the rubber ball with greater or lesser intensity, depending on the strength of the springs; when the rubber ball is stretched, between the elastic forces of the springs—

liquid and rubber will come into equilibrium. Such a rubber balloon with the springs inserted in it represents the solution.

Let us draw several conclusions that follow as consequences solely from the sketched mechanical scheme of the phenomenon of dissolution and of the equilibrium of forces in the absence and in the presence of a semipermeable partition. Namely: 1) we shall derive a probable, entirely exact relation between the partial density of the solvent in the liquid phase and the elasticity of its vapor; 2) we shall calculate the probable true specific volume of the dissolved body in the solution; 3) finally, we shall describe the relation between the partial density of the solvent in the solution and the coefficient of compression of the solution.

The exact form of the relation between the partial density of the solvent in the liquid phase and the elasticity of its vapor. Let us return again to Duhem’s scheme (Fig. 5). Let the solution, whose vapor elasticity is \(p_1\), be in osmotic equilibrium with the pure solvent. The force that must be applied in this case to the solvent \((P')\) can be calculated quite exactly by means of relation (28) and approximately by formula (29).

Let us assume that there is the simplest dependence between the change in the specific volume of the solvent and the magnitude of the forces acting on it in a stretching manner. Then the density, changed by the force \(P'\), of an infinitely thin layer of pure solvent immediately adjacent to the semipermeable partition \((s'_1)\), is calculated by the formula:

\[ s'_1=\frac{s_0}{1-k'(P'-p_0)} \tag{47} \]

where \(s_0\) is the density of the solvent under the pressure of its own vapor;

\[ \frac{1}{k} \]

is the coefficient of elasticity;

\(P'\)—the force applied to the solvent and acting on the solvent in a stretching manner.

We calculate the magnitude \(P'\) by the simplest formula (29). Then, substituting its value in place of the quantity \(P'\) in formula (47), we obtain:

\[ s'_1=\frac{s_0}{1-k\left(-s_0RT\ln\frac{p_0}{p_1}-p_0\right)} \tag{48} \]

If it is true that \(s'_1=s_1\), i.e., if it is true that the density of the solvent in the solution is equal to the density of the pure solvent that is in osmotic equilibrium with it, then expression (48) will give us the relation between the magnitude of the partial density of the solvent in the solution and the magnitude of the elasticity of its vapor.

Expression (48) can be derived in a strictly exact form if, in calculating \(P'\), one uses formula (28), and if the coefficient of elasticity of the solvent is known when it is stretched. Since numerical data from investigations on the stretching of liquids, apart from Worthington’s indication 1), that the coefficient of elasticity of alcohol under stretching and under

1) Loc. cit.

freezing remains unchanged, I have not been able to ascertain; and since it still remains unclear whether in fact \(s'_1=s_1\), and whether we possess methods for calculating \(s_1\) quite accurately, I propose to present a more detailed investigation of relation (48), to which I attach special importance, elsewhere. Here I shall confine myself to showing in what case and under what conditions expression (48) becomes the expression

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0}. \]

Let us write expression (48) in a simplified form:

\[ s'_1=\frac{s_0}{1-k\left(-s_0RT\frac{p_0-p_1}{p_0}-p_0\right)} \tag{49} \]

From this equation, after making a transformation and discarding the quantity \(p_0k\) as very small, we obtain:

\[ ks'_1RT\frac{p_0-p_1}{p_0}=\frac{s_0-s_1}{s_0}. \tag{50} \]

And hence it follows that the relation \(\frac{s'_1}{s_0}=\frac{p_1}{p_0}\) holds in the case if

\[ RTs'_1=\frac{1}{k} \tag{51} \]

i.e. in the case where, under tension, liquids behave as highly compressed gases obeying the Mariotte–Gay-Lussac laws. This conclusion had already once been obtained, and moreover by a route entirely different from the one just used (p. 65).

I attach special importance to expression (48) for the following reasons:

1) the experimental data cited above show that the equality

\[ \frac{p_1}{p_0}=\frac{s_1}{s_0} \]

is approximately satisfied in the case of non-associated solvents and, apparently, the less associated the solvent, the better; and this indicates that \(s'_1=s_1\), i.e. that osmotic equilibrium is established in the case when the solvent on either side of the semipermeable partition has the same density, and that the calculation of the partial density of the solvent in a solution can, without gross error in many cases, be carried out by the formulas that I used in the text;

2) since this is so, then, if the coefficient of elasticity \(k\) is known from experiment or calculated by means of an equation, for example, that of van der Waals, the correction to the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) is also known; and knowledge of this correction provides a very exact and practically important method of calculation from the dens—

the elasticity of vapor of solutions, and also the osmotic pressure and the molecular weight of dissolved substances;

3) equation (50) shows that the inaccuracy of the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) is rooted in the fact that strongly compressed gases depart from the laws of ideal gases; i.e., the correction coefficient for each solvent must have its own particular value and be connected with the quantities \(a\) (attraction between gas molecules) and \(b\) (the volume of its molecules) of the Van der Waals equation;

4) since the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) is derived by applying the law of acting masses to the equilibrium between liquid and vapor, it also follows from equation (50) that the law of acting masses in its usual formulation cannot be applied to substances at a spatial concentration close to the spatial concentration of liquids, and that the constants \(a\) and \(b\) of the Van der Waals equation must enter here as correction terms.

Calculation of the molecular volume of dissolved substances. In an experimental verification of the relation \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\), it turned out that the probable causes of the deviations lie not only in the fact that stretched liquids, as has just been clarified, depart from the laws of ideal gases, but also in the fact that, in calculating the partial density of the solvent in the solution, it was assumed that the volume occupied by the solution is at the same time the volume occupied by the solvent; that is, the volume occupied by the molecules of the dissolved substance was ignored. Having recognized that, in calculating the partial density of the solvent in a solution, it is necessary to take into account also the volume of the dissolved substance, and assuming that deviations from the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) may serve as a measure of this volume, the probable molecular volumes of certain nonelectrolytes were calculated above. We shall now try to calculate these same molecular volumes by another method, namely, proceeding from the proposition that the densities of the solvent on both sides of a semipermeable partition are equal if the solution is in osmotic equilibrium with the pure solvent, and that in a solution the solvent is stretched by osmotic forces.

A liter of an aqueous solution containing in the dissolved state 1 gram-molecule of sugar (342 g) weighs 1132 g. Consequently, a liter of such a solution contains 342 g of sugar and 790 g of water. If the water were not under the action of any forces, it would occupy a volume of 790.2 cc (the calculation was made for a temperature of 12°). But the forces of the osmotic pressure of the dissolved substance are applied to the water, namely, approximately 22.42 Atm. Since these forces act in the direction of increasing the volume, the volume of 790 g of water in the solution will be larger. Specifically, assuming that the coefficient of elasticity of the liquid remains unchanged both under compression and under stretching, we obtain the number—791.

Thus, the water entering into the composition of the solution occupies a volume of 791 cc; the solution itself occupies a volume of 1000 cc. Consequently,

\(1000-791=209\) cc are occupied by 342 g of dissolved substance. In other words, 209 cc is the volume of the sugar molecule.

If the sugar solution in question is brought into contact, by means of a semipermeable partition, with pure water, then equilibrium will occur only when we apply to the solution a pressure approximately equal to 22.42 atm. The applied pressure will now balance the osmotic pressure of the dissolved substance, and the water in the solution will assume the same volume as it has when no external forces act upon it. One liter of sugar solution under a pressure of 22.42 atm.\(^1\) will occupy a volume
\(1000-1000 \times 34.3 \cdot 10^{-6} \cdot 22.42 = 999.3\) cc. In this solution, according to the preceding, the water occupies a volume of 790.2 cc. Consequently, \(999.3\) cc \(- 790.2\) cc \(= 209.1\) cc is again the volume of the sugar molecule.

Analogous calculations, carried out for a solution of 1 gram-molecule of urea in a liter of solution, gave 40.6 for the molecular volume of urea; for the molecular volume of resorcinol the number 86.3 cc was obtained, and so on.

These numbers are close and are of the same order as the values of the molecular volumes calculated from the atomic volumes of the elements. Thus, taking, together with Traube,\(^2\) the atomic volumes: for carbon—9.9, for hydrogen—3.1, for nitrogen—1.5, and for oxygen—2.3, we obtain the following molecular volumes: sugar—221.9 cc, urea—30.8 cc, resorcinol—74.5 cc.\(^3\)

In the calculation of the molecular volumes just carried out, however, it was assumed that the coefficient of elasticity of water in tension and in compression is one and the same.

Calculation of the coefficients of compression of solutions. In order to find the relation between the coefficients of compression of solutions and the coefficient of compression of the solvent, let us carry out the following reasoning in general form. Let there be some volume of solution containing, for example, a gram-molecule of the dissolved substance and under the pressure of its own vapor. If we assume that the volume of the solution is equal to the volume of the solvent contained in the given solution and stretched by the osmotic pressure of the dissolved substance \((P'-)\), plus the volume of the dissolved substance, then the volume of the solution at pressure \(p_1\) will be expressed as follows:

\[ V_s = V_{p_0}\left[1-k_0(P' - p_0)\right] + V_M,\quad \text{where} \tag{52} \]

\(V_s\) is the volume of the solution at pressure \(p_1\);

\(V_{p_0}\) is the volume of the solvent contained in the volume of the given solution at pressure \(p_0\);

\(k\)—the coefficient of extension of the solvent;

\(^1\) We have left out of account the influence on the osmotic pressure of temperature and of the change of volume due to compression.

\(^2\) Traube, Über der Raum der Atome. 1899.

\(^3\) I should like here once more to point out what I have already called attention to once before; namely, that the calculation of molecular volumes is only one of the ways of seeking the correction to the equality
\(\dfrac{s_1}{s_0}=\dfrac{p_1}{p_0}\); it is possible that this correction will be found even without the hypothesis of the molecular volume of dissolved substances.

$P'$ is the pressure of expansion (osmotic pressure) of the dissolved substance at the time when the solution occupies the volume \(V_{p_1}\);

\(p_0\)—the elasticity of the vapor of the solvent;

\(V_M\)—the volume of a molecule of the dissolved substance.

Let us apply to the solution a pressure \(P\) equal to the pressure at which the solution will be in osmotic equilibrium with the pure solvent under the pressure of its own vapor. According to our scheme, the solvent will then occupy the same volume that it would have if it were under the pressure of its own vapor \((p_0)\), i.e. \(V_{p_0}\). Consequently, the volume of the solution compressed by the pressure \(P\) may be expressed as follows:

\[ V_{p_0}+V_{1M}=V_s[1-k_1(P-p_1)], \quad \text{where} \tag{53} \]

\(k_1\) is the coefficient of compression of the solution;

\(V_{1M}\) is the volume of a molecule of the dissolved substance under the pressure \(P\).

Assuming that \(V_M=V_{1M}\), i.e., that the true volume of the molecule under pressure does not change or changes only insignificantly, from equations (52) and (53) we obtain:

\[ - V_{p_0} k_0 (P'-p_0)-V_s k_1(P-p_1)=0 . \tag{54} \]

The pressure \(P'\) is the pressure of expansion of the dissolved substance in the case when it occupies the volume \(V_s\); the pressure \(P\) is the pressure of expansion of the dissolved substance in the case when it occupies the volume \(V_s[1-k_1(P-p_1)]\). If the pressure of expansion of the dissolved substance is not very large, one may, without great error, set:

\[ P'-p_0=P-p_1 \tag{55} \]

Then equation (54) becomes:

\[ - V_{p_0} k_0=V_s k_1 \tag{56} \]

Finally, assuming that the coefficient of elasticity remains unchanged during compression and expansion of liquids, i.e. that \(k_0=-k_0\), we obtain:

\[ \frac{V_{p_0}}{V_s}=\frac{k_1}{k_0}, \quad \text{whence} \]

\[ k_1=k_0 \times \frac{V_{p_0}}{V_s} \tag{57} \]

That is, the coefficient of compression of the solution is related to the coefficient of compression of the solvent as the volume of the solution is related to the volume of the pure solvent contained in the given solution.

If one makes the assumption that the volume of the solution is at the same time the volume occupied by the solvent in the solution, i.e., if the partial

density of the solvent in the solution be calculated by formulas (1), then relations (57) may be represented in the following form:

\[ \frac{s_1}{s_0}=\frac{k_1}{k_0} \quad \text{and} \]

\[ k_1=k_0 \times \frac{s_1}{s_0} \tag{58} \]

That is, the coefficient of compression of the solution is related to the coefficient of compression of the pure solvent as the partial density of the solvent in the solution is related to the density of the pure solvent.

Thus, equations (57) and (58) make it possible to calculate the coefficients of compression of a solution from the specific volume of the solution and from the partial density of the solvent in the solution.

In the following table these calculations are carried out for several nonelectrolytes.

Table XXIX.

Dissolved substances.	Number of gram-molecules in one liter of solution.	Density.	$\dfrac{V_{p_0}}{V_s}$	$\dfrac{k_1}{k_0}$ (experiment)	$k_0\dfrac{V_{p_0}}{V_s}\cdot 10^{-6}$	$k_1\cdot 10^{-6}$ direct experiment.
Urea	1	1,0183	0,958	0,925	44,5	43,0
Acetone	1	0,9948	0,936	0,936	43,5	43,6
Alcohol	1	0,9920	0,946	0,950	44,0	44,2
" "	2	0,9851	0,893	0,909	41,5	42,3
Resorcinol	1	1,0228	0,913	0,922	42,46	42,9
Sugar	1	1,1320	0,790	0,746	36,73	34,7

From the table it is seen that the ratios $\dfrac{V_{p_0}}{V_s}$ and $\dfrac{k_1}{k_0}$ are in general close, and the coefficients of compression calculated by formula (57) are also close to the observed ones. There is no complete agreement. There is no doubt, however, that the changes in the coefficients of compression of a liquid and in its partial specific volume, as a consequence of the dissolution in the liquid of a foreign body, are of the same order and proceed in parallel. These relations stand out quite clearly if we compare substances whose molecular weights differ considerably, for example, acetone (60) and sugar (342).

Let us also draw attention to one more consequence of equalities (57) and (58).

Since, by assumption, the partial density of the solvent in the solution is always less than the density of the pure solvent, and the volume of the solution is always greater than the volume of the pure solvent contained in the solution (otherwise there would be chemical interaction, not dissolution), then, if the rela-

equations (57) and (58) are correct; the coefficient of compression of the solution must always be less than the coefficient of compression of the pure solvent.

The experimental data at my disposal apparently confirm this. For example, the coefficient of compression of water is \(46.5 \times 10^{-6}\); the coefficient of compression of acetone is \(109 \times 10^{-6}\); the coefficient of compression of alcohol is \(94.5 \times 10^{-6}\). One might have expected that, for mixtures of acetone and alcohol with water, the coefficients of compression would lie between the limits of the coefficients of compression of the pure liquids, i.e., that with an increase in the mixture’s content of alcohol or acetone the coefficients of compression would increase. Experiment shows that they decrease, and approximately in the ratio required by equation (57).

With this I shall for the time being conclude my chapter on the relation between partial density and osmotic pressure, intending in the near future once more, and on a broader scale, to turn to the investigation of the relations indicated.

Partial Density and Concentration.

Stoichiometric relations. The term “concentration” is used in different senses. Most often, concentration is understood to mean the relation between the masses of the bodies forming a solution. In doing so, either the mass of the solvent is set equal to 100, or the relation is given between the mass of a given component of the solution and the total mass of the solution. The masses of the one and the other component are measured either in grams or in molecules.\(^1\)

In this definition of concentration, for the association of given bodies only one condition is fixed—namely, that under given conditions of temperature and pressure these masses form a solution, i.e. a physically homogeneous body, the ratio between whose masses, without violation of homogeneity, may vary in either direction continuously—within certain limits or to infinity.

In such a definition of concentration there is rooted a functional dependence between the concentration and the capacity of given bodies to form a solution. If the bodies are capable of forming a solution in all ratios, then the series of numbers giving the concentration will either be infinite, or will form a series between 0 and 100, depending on how the concentration is expressed—by the ratio between the masses of the components, or by the ratio between the mass of a given component and the mass of the solution set equal to 100. If the bodies are capable of forming a solution only within certain limits, then the corresponding numerical quantities giving the concentration will likewise lie between certain limits.

Between the numerical quantities representing series of concentrations of solutions of different bodies, one may seek stoichiometric relations

\(^1\) When the question concerns solutions of the same bodies, it is all the same in what units their masses are measured; but when it is necessary to compare solutions of different bodies, the measurement of masses in equivalents or molecules presents certain advantages.

(for the time being they are unknown); but it may be predicted in advance that these stoichiometric ratios will be of a different kind than the stoichiometric ratios of a series of “concentrations” of bodies forming an association of the type of a chemical compound. Indeed, in the definition of a chemical compound there is included, besides physical homogeneity, yet another condition which is not present in the definition of a solution—namely, “physical individuality”; i.e., bodies forming associations of the type of a chemical compound are not only physically homogeneous, but they also have, in addition, a fixed definite crystalline form, a definite boiling temperature, and other “indivisible”¹ properties. The stoichiometric ratios in the series of “concentrations” of chemical compounds are generally known and constitute the core of those fundamental laws which determined the entire character of the scientific discipline of chemistry in the period after Lavoisier.

But in defining the concentration of a solution, besides the condition that this association is an association of the type of a solution, other conditions may also be fixed for the solution. For example, one may impose the condition that the concentrations of a series of solutions be compared when they are placed under such conditions that they have one and the same vapor pressure, i.e., compare solutions to which are applied forces equal to the osmotic pressure of the dissolved body. One may fix for the solutions being compared a definite volume, i.e., compare equal volumes of solutions, and so on.

It may be expected that, with such a method of comparison, various kinds of stoichiometric regularities may in general be discovered more easily. For example, if one compares solutions to which forces equal to the osmotic pressure of the dissolved bodies are applied, then the specific volume, as is predicted by the scheme of equilibrium of forces in a solution in the absence of a semipermeable partition set forth above, must appear, for solutions of all bodies, as a linear function of the concentration.

It may also be expected that, with such a method of comparison, when for a series of solutions “one and the same indivisible property” is fixed, i.e., when the series itself becomes as it were indivisible, the stoichiometric ratios will be analogous to the stoichiometric ratios of chemical compounds. We shall now show that, if a definite volume is fixed for a solution, then to a certain extent these predictions are indeed justified.

The partial density of one or another component of a solution is otherwise the content of this component in a unit volume of the solution. A series of numbers for the partial density of a solution, consequently, gives the content of one or another component in the solution under the condition that equal volumes of solutions are always compared. With the aid of this series of numbers it is easy to carry out calculations of what mass of dissolved body must replace a molecule of solvent in a solution so that the volume of the solution is not changed thereby.

Such calculations are also made in Tables XXX–XLVII for a series of solutions and mixtures whose density was measured by me (Chapter III). Tables XXX–XLVII contain the following columns:

t°/%—concentration in weight percent;

$S \dfrac{t^0}{4^0}$ — specific gravity of the entire solution;

$s_1 \dfrac{t^0}{4^0}$ — partial density of either component of the mixture;

$\dfrac{s'_1}{s_0 - s_1} \times M$ — the quantity of the second component replacing in the solution a molecule of the first component, under the condition that with such replacement the volume of the solution does not change;

($s_0$ is the specific gravity of the first component, $s_1$—the partial density of this component in the solution, $s'_0$—the specific gravity of the second component of the solution, $s'_1$—the partial density of the second component in the solution, $M$—the molecular weight of one or the other component).

Table XXX.

Ether and aniline. $(C_2H_5)_2O = 74.08;$ $C_6H_5 \cdot NH_2 = 93.10.$

$n^0/o$	$S \dfrac{15^0}{4^0}$	$s_1 \dfrac{15^0}{4^0}$ ether	$s'_1 \dfrac{15^0}{4^0}$ aniline	$\dfrac{s_1 \text{ anil.}}{s_0 - s_1 \text{ eth.}} \times 74.$	$\dfrac{s_1 \text{ ether}}{s'_0 - s_1 \text{ anil.}} \times 93.$
0	0,7195	0,7195	0
1,45	0,7239	0,7127	0,0112	115,0	65,36
2,59	0,7267	0,7079	0,0188	119,9	65,38
12,46	0,7556	0,6622	0,0934	120,6	66,06
17,25	0,7898	0,6360	0,1338	118,6	66,32
24,86	0,7921	0,5952	0,1969	117,2	66,79
52,75	0,8752	0,4135	0,4617	111,6	68,20
72,64	0,9368	0,2563	0,6805	108,7	69,07
92,07	0,9991	0,0792	0,9199	106,3	69,68
98,78	1,0216	0,0124	1,0092	105,6	70,32
100	1,0256	0	1,0256

Table XXXI.

Ether and nitrobenzene \((C_2H_5)_2O\)—74.08; \(C_6H_5NO_2\)—123.08.

\(\pi^0/\%\)	\(S\,\dfrac{15^0}{4^0}\)	\(s_1\,\dfrac{15^0}{4^0}\) ether	\(s_1\,\dfrac{15^0}{4^0}\)-nitrob.	\(\dfrac{s_1\ \text{nitrob.}}{s_0-s_1\ \text{eth.}}\times 74\)	\(\dfrac{s_1\ \text{ether}}{s'_0-s_1\ \text{nitrob.}}\times 123\)
0	0.7195	0.7195	0
1.72	0.7254	0.7129	0.0125	140	73.3
9.70	0.7536	0.6805	0.0731	138	73.7
17.06	0.7808	0.6475	0.1332	137	74.1
22.33	0.8014	0.6224	0.1790	136	74.4
25.14	0.9099	0.6109	0.1990	135	74.5
49.82	0.9191	0.4612	0.4579	131	75.6
69.13	0.0181	0.3142	0.7038	128	76.6
74.12	1.0455	0.2706	0.7749	127	76.8
90.75	1.1460	0.1060	1.0400	125	77.4
98.86	1.2006	0.0137	1.1869	124	77.8
100	1.2085	0	1.2085

Table XXXII.

Benzene and ethylene bromide. \(C_6H_6\)—78; \(C_2H_4Br_2\)—188.

\(\pi^0/\%\) \(C_2H_4Br_2\)	\(S\,\dfrac{25^0}{4^0}\)	\(s_1\,\dfrac{25^0}{4^0}\) benz.	\(s_1\,\dfrac{25^0}{4}\) br. eth.	\(\dfrac{s_1\ \text{br. eth.}}{s_0-s_1\ \text{benz.}}\times 78\)	\(\dfrac{s_1\ \text{benz.}}{s'_0-s_1\ \text{br. eth.}}\times 188\)
0	0.8741	0.8741	0
0.98	0.8787	0.8700	0.0864	164.37	74.48
4.77	0.8989	0.8561	0.0429	175.90	75.72
8.33	0.9188	0.8422	0.0766	187.30	75.70
8.02	0.9170	0.8435	0.0736	187.61	75.71
19.51	0.9866	0.7940	0.1926	187.55	75.56
29.51	1.0586	0.7463	0.3123	190.60	75.60
36.31	1.1176	0.7062	0.4114	191.12	75.57
35.39	1.1055	0.7143	0.3912	190.94	75.57
47.23	1.2141	0.6430	0.5715	192.89	75.72
56.63	1.3165	0.5710	0.7455	191.84	75.45
69.56	1.4904	0.4533	1.0371	192.23	75.34
81.70	1.7022	0.3115	1.3907	192.80	75.32
88.99	1.8610	0.2049	1.6561	193.03	75.22
98.97	2.1346	0.0298	2.1127	193.39	74.46
100	2.1682	0	2.1682

Table XXXIII.

Benzene and chloroform. \(C_6H_6 — 78;\ CHCl_3 — 119.3\).

\(t^\circ/\%\ CHCl_3\)	\(S\dfrac{25^\circ}{4^\circ}\)	\(s_1\dfrac{25^\circ}{4^\circ}\) benz.	\(s_1\dfrac{25^\circ}{4^\circ}\) chloroform	\(\dfrac{s_1\ \text{chloroform}}{s_0-s_1\ \text{benz.}}\times 78\)	\(\dfrac{s_1\ \text{benz.}}{s_0-s_1\ \text{chloroform}}\times 119.3\)
0	0.8739	0.8739	0	—	—
1.45	0.8790	0.8662	0.0127	129.32	70.45
7.07	0.8995	0.8359	0.0636	130.79	70.43
12.35	0.9198	0.8062	0.1136	130.92	70.41
20.31	0.9511	0.7579	0.1932	129.93	70.29
43.11	1.0595	0.6028	0.4567	131.41	70.30
61.60	1.1664	0.4479	0.7185	131.56	70.20
79.06	1.2899	0.2701	1.0198	131.74	70.08
88.65	1.3706	0.1556	1.2150	131.94	70.15
94.85	1.4277	0.0735	1.3542	131.97	69.92
98.04	1.4596	0.0286	1.4310	132.05	70.20
98.90	1.4682	0.0161	1.4521	132.05	70.06
100	1.4796	0	1.4796

Table XXXIV.

Benzene and chlorobenzene. \(C_6H_6 — 78;\ C_6H_5Cl — 112.5\).

\(t^\circ/\%\ C_6H_5Cl\)	\(S\dfrac{25^\circ}{4^\circ}\)	\(s_1\dfrac{25^\circ}{4^\circ}\) benz.	\(s_1\dfrac{25^\circ}{4^\circ}\) chlorobenz.	\(\dfrac{s_1\ \text{chlorobenz.}}{s_0-s_1\ \text{benz.}}\times 78\)	\(\dfrac{s_1\ \text{benz.}}{s_0-s_1\ \text{chlorobenz.}}\times 112.5\)
0	0.87376	0.87376	0	—	—
2.33	0.87794	0.85747	0.02046	99.8	89.27
4.90	0.88257	0.83930	0.04326	99.8	89.26
7.98	0.88826	0.81739	0.07087	100.0	89.26
24.12	0.91937	0.69761	0.22176	100.1	89.26
29.67	0.92831	0.65288	0.27543	99.2	88.97
36.83	0.94527	0.59710	0.34817	100.1	89.22
47.36	0.96811	0.50958	0.45853	100.1	89.23
60.48	0.99800	0.39436	0.60364	100.1	89.20
70.86	1.02311	0.29813	0.72498	100.2	89.19
80.00	1.04626	0.20927	0.83699	100.2	89.17
89.01	1.07019	0.11756	0.95263	100.2	89.14
95.22	1.08729	0.05193	1.03537	100.2	89.01
98.66	1.09703	0.01466	1.08238	100.2	88.57
100	1.10100	0	1.10100

Table XXXV.

Benzene and bromobenzene. \(C_6H_6\)—78; \(C_6H_5Br\)—157.

\(\pi\%\ C_6H_5Br\)	\(S\frac{25^\circ}{4^\circ}\)	\(s_1\frac{25^\circ}{4^\circ}\) benzene	\(s_1\frac{25^\circ}{4^\circ}\) bromobenzene	\(\dfrac{s_1\ \text{bromobenz.}}{s_0-s_1\ \text{benz.}}\times 78\)	\(\dfrac{s_1\ \text{benz.}}{s'_0-s_1\ \text{bromobenz.}}\times 157\)
0	0,87378	0,87378	0	—	—
1,53	0,87930	0,86602	0,01328	133,5	92,27
4,29	0,88957	0 85140	0,03816	133,0	92,27
12,98	0,92322	0,80334	0,11988	132,7	92,26
18,32	0,94519	0,77198	0,17321	132,7	92,26
30,37	0,99890	0,69554	0,30336	132,8	92,27
41,09	1,05190	0,61965	0,43226	132,7	92,25
54,56	1,12034	0,50906	0,61128	130,7	91,28
63,70	1,18510	0,43013	0,75497	132,7	92,27
79,44	1,29936	0,26708	1,03228	132,7	92,24
88,95	1,38047	0,15222	1,22825	132,8	92,42
95,22	1,43865	0,06872	1,36993	132,8	92,30
99,01	1,47701	0,01468	1,46233
100	1,48682	0	1,48682

Table XXXVI.

Carbon tetrachloride and aniline. \(CCl_4\)—153,8; \(C_6H_5.NH_2\)—93.

\(\pi\%\ C_6H_5NH_2\)	\(S\frac{25^\circ}{4^\circ}\)	\(s_1\frac{25^\circ}{4^\circ}\ CCl_4\)	\(s_1\frac{25^\circ}{4^\circ}\) aniline	\(\dfrac{s_1\ \text{anil.}}{s_0-s_1\ CCl_4}\times 153{,}8\)	\(\dfrac{s_1\ CCl_4}{s'_0-s_1\ \text{anil.}}\times 93\)
0	1,5845	1,5845	0	—	—
1,48	1,5718	1,5485	0,02326	99,6	144,9
5,80	1,5359	1,4468	0,08903	99,6	145,0
11,57	1,4907	1,3182	0,17249	99,8	145,2
20,24	1,4273	1,1386	0,28865	99,7	145,5
31,25	1,3534	0,9304	0,42302	99,6	145,7
37,46	1,3149	0,8223	0,49259	99,5	145,9
51 37	1,2353	0,6007	0,63465	99,3	146,2
56,46	1,2084	0,5261	0,68231	99,3	146,3
68,72	1,1479	0,3590	0,78884	99,1	146,5
83,29	1,0831	0,1810	0,90218	99,0	146,8
94,52	1,0376	0,0569	0,98078	99,1	146,8
88,91	1,0600	0,1175	0,94248	98,9	147,0
98,96	1,0207	0,0106	1,01013	98,8	147,9
100	1,0168	0	1,01684	—	—

Table XXXVII.

Benzene and acetic acid. \(C_6H_6—78;\ CH_3\cdot CO\cdot OH—60.\)

\(\%\, CH_3.CO.OH\)	\(S^{25^\circ}_{4^\circ}\)	\(s_1\dfrac{25^\circ}{4^\circ}\) benzene	\(s_1\dfrac{25^\circ}{4^\circ}\) acid	\(\dfrac{s_1\ \text{acid}}{s_0-s_1\ \text{benz.}}\times 78\)	\(\dfrac{s_1\ \text{benz.}}{s'_0-s_1\ \text{acid}}\times 60\)
0	0,87388	0,87388	0	—	—
2,04	0,87577	0,85793	0,01784	87,24	50,17
6,62	0,88101	0,82269	0,05832	88,86	50,09
10,62	0,88553	0,79147	0,09407	89,03	50,00
19,57	0,89634	0,72091	0,17543	89,45	49,81
30,76	0,91110	0,63083	0,28027	89,94	49,57
39,15	0,92317	0,56176	0,36141	90,32	49,40
56,31	0,95071	0,41537	0,53534	91,07	49,02
56,75	0,95144	0,41145	0,53999	91,08	49,01
80,06	0,99627	0,19866	0,79761	92,14	48,43
87,64	1,01320	0,12524	0,88796	92,51	48,24
95,95	1,03323	0,04186	0,99137	92,94	47,96
98,94	1,04091	0,01104	1,02987	—	—
100	1,04374	0	1,04374	—	—

Table XXXVIII.

Solutions of iodine in carbon disulfide. \(CS_2—76.\)

\(\%\,\) iodine	\(S^{25^\circ}_{4^\circ}\)	\(s_1\dfrac{25^\circ}{4^\circ}\) carbon disulfide	\(s_1\dfrac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1\ \text{iodine}}{s_0-s_1\ \text{carbon disulfide}}\times 76\)
0	1,25589	1,25589	0	—
1,13	1,26574	1,25142	0,01432	243,4
2,82	1,28096	1,24487	0,03609	166,6
3,34	1,28571	1,24272	0,04299	248,1
4,83	1,30003	1,23727	0,06276	256,2
6,12	1,31199	1,23166	0,08033	252,0
2,02	1,27297	1,24719	0,02578	225,2
0,60	1,26112	1,25361	0,00751	250,3
6,48	1,31526	1,23001	0,08525	250,3
5,85	1,30934	1,23256	0,07675	250,4
9,07	1,34088	1,21920	0,12168	252,1
11,85	1,36913	1,20695	0,16218	251,9

Table XXXIX.

Solutions of iodine in chloroform. \(CHCl_3\)—119.3.

% iodine	\(S\frac{25^\circ}{4^\circ}\)	\(s_1\frac{25^\circ}{4^\circ}\) chloroform	\(s_1\frac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1\ \text{iodine}}{s_0-s_1\ \text{chloroform}}\times119.3\)
0	1.47896	1.47896	0	—
0.78	1.48654	1.47492	0.01162	343
1.75	1.49536	1.46922	0.02614	328
2.79	1.50503	1.46301	0.04202	315

Table XL.

Solutions of iodine in carbon tetrachloride. \(CCl_4\)—154.

% iodine	\(S\frac{25^\circ}{4^\circ}\)	\(s_1\frac{25^\circ}{4^\circ}CCl_4\)	\(s_1\frac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1\ \text{iodine}}{s_0-s_1CCl_4}\times154\)
0	1.58431	1.58431	0	—
0.22	1.58655	1.58309	0.00346	430
0.49	1.58916	1.58140	0.00776	408
0.51	1.58903	1.58096	0.00807	369
0.94	1.59331	1.57835	0.01496	386
1.44	1.59782	1.57484	0.02298	373
2.72	1.59859	1.55512	0.04347	229

Table XLI.

Solutions of iodine in ethylene bromide; \(C_2H_4Br_2\)—188.

% iodine	\(S\frac{25^\circ}{4^\circ}\)	\(s_1\frac{25^\circ}{4^\circ}C_2H_4Br_2\)	\(s_1\frac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1\ \text{iodine}}{s_0-s_1C_2H_4Br_2}\times188\)
0
0.28	2.16714	2.16714	0	—
0.91	2.17616	2.15642	0.01974	346
1.82	2.18546	2.14577	0.03969	349

Table XLII.

Solutions of iodine in benzene. \(C_6H_6—78\).

wt.% iodine	\(S\,\dfrac{25^\circ}{4^\circ}\)	\(s_1\,\dfrac{25^\circ}{4^\circ}\) benzene	\(s_1\,\dfrac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1}{s_0-s_1}\dfrac{\text{iodine}}{\text{benzene}}\times 78\)
0	0,87352	0,87352	0	—
0,55	0,87698	0,87218	0,00480	358
0,87	0,87962	0,87200	0,00762	391
2,27	0,88933	0,86912	0,02021	358
4,05	0,90222	0,86568	0,03655	364
6,02	0,91668	0,86152	0,05516	358
8,34	0,93452	0,85661	0,07791	359
9,40	0,94298	0,85435	0,08863	360
13,68	0,97811	0,84434	0,13377	357

Table XLIII.

Solutions of iodine in nitrobenzene. \(C_6H_5.NO_2—123\).

wt.% iodine	\(S\,\dfrac{25^\circ}{4^\circ}\)	\(s_1\,\dfrac{25^\circ}{4^\circ}\) nitrobenzene	\(s_1\,\dfrac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1}{s_0-s_1}\dfrac{\text{iodine}}{\text{nitrobenzene}}\times 123\)
0	1,19908	1,19908	0	—
0,49	1,20233	1,19639	0,00594	272
0,93	1,20575	1,19454	0,00112	304
1,87	1,21368	1,19092	0,02276	343
2,58	1,21963	1,18813	0,03150	354
3,46	1,22716	1,18465	0,04251	362
4,90	1,23935	1,17856	0,06079	364

Table XLIV.

Solutions of iodine in aniline. \( \mathrm{C_6H_5 \cdot NH_2} — 93.\)

\(n\%\) iodine	\(S \dfrac{25^\circ}{4^\circ}\)	\(s_1 \dfrac{25^\circ}{4^\circ}\) aniline	\(s_1 \dfrac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1\ \text{iodine}}{s_0 - s_1\ \text{aniline}} \times 93\)
0	1,01693	1,01693	0	—
0,47	1,02105	1,01623	0,00482	640
2,45	1,03878	1,01331	0,02547	654
3,87	1,05172	1,01098	0,04074	636
7,15	1,08213	1,00474	0,07739	590

Table XLV.

Solutions of iodine in ether. \((\mathrm{C_2H_5})_2\mathrm{O} — 74.\)

\(n\%\) iodine	\(S \dfrac{25^\circ}{4^\circ}\)	\(s_1 \dfrac{25^\circ}{4^\circ}\) ether	\(s_1 \dfrac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1\ \text{iodine}}{s_0 - s_1\ \text{ether}} \times 74\)
0	0,70812	0,70812	0	—
0,70	0,71217	0,70719	0,00498	396
1,83	0,71988	0,70670	0,01318	691
3,10	0,72757	0,70498	0,02259	534
3,65	0,73090	0,70421	0,02669	506
4,82	0,73848	0,70288	0,03560	503
4,91	0,73912	0,70281	0,03631	507
6,13	0,74733	0,70154	0,04579	515
7,37	0,75504	0,69941	0,05563	473

Table XLVI.

Solutions of iodine in acetic acid \(CH_3.CO.OH \times 1.66 = 99.66\).

% iodine	\(S \dfrac{25^\circ}{4^\circ}\)	\(s_1 \dfrac{25^\circ}{4^\circ}\) acid	\(s_1 \dfrac{25^\circ}{4^\circ}\) iodine	\(\dfrac{s_1}{s_0-s_1}\dfrac{\text{iodine}}{\text{acid}} \times 99.6\)
0	1.043675	1.04367	0	—
0.48	1.04737	1.04220	0.00517	350.3
0.91	1.05052	1.04100	0.00952	344.8
1.35	1.05388	1.03966	0.01422	346.2
1.94	1.05829	1.03778	0.02051	342.2
2.45	1.06222	1.03624	0.02598	344.6
2.54	1.06294	1.03592	0.02702	343.7

Table XLVII.

Aqueous solutions of cane sugar. \(C_{12}H_{22}O_{11} — 342\).

%	\(S \dfrac{17.5^\circ}{17.5^\circ}\)	\(s_1 \dfrac{17.5^\circ}{17.5^\circ}\) water	\(s_1 \dfrac{77.5^\circ}{17.5^\circ}\) sugar	\(\dfrac{s_1}{s_0-s_1}\dfrac{\text{sugar}}{\text{water}} \times 18\)
6.40	1.02535	0.95950	0.06585	29.26
21.48	1.08995	0.85583	0.23412	29.22
31.64	1.13759	0.77766	0.35993	29.13
38.10	1.16971	0.72405	0.44566	29.06
45.08	1.20618	0.66243	0.54375	28.98
50.64	1.23610	0.61014	0.62596	28.97

The numerical material presented in Tables XXX–XLVII permits the following generalization to be made: the quantities of components that replace one another in solutions, under the condition that the volume of the solution thereby remains unchanged, are related to one another as numbers very close to their molecular weights. For example, from a given volume of ether, provided that this volume remains unchanged, we can prepare an infinite series of mixtures of ether with aniline, replacing the ether little by little with aniline; but in this process the mass of ether replaced each time must be related to the replacing mass of aniline as the numbers 74 and 105–115 (molecular weight of ether 74, molecular weight of aniline 93). In the same kind of replacement of carbon tetrachloride by aniline, the masses of the carbon tetrachloride replaced are related to the masses of the replacing aniline as the numbers 153 and 99–98 (molecular weight \(CCl_4\)—153.8, molecular weight \(C_6H_6NH_2\)—93); for mixtures of benzene and ethylene bromide, the ratios of the masses of ethylene bromide and benzene are 188 and 75–74 (\(C_2H_4Br_2\)—188, \(C_6H_6\)—78), etc.

This generalization seems to me very important and deserving of full attention and comprehensive investigation. It may be interpreted in different ways. One interpretation or another will establish the definite point of view by which the further course of the investigation will be determined. Let us note two such possible points of view.

One may suppose that the replacement of one component of a solution by another, while keeping the total volume unchanged, takes place strictly in the ratio of the molecular weights. Then the explanation of the deviations from this rule that are observed must be sought either in the chemical interaction of the solvent with the dissolved substance, or in association of the solvent, or, finally, in dissociation.

From the material collected in Tables XXX–XLVII, much evidence can be extracted in favor of such a view. Namely, aqueous solutions of nonelectrolytes (Table XXXVII) by no means satisfy the rule of the “molecular composition of solutions.” Mixtures of liquids that are known to be associated (Tables XXXVII and XLVI) satisfy the rule only if their association is taken into account—otherwise, they give sharp deviations. Mixtures of liquids belonging to the group of nonassociated (slightly associated) liquids fairly closely satisfy the rule of “molecular composition” and, apparently, the better the less strongly the given pair of liquids is associated (Tables XXXII, XXXIII, XXXVI). Solutions in which chemical interaction undoubtedly occurs between the dissolved substance and the solvent (solutions of iodine in ether\(^1\) and solutions of iodine in aniline\(^2\)) clearly do not satisfy the rule of molecular composition.

Thus, the first point of view is that a solution, like a chemical compound, obeys the law of chemical shares; the observed deviations are the result of side reactions and of processes of association and dissociation.

The second possible point of view is that fixing, for solutions of various concentrations, a certain volume that is the same for all solutions is still not sufficient to place the solutions under the conditions in which chemical compounds are found. In order to obtain regular stoichiometric ratios when comparing solutions of different—

\(^1\) See p. 32.
\(^2\) Chapter III.

of various concentrations it is necessary, in addition to the invariable volume, to fix also other conditions and, perhaps, even conditions not identical for solutions of different concentrations; for example, to place these solutions under corresponding conditions in the sense of the van der Waals theory. If these conditions were fulfilled exactly, then those regularities which now appear in the form of a hint at a law, as it were in the form of a semi-law, would then appear in the definite and clear form of an exact law.

Such is the second point of view. To carry out investigations and inquiries in this direction, however, is very difficult, since the factual material necessary for this and the corresponding theoretical studies are still almost completely lacking.

In the form in which the rule of the “molecular composition” of solutions has been given above, it may nevertheless be regarded as one more piece of evidence in favor of the proposition that there is no essential difference between associations of the type of a solution and those of the type of a chemical compound; that which until now has essentially distinguished a solution from a chemical compound—namely, that the composition of a solution from its components does not obey an apparently fixed law—falls away and, one may hope, will in the future be eliminated completely; a chemical compound will then appear as a special case of a solution, namely, a solution fixed by a totality of definite external conditions, such as a definite crystalline form, etc.

The law of the “molecular composition of solutions” is discernible not only in the relations examined, but, without doubt, also in the long-known laws of Raoult. It is curious that these laws, which establish an analogy between solutions and chemical compounds and, consequently, confirm the “chemical theory of solutions,” were found empirically by Raoult and were later given a thermodynamic foundation by the supporters of the “physical theory of solutions” with the aid of a mechanical scheme, and were regarded as one of the brilliant successes of this theory. At the present time they must serve as the link that will connect both these theories.

The law of the “molecular composition of solutions,” like Raoult’s laws, can obviously also have practical significance; namely, in determining molecular weight it will make it possible to orient oneself as to which of the possible molecular weights one should settle upon.

Partial density as a function of the molecular concentration of a solution. As is known, the relation between the concentration of a solution and its vapor pressure is formulated by Raoult’s law in the following way:

\[ \frac{p_0-p_1}{p_0}=\frac{n}{N+n},\quad \text{where} \tag{59} \]

\[ \frac{p_0-p_1}{p_0} \]

is the relative lowering of the vapor pressure of the solvent as a consequence of the dissolution in it of a foreign body;

\[ \frac{n}{N+n} \]

is the ratio of the number of molecules of the dissolved substance to the total number of molecules composing the solution.

If we assume that \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\), then from equation (59) one obtains:

\[ \frac{s_0-s_1}{s_0}=\frac{n}{N+n}, \quad \text{where} \tag{60} \]

\[ \frac{s_0-s_1}{s_0} \]

is the relative lowering of the partial density of the solvent in the solution.

Equation (60) expresses the sought functional dependence between the partial density of the solvent in the solution and the concentration of the solution. It is read as follows: when, in some definite volume of solution, solvent molecules are replaced by molecules of the dissolved substance, the volume of the solution remains unchanged.

Consequently, proceeding from Raoult’s law, we again arrive at the very proposition that was just established under the name “molecular composition of solutions.”

If we translate this into the language of the scheme of osmotic equilibrium set forth above, then equation (60) should be read thus: equimolecular amounts of any substances whatsoever, possessing the same dissolution pressure, dissolve one and the same mass of one and the same solvent in the same way.

Of course, both these propositions, as well as others analogous to them, will be strictly exact only in that ideal case in which the true volume of the molecules and the attraction between them may be neglected, and also when the substances forming the solution are not associated and do not form complexes with one another. The simultaneous presence of all these conditions cannot occur very often, and therefore reality must give greater or lesser deviations from both propositions and, consequently, from equality (60). In order to represent visually those deviations from equality (60) which experiment gives, I again turned to the material I had obtained by the method of weighing mixtures of liquids miscible with one another in all proportions, and this time made use of a graphical method.

The curves expressing the functional dependence between the molecular concentration and the partial density in the solution of one or the other component of the mixture were constructed in the following way.

Along the axis of abscissae were laid off quantities proportional to the molecular concentration in percent, i.e. to the content of the number of molecules of some component of the mixture in 100 mol. of the mixture. Along the axes of ordinates were laid off the quantities of the relative partial density of the given component in the solution, i.e. the partial densities of the given component referred to the density of this same component in the pure state at the same temperature and pressure (atmospheric). If the partial density were a linear function of the molecular concentration, i.e., if equality (60) were satisfied, then the curve of relative partial densities

\[ \left(\frac{s_1}{s_0}\right) \]

would coincide with the diagonal of the drawing, which is made by a dotted line. If this is not so, it will represent a curve of one form or another, more or less removed from the diagonal.

All the curves were drawn on a large scale and then photographically reduced to the dimensions of the text.

The numerical material necessary for constructing the given curve is placed before the corresponding drawing in the form of tables, in which are given the concentration of the solution in weight percent (wt. %) and molecular percent (% Mol.)

in percent by weight $\left(S\frac{t^0}{4^0}\right)$ and the relative partial densities of the one and the other component in the solution $\left(\frac{s_1}{s_0}\right)$.

Table XLVIII.

Ether and aniline $(C_2H_5)_2O$—74, $C_6H_5.NH_2$—93.

wt.% $C_6H_5.NH_2$	Mol.% $C_6H_5.NH_2$	$S\ \dfrac{25^0}{4^0}$	$\dfrac{s_1}{s_0}$ ether	$\dfrac{s_1}{s_0}$ anil.
0	0	0,7195	1,0000	0
1,545	1,233	0,7239	0,9906	0,0109
2,59	2,072	0,7267	0,9845	0,0183
12,46	10,17	0,7556	0,9204	0,0910
17,25	14,23	0,7698	0,8841	0,1304
24,86	20,84	0,7921	0,8274	0,1919
52,75	47,04	0,8752	0,5748	0,4501
72,64	67,87	0,9368	0,3562	0,6633
92.07	90,22	0,9991	0,1101	0,8966
98,78	98,56	1,0216	0,0172	0,9836
100	100	1,0256	0	1,0000

Table XLIX.

Ether and nitrobenzene; \((C_2H_5)_2O — 74;\ C_6H_5 \cdot NO_2 — 123.\)

\(\%\, C_6H_5 \cdot NO_2\)	\(\%\, Mol\ C_6H_5 \cdot NO_2\)	\(S\ \dfrac{25^0}{4^0}\)	\(\dfrac{s_1}{s_0}\) ether	\(\dfrac{s_1}{s_0}\) nitrobenz.
0	0	0,7195	1,0000	0
1,72	1,311	0,7254	0,9908	0,0103
9,70	6,028	0,7536	0,9458	0,0605
17,06	11,02	0,7808	0,8999	0,1103
22,33	14,76	0,8014	0,8652	0,1177
25,14	16,81	0,8099	0,8489	0,1647
49,82	37,40	0,9191	0,6410	0,3791
69,13	57,41	1,0181	0,4366	0,5825
74,12	63,28	1,0455	0,3761	0,6414
90,75	85,51	1,1460	0,1473	0,8608
98,86	98,11	1,2006	0,0190	0,9827
100	100	1,2085	0	1,0000

Fig. 7.

Table L.

Benzene and ethylene bromide; $C_6H_6$—78; $C_2H_4Br_2$—188.

% $C_2H_4Br_2$	Mol % $C_2H_4Br_2$	$S\frac{25^\circ}{4^\circ}$	$\frac{s_1}{s_0}$ benz.	$\frac{s_1}{s_0}$ ethyl. bromide
0	0	0,8741	1,0000	0
0,98	0,41	0,8787	0,9954	0,0040
4,77	2,037	0,8989	0,9793	0,0198
8,33	3,633	0,9188	0,9634	0,0353
8,02	3,493	0,9170	0,9649	0,0339
19,51	9,141	0,9866	0,9082	0,0888
29,51	14,80	1,0586	0,8537	0,1440
36,81	19,47	1,1176	0,8078	0,1898
35,39	18,53	1,1055	0,8171	0,1898
47,23	27,09	1,2141	0,7355	0,2645
56,63	35,14	1,3165	0,6531	0,3535
69,56	48,66	1,4904	0,5186	0,4783
81,70	64,91	1,7022	0,3564	0,6415
88,99	76,98	1,8610	0,2344	0,7638
98,97	97,52	2,1346	0,0250	0,9745
100	100	2,1682	0	1,0000

Table LI.

Benzene and chloroform $C_6H_6$—78; $CHCl_3$—119,3.

% $CHCl_3$	Mol % $CHCl_3$	$S\frac{25^\circ}{4^\circ}$	$\frac{s_1}{s_0}$ benz.	$\frac{s_1}{s_0}$ chloroform
0	0	0,8739	1,0000	0
1,45	0,954	0,8662	0,9911	0,0086
7,07	4,737	0,8359	0,9563	0,0429
12,35	8,428	0,8062	0,9223	0,0767
20,31	14,29	0,7579	0,8672	0,1305
43,11	33,13	0,6028	0,6898	0,3085
61,60	51,19	0,4479	0,5125	0,4854
79,06	71,19	0,2701	0,3090	0,6891
88,65	83,64	0,1556	0,1780	0,8209
94,85	92,32	0,0735	0,0841	0,9147
98,04	97,03	0,0286	0,0327	0,9667
98,90	98,33	0,0161	0,0185	0,9811
100	100	1,4796	0	1,0000

Fig. 8.

Table LII.

Carbon tetrachloride and aniline. \(CCl_4 — 154;\ C_6H_5.NH_2 — 93.\)

wt. % \(C_6H_5.NH_2\)	mol % \(C_6H_5.NH_2\)	\(S^{25^\circ}_{4^\circ}\)	\(\dfrac{s_1}{s_0} CCl_4\)	\(\dfrac{s_1}{s_0} C_6H_5.NH_2\)
0	0	1.58448	1.0000	0
1.48	2.424	1.57176	0.9768	0.0228
5.80	9.228	1.53587	0.9131	0.0875
11.57	17.78	1.49073	0.8316	0.1696
20.24	29.54	1.42727	0.7186	0.2838
31.25	42.89	1.35339	0.5871	0.4159
37.46	49.76	1.31486	0.5188	0.4844
51.37	63.56	1.23535	0.3791	0.6240
56.46	68.16	1.20841	0.3320	0.6710
68.72	78.42	1.14789	0.2265	0.7757
83.29	89.15	1.08315	0.1142	0.8872
94.52	96.61	1.03764	0.0359	0.9645
88.91	92.98	1.05999	0.0741	0.9268
98.96	99.36	1.02074	0.0128	0.9931
100	100	1.01684	0	1.0000

Fig. 9.

Table LIII.

Benzene and chlorobenzene. \(C_6H_6\)—78; \(C_6H_5Cl\)—112.5.

\(t^\circ\!/\!_\circ\ C_6H_5Cl\)	\(\%\,Mol\ C_6H_5Cl\)	\(S^{25^\circ}_{4^\circ}\)	\(\dfrac{s_1}{s_0}\ C_6H_6\)	\(\dfrac{s_1}{s_0}\ C_6H_5Cl\)
0	0	0.87376	1.0000	0
2.33	1.627	0.87794	0.9813	0.0186
4.90	3.451	0.88257	0.9605	0.0393
7.98	5.673	0.88826	0.9354	0.0644
24.12	18.06	0.91937	0.7984	0.2015
29.67	23.23	0.92831	0.7471	0.2501
36.83	28.79	0.94527	0.6833	0.3169
47.36	38.41	0.96811	0.5832	0.4164
60.48	51.48	0.99800	0.4513	0.5482
70.86	62.78	1.02311	0.3412	0.6584
80.00	73.50	1.04626	0.2396	0.7602
89.01	84.86	1.07019	0.1346	0.8652
95.22	93.03	1.08729	0.0594	0.9399
98.66	98.06	1.09703	0.0167	0.9827
100	100	1.10100	0	1.0000

Table LIV.

Benzene and bromobenzene. \(C_6H_6\)—78; \(C_6H_5Br\)—157.

\(x^0_0\) \(C_6H_5Br\)	% Mol \(C_6H_5Br\)	\(S^{25^\circ}_{4^\circ}\)	\(\dfrac{s_1}{s_0} C_6H_6\)	\(\dfrac{s_1}{s_0} C_6H_5Br\)
0	0	0,87378	1,0000	0
1,53	0,765	0,87930	0,9911	0,0089
4,29	2,179	0,88957	0,9743	0,0257
12,98	6,902	0,92322	0,9194	0,0806
18,32	10,03	0,94519	0,8835	0,1165
30,37	17,81	0,99890	0,7960	0,2040
41,09	25,74	1,05191	0,7091	0,2907
54,56	37,37	1,12034	0,5826	0,4111
63,70	46,56	1,18510	0,4923	0,5077
79,44	65,74	1,29936	0,3057	0,6941
88,95	79,98	1,38047	0,1742	0,8258
95,22	90,80	1,43865	0,0786	0,9213
99,01	98,04	1,47701	0,0168	0,9831
100	100	1,48682	0	1,0000

Fig. 10.

Table LV.

Benzene and acetic acid. \(C_6H_6—78;\ CH_3.CO.OH—60.\)

% Acid	% Mol \(CH_3.CO.OH=60\)	\(S^{25^\circ}_{4^\circ}\)	\(\dfrac{s_1}{s_0}\) benzene	\(\dfrac{s_1}{s_0}\) acid
0	0	0.87388	1.0000	0
2.04	2.632	0.87577	0.9815	0.0171
6.62	8.139	0.88101	0.9412	0.0558
10.62	15.72	0.88553	0.9057	0.0901
19.57	24.03	0.89634	0.8249	0.1680
30.76	36.61	0.91110	0.7218	0.2685
39.15	45.54	0.92317	0.6428	0.3462
56.31	62.62	0.95071	0.4753	0.5127
56.75	63.04	0.95144	0.4708	0.5172
80.06	83.93	0.99627	0.2274	0.7640
87.64	90.20	1.01320	0.1433	0.8506
95.95	96.85	1.03325	0.0479	0.9495
98.94	99.20	1.04091	0.0126	0.9865
100	100	1.04374	0	1.0000

Fig. 11.

Graph annotations: \(\dfrac{s_1}{s_0}\) benzene; \(\dfrac{s_1}{s_0}\) acid; benzene and acetic acid; % mol \(C_6H_6\) \((M=60)\).

From the data and drawings presented it follows that, of the 8 pairs of liquids investigated, the equality

\[ \frac{s_0-s_1}{s_0}=\frac{n}{N+n} \]

is fully¹ satisfied only by mixtures of ethylene bromide and benzene (Table L, Fig. 8). For this pair of liquids the curve of the partial densities of one and the other component of the mixtures coincides with the diagonal over the entire extent of the curve, passing at its limiting ends into the densities of the pure liquids.

Thus, mixtures of ethylene bromide and benzene at all possible concentrations behave as ideal solutions and, consequently, also as mixtures of ideal gases. Their molecular volumes in the liquid state are equal; consequently, their specific weights are related as their molecular weights. The osmotic pressure of each component of the mixture is equal to the pressure of an ideal gas with the same molecular weight and at the same temperature and concentration. Finally, for them the equality

\[ \frac{s_1}{s_0}=\frac{p_1}{p_0}. \]

is satisfied.

Of the other pairs of liquids, the mixtures of carbon tetrachloride and aniline satisfy the equality

\[ \frac{s_0-s_1}{s_0}=\frac{n}{N+n} \]

very closely; for this pair of liquids the curve of their partial densities is very close to the diagonal.

For all the other pairs of liquids the curves depart more or less from the diagonal, and most of all for mixtures of benzene and acetic acid. The difference between the curves of the partial densities of mixtures of benzene with strongly associated acetic acid and the curves of the other pairs of liquids (these latter belong to the number of comparatively little-associated ones) is sharply conspicuous.

Thus, comparison of the results of the investigation, by specific weight, of the relations of pairs of liquids that mix with one another in all proportions, obtained both in this chapter and earlier, may be formulated as follows:

Liquids whose molecular volumes in the liquid state are equal, when mixed with one another in all proportions, form mixtures that behave, at all possible mixing ratios, as ideal gases; for these mixtures the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) is satisfied; the criterion by which such pairs of liquids are recognized is the equality of their molecular volumes.

Calculation of the molecular weight of dissolved substances from the density of a solution.

Raoult’s law, as is known, makes it possible to calculate the molecular weight of a dissolved substance from the lowering of the vapor pressure of the volatile solvent when that substance is dissolved in it. We shall take the formula for calculating the molecular weight from the lowering of the vapor pressure of the solvent

in the form in which it is given by Nernst (Theoretische Chemie. 4te Auflage. 1903). Namely,

\[ M = M_0 \frac{c\,p_1}{100\,(p_0-p_1)}, \tag{61} \]

where the symbols denote:

\(M\)—the molecular weight of the dissolved substance,

\(M_0\)—the molecular weight of the solvent,

\(c\)—the number of grams of dissolved substance in 100 g of solvent,

\(p_0\)—the vapor pressure of the solvent,

\(p_1\)—the vapor pressure of the solution.

In deriving this formula Nernst makes the assumption that Raoult’s law is expressed as follows:

\[ \frac{p_0-p_1}{p_1} = \frac{n}{N}, \]

where

\(n\)—is the number of molecules of the dissolved substance,

\(N\)—the number of molecules of the solvent forming the solution.

For those cases in which the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) holds, formula (61) takes the form:

\[ M = M_0 \frac{c s_1}{100\,(s_0-s_1)} \tag{62} \]

Thus, for those cases in which the equality \(\frac{s_1}{s_0}=\frac{p_1}{p_0}\) holds, the molecular weight of the dissolved substance can be calculated from the decrease in the partial density of the solvent in the solution.

The theoretical justification of the method for calculating molecular weight from the decrease in the partial density of the solvent in the solution has already been given above. Here we shall present some results obtained by applying formula (62).

In Table LVI, the molecular weights of substances dissolved in ether are calculated according to formula (62). Alongside them are calculated the molecular weights of the same substances, for solutions of the same concentrations, according to formula (61). In Table LVI, \(S^{t^0}\) denotes the specific gravity of the solution, \(\frac{s_1}{s_0}\) the specific partial density of the solvent in the solution, and \(\frac{p_1}{p_0}\) the specific vapor pressure of the solution.

The concentration of the solution is expressed either by the content of grams of salt in 100 parts by weight of the solution (\(t^\circ/\%\)), or by the ratio of the mass of the dissolved substance to the mass of the solvent, taken as 100 (\(c\)).

Table LVI.

Comparison of the values of the molecular weight, calculated from the decrease in partial density and from the lowering of the vapor pressure of the solvent.

Solutions in ether; \((C_2H_5)_2O\)—74.

Concentration \(c\)	\(S \dfrac{12,9^\circ}{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	\(M\) from the decrease in partial density	\(M\) from the lowering of vapor pressure
Naphthalene \(C_{10}H_8\); \(M=128\) ¹).	Naphthalene \(C_{10}H_8\); \(M=128\) ¹).	Naphthalene \(C_{10}H_8\); \(M=128\) ¹).	Naphthalene \(C_{10}H_8\); \(M=128\) ¹).	Naphthalene \(C_{10}H_8\); \(M=128\) ¹).	Naphthalene \(C_{10}H_8\); \(M=128\) ¹).
0	0,7206	1,0000	1,000	—	—
1	0,7232	0,9943	0,993	129	105
5	0,7330	0,9688	0,970	115	120
10	0,7443	0,9390	0,945	114	127
20	0,7663	0,8862	0,901	115	135
24	0,7746	0,8669	0,885	116	137
Azobenzene \(C_{12}H_{10}N_2\); \(M=182\) ¹).	Azobenzene \(C_{12}H_{10}N_2\); \(M=182\) ¹).	Azobenzene \(C_{12}H_{10}N_2\); \(M=182\) ¹).	Azobenzene \(C_{12}H_{10}N_2\); \(M=182\) ¹).	Azobenzene \(C_{12}H_{10}N_2\); \(M=182\) ¹).	Azobenzene \(C_{12}H_{10}N_2\); \(M=182\) ¹).
0	0,7206	1,0000	1,000	—	—
1	0,7234	0,9940	0,995	123	147
5	0,7345	0,9707	0,980	123	181
10	0,7473	0,9428	0,962	122	187
20	0,7704	0,8909	0,929	121	194
Benzophenone \(C_{13}H_{10}O\); \(M=182\) ²).	Benzophenone \(C_{13}H_{10}O\); \(M=182\) ²).	Benzophenone \(C_{13}H_{10}O\); \(M=182\) ²).	Benzophenone \(C_{13}H_{10}O\); \(M=182\) ²).	Benzophenone \(C_{13}H_{10}O\); \(M=182\) ²).	Benzophenone \(C_{13}H_{10}O\); \(M=182\) ²).
0	0,7210	1,0000	1,000	—	—
1	0,7236	0,9937	0 996	117	184
5	0,7351	0,9710	0,979	124	173
13	0,7492	0,9446	0,962	126	187
20	0,7741	0,8947	0,933	126	206
Diphenylamine \(C_{12}H_{11}N\); \(M=169\) ²).	Diphenylamine \(C_{12}H_{11}N\); \(M=169\) ²).	Diphenylamine \(C_{12}H_{11}N\); \(M=169\) ²).	Diphenylamine \(C_{12}H_{11}N\); \(M=169\) ²).	Diphenylamine \(C_{12}H_{11}N\); \(M=169\) ²).	Diphenylamine \(C_{12}H_{11}N\); \(M=169\) ²).
0	0,7210	1,0000	1,000	—	—
1	0,7238	0,9939	0,995	121	147
5	0,7357	0,9718	0,976	128	150
10	0,7494	0,9449	0,955	127	157
16	0,7645	0,9141	0,931	126	180

¹) Noyes and Abbot, Zeitschr. phys. Chem. 23, 56. 1897.
²) Goodwin and Burgers, Zeitschr. phys. Chem. 28, 99.

Concentration \(x\%\)	\(S \dfrac{15^\circ}{4^\circ}\)	\(\dfrac{s_1}{s_0}\)	\(\dfrac{p_1}{p_0}\)	\(M\) from the lowering of the partial density	\(M\) from the lowering of the vapor pressure
Aniline \(C_6H_5.NH_2;\ M = 93\) ¹).	Aniline \(C_6H_5.NH_2;\ M = 93\) ¹).	Aniline \(C_6H_5.NH_2;\ M = 93\) ¹).	Aniline \(C_6H_5.NH_2;\ M = 93\) ¹).	Aniline \(C_6H_5.NH_2;\ M = 93\) ¹).	Aniline \(C_6H_5.NH_2;\ M = 93\) ¹).
0	0,7195	1,0000	1,000	—	—
4,8	0,7334	0,9700	0,960	121	90
9,5	0,7476	0,9403	0,919	122	88
18,1	0,7721	0,8789	0,846	119	90
24,5	0,7309	0,8289	0,803	116	98
55,3	0,8829	0,5485	0,576	111	124
73,4	0,9382	0,347	0,404	108	138
Nitrobenzene \(C_6H_5.NO_2;\ M = 123\) ¹).	Nitrobenzene \(C_6H_5.NO_2;\ M = 123\) ¹).	Nitrobenzene \(C_6H_5.NO_2;\ M = 123\) ¹).	Nitrobenzene \(C_6H_5.NO_2;\ M = 123\) ¹).	Nitrobenzene \(C_6H_5.NO_2;\ M = 123\) ¹).	Nitrobenzene \(C_6H_5.NO_2;\ M = 123\) ¹).
0	0,7195	1,0000	1,000	—	—
1,718	0,7254	0,9908	—	139	—
9,701	0,7536	0,9458	0,943	139	131
17,06	0,7808	0,8999	0,902	137	140
22,33	0,8014	1,8652	0,874	137	148
25,14	0,8099	0,8489	0,859	140	151
49,82	0,9191	0,6410	0,719	131	188
69,13	1,0181	0,4366	0,571	128	221
74,12	1,0455	0,3761	0,517	128	227
90,75	1,1460	0,1473	0,268	125	266
98,89	1,2006	0,0190	—	131	—

¹ Chapters III and IV.

Concentration $n\%$	$S \dfrac{25^\circ}{4^\circ}$	$\dfrac{s_1}{s_0}$	$\dfrac{p_1}{p_0}$	$M$ from the lowering of the partial density	$M$ from the lowering of the vapor tension
Solutions of iodine in ether; $J_2 = 254$; $J_4 = 508$ ¹).	Solutions of iodine in ether; $J_2 = 254$; $J_4 = 508$ ¹).	Solutions of iodine in ether; $J_2 = 254$; $J_4 = 508$ ¹).	Solutions of iodine in ether; $J_2 = 254$; $J_4 = 508$ ¹).	Solutions of iodine in ether; $J_2 = 254$; $J_4 = 508$ ¹).	Solutions of iodine in ether; $J_2 = 254$; $J_4 = 508$ ¹).
0	0,70811	1,0000	1,0000	—	—
0,70	0,71217	0,9986	0,9978	372	237
1,83	0,71988	0,9979	0,9945	656	249
3,10	0,72757	0,9956	0,9905	536	247
3,65	0,73090	0,9945	0,9887	507	245
4,82	0,73848	—	0,9850	—	246
4,91	0,73912	0,9924	0,9847	499	246
6,13	0,74733	0,9906	0,9808	509	247
7,37	0,75504	0,9876	0,9770	469	250
8,03	0,76184	0,9895	0,9748	609 ²)	250 ²)
Solutions of iodine in carbon disulfide. $CS_2 = 76$; $J_2 = 254$ ¹).	Solutions of iodine in carbon disulfide. $CS_2 = 76$; $J_2 = 254$ ¹).	Solutions of iodine in carbon disulfide. $CS_2 = 76$; $J_2 = 254$ ¹).	Solutions of iodine in carbon disulfide. $CS_2 = 76$; $J_2 = 254$ ¹).	Solutions of iodine in carbon disulfide. $CS_2 = 76$; $J_2 = 254$ ¹).	Solutions of iodine in carbon disulfide. $CS_2 = 76$; $J_2 = 254$ ¹).
0	1,25589	1,0000	1,0000	—	—
0,60	1,26112	0,9982	0,9985	254	305
1,13	1,26574	0,9964	0,9974	240	333
2,02	1,27297	0,9930	0,9948	222	300
2,82	1,28096	0,9912	0,9926	248	296
3,34	1,28571	0,9895	0,9912	247	296
4,83	1,30003	0,9852	9,9870	257	293
5,85	1,30934	0,9814	0,9840	249	290
6,12	1,31199	9,9807	0,9832	252	290
6,48	1 31526	0,9794	0,9821	250	289
9,07	1,34088	0,9708	9,9742	252	286
11,85	1,36913	9,9610	0,9652	252	283

¹) Chapters III and IV.

²) It was clarified above that the differences between the quantities $\dfrac{p_1}{p_0}$ and $\dfrac{s_1}{s_0}$ for solutions of iodine in ether are due to the formation in solution of complexes of iodine with ether.

Obviously, the worse the equality \(\dfrac{p_1}{p_0}=\dfrac{s_1}{s_0}\) is satisfied, the more the molecular weights calculated by the one and the other method will differ. The satisfaction of the equality \(\dfrac{p_1}{p_0}=\dfrac{s_1}{s_0}\) will be affected, as was explained above, by a whole series of causes; such are: association of the solvent molecules with one another, association between the molecules of the solvent and of the dissolved substance, the size of the molecules of the dissolved substance, and others.

In discussing the influence of these causes on the magnitude of the calculated molecular weight, one cannot fail to note, among other things, that, in addition to general and accidental causes, a large role is also played by the construction of the formulas themselves (61 and 62), by which the molecular weight is calculated. Indeed, in these formulas a certain quantity, \(M_0 \times \dfrac{c}{100}\) or \(M_0 \times \dfrac{\pi}{100-\pi}\), is multiplied by the term \(\dfrac{p_1}{p_0-p_1}\) or \(\dfrac{s_1}{s_0-s_1}\), i.e., by the reciprocal of the relative lowering of the vapor pressure or of the partial density of the solvent.

If this lowering is small, then a comparatively small difference in the magnitudes of the partial pressure and the partial density is reflected considerably in the value of the molecular weight calculated. For example, for a solution of iodine in chloroform (\(\pi = 1.748\%\)) the relative partial density of the solvent in the solution, \(\dfrac{s_1}{s_0}\), was found to be 0.9931, whereas the relative partial vapor pressure, \(\dfrac{p_1}{p_0}\), was 0.9955. The numbers 0.9931 and 0.9955 are to one another as \(1:1.002\). The molecular weights calculated by formulas (61) and (62), 305 and 468, however, are related as the numbers \(1:1.5\).

The numbers given in Table LVI are too few to allow a final conclusion to be drawn as to the suitability or unsuitability, in practice, of the method of determining the molecular weights of dissolved substances from density. The present work, moreover, did not have as its object the development of this method. The chief aim of the work was to ascertain whether the magnitude of the partial density of the solvent in a solution can be expressed as a single-valued function only of the osmotic pressure of the dissolved substance, or whether other constants must also be taken into account, for example, the size of the molecules of the dissolved substance, etc. The calculation of molecular weights from the density of the solution is closely connected with one or another solution of this first problem and cannot be solved before this first problem has been solved.

Thus, a more detailed investigation of the method of partial densities, as applied to the calculation of the molecular weights of dissolved substances, was postponed until the fundamental question of the form of the relation between the magnitudes of the osmotic pressure of the dissolved substance and the partial density of the solvent had been clarified. Here we shall present only some materials accumulated in the course of work on the question of the “relation between the vapor pressure of a solution and the partial density of the solvent in the solution.”

Calculation from density of the molecular weight of liquids miscible with one another in all proportions.

In deriving formula (61), Raoult’s law was formulated as follows:

\[ \frac{p_0-p_1}{p_1}=\frac{n}{N}. \]

where \(\frac{n}{N}\) is the ratio between the number of molecules of the dissolved substance and the number of molecules of the solvent forming the solution.

But Raoult’s law is often expressed in another form as well. Namely:

\[ \frac{p_0-p_1}{p_0}=\frac{n}{N+n}, \]

where

\[ \frac{n}{N+n} \]

is the ratio between the number of molecules of the dissolved substance and the total number of molecules forming the solution.

For those cases in which the relation \(\frac{p_1}{p_0}=\frac{s_1}{s_0}\) holds, Raoult’s law is evidently transferred also to the partial densities of the solvent, and will then be expressed as follows:

\[ \frac{s_0-s_1}{s_0}=\frac{n}{N+n}. \]

In this equation the quantities \(N\) and \(n\) are to be expressed through the partial densities of the solvent and of the dissolved substance. We obtain:

\[ \frac{s_0-s_1}{s_0}=\frac{s_2M_0}{s_2M_0+s_1M}. \]

Whence

\[ M=M_0\times\frac{s_2}{s_0-s_1} \tag{62 bis} \]

In this last equation \(s_2\) denotes the partial density in the solution of the dissolved substance; \(s_1\), the partial density in the solution of the solvent; \(s_0\), the density of the pure solvent (i.e. when nothing is dissolved in it). \(M_0\) and \(M\), as before, denote the molecular weights of the solvent and of the dissolved substance¹.

We have already once used formula (62 bis) (pp. 77–89) to establish the law of the molecular composition of solutions in the case when, in a series of solutions, some one and the same volume is fixed. Now we shall use this same formula for calculating the molecular weight of dissolved substances from density.

For liquids miscible with one another in all proportions, the calculations of the molecular weights of both components of the mixture, for concentrations varying within the limits \(0\%\)–\(100\%\), are given in Tables XXX–XXXVII. A summary of the molecular-weight values found there is placed in Table LVII A. Table LVII B gives similar calculations for mixtures of benzene and alcohol, ether and alcohol, and benzene and ether.

Table LVII A.

Liquids that mix with one another in all proportions.

Name	Formula	Molecular weight, according to the formula	Molecular weight according to partial density
ether	$(C_2H_5)_2O$	74	65—70	According to the partial density of aniline in mixtures of ether and aniline.
ether	$(C_2H_5)_2O$	74	73—78	According to the partial density of nitrobenzene in mixtures of ether and nitrobenzene.
benzene	$C_6H_6$	78	74—75	According to the partial density of ethylene bromide in mixtures of benzene with ethylene bromide.
benzene	$C_6H_6$	78	70.4—70.6	According to the partial density of chloroform in mixtures of benzene with chloroform.
benzene	$C_6H_6$	78	89—88	According to the partial density of chlorobenzene in mixtures of benzene with chlorobenzene.
benzene	$C_6H_6$	78	92.2—92.3	According to the partial density of bromobenzene in mixtures of benzene with bromobenzene.
benzene	$C_6H_6$	78	50—48	According to the partial density of acetic acid in mixtures of benzene with acetic acid.
aniline	$C_6H_5.NH_2$	93	115—105	According to the partial density of ether in mixtures of ether and aniline.
aniline	$C_6H_5.NH_2$	93	99—98	According to the partial density of carbon tetrachloride in mixtures of aniline and carbon tetrachloride.
nitrobenzene	$C_6H_5.NO_2$	123	140—124	According to the partial density of ether in mixtures of ether and nitrobenzene.
ethylene bromide	$C_2H_4Br_2$	188	164—193	According to the partial density of benzene in mixtures of ethylene bromide and benzene.
chloroform	$CHCl_3$	119	129—132	According to the partial density of benzene in mixtures of benzene and chloroform.
chlorobenzene	$C_6H_5Cl$	112	99.8—100	According to the partial density of benzene in mixtures of benzene and chlorobenzene.
bromobenzene	$C_6H_5Br$	157	133.5—132.8	According to the partial density of benzene in mixtures of bromobenzene with benzene.
acetic acid	$CH_3.CO.OH$	60	87—93	According to the partial density of benzene in its mixtures with acetic acid.
carbon tetrachloride	$CCl_4$	154	145—148	According to the partial density of aniline in mixtures of aniline and carbon tetrachloride.

Table LVII B.

Alcohol and benzene. \(C_2H_5OH—46;\ C_6H_6—78.\)

\(r_0\%\) benzene	\(S^{20^\circ}\)	\(s_1\)	\(s_2\)	\(M\) benzene	\(M\) alcohol	Author from whom the sp. weights were taken
0	0,79350	0,79350	0	--	--	Buchkremer.
20.18	0,8098	0,6464	0,1634	51	70	Zeitschr. phys
40.76	0,82689	0,4899	0,3370	51	70	Chem. 6, 161.
51,53	0,83558	0,4050	0,4306	51	70
61,72	0,84414	0,3231	0,5210	51	70
76.54	0,85744	0,2011	0,6563	51	70
100	0,87953	0	0,87953	51	--

Ether and benzene. \((C_2H_5)_2O—74;\ C_6H_6—78.\)

\(r_0\%\) benzene	\(S^{20^\circ}\)	\(s_1\)	\(s_2\)	\(M\) benzene	\(M\) ether	Author from whom the sp. weights were taken
0	0,72078	0,72078	0	--	64	Buchkremer.
21,06	0,75299	0,59442	0,15857	93	64	Zeitschr. phys.
40.36	0,78227	0,46655	0,31572	92	65	Chem. 6, 161.
58,95	0,81100	0,33288	0,47812	91	65
79,66	0,84440	0,17175	0,67265	91	65
100	0,87953	0	0,87953	90	--

Ether and alcohol; \((C_2H_5)_2O—74;\ C_2H_5OH—46.\)

\(r_0\%\) alcohol	\(S^{20^\circ}\)	\(s_1\)	\(s_2\)	\(M\) alcohol	\(M\) ether	Author from whom the sp. weights were taken
0	0,72078	0,72078	0	--	42	Buchkremer
20,71	0,73893	0,58586	0,15307	84	42	loco cit.
40,01	0,75412	0,45237	0,30175	83	42
61,17	0,76936	0,29881	0,47055	83	43
78,85	0,78107	0,16519	0,61588	82	43
100	0,793495	0	0,793495	81	--

Reviewing the results of calculations from the density of solutions of the molecular weights of liquids miscible with one another in all proportions, presented in Tables LVII A and B, we note the following conclusions.

1) The values of the molecular weights of these liquids, calculated from the density of the solutions by formula (62 bis), change very little with the concentration of the solutions. For example, the molecular weight of ether from the partial density of aniline, in mixtures of ether and aniline, is calculated to lie within the limits 65–70; the molecular weight of benzene from the partial density of ethylene bromide, in mixtures of benzene with ethylene bromide, is calculated as 74–75; finally, the molecular weight of chlorobenzene from the partial density of benzene, in mixtures of benzene with chlorobenzene, is calculated as 132.8–133.5; meanwhile, in all these cases the concentration of the solutions used for calculating the molecular weight varied from 0% to 100%.

2) If both liquids forming the mixture are only slightly associated, then the molecular weights calculated from the density of the solutions may be considered to agree with the molecular weights corresponding to the formulas (if the liquids were completely unassociated, the molecular weights would have had to correspond exactly to the formula). For example, from the density of mixtures of benzene and ethylene bromide, whose concentration varies from 0% to 100%, the molecular weight of benzene is calculated as 74–75 ($C_6H_6$—78), and the molecular weight of ethylene bromide as numbers lying between 176–193 ($C_2H_4Br_2$—188); the molecular weight of ether from the partial density of aniline and nitrobenzene, in mixtures of ether with aniline and nitrobenzene, is calculated as numbers lying between 65–78 [$(C_2H_5)_2O$—74]; the molecular weight of benzene, calculated from the partial densities of ethylene bromide, chlorobenzene, chloroform, and bromobenzene in mixtures of benzene with these bodies, fluctuates within the limits 70–92 ($C_6H_6$—78), etc.

If at least one of the liquids forming the mixture is associated, the molecular weights calculated from the density of the mixtures do not at all correspond to the chemical formulas. For example, the molecular weight of acetic acid, from the partial density of benzene in mixtures of benzene with acetic acid, is calculated as 87–92 ($CH_3 \cdot COOH$—60), while the molecular weight of benzene, from the partial density of acetic acid in its mixtures with benzene, is calculated as 48–50 ($C_6H_6$—78). The molecular weight of alcohol, calculated from the partial densities of benzene and ether, in mixtures of benzene and ether with alcohol, lies between the numbers 70–84 ($C_2H_5OH$—46); at the same time the molecular weight of benzene, from the partial densities of alcohol, in mixtures of benzene with alcohol, is calculated as 51 ($C_6H_6$—78), and the molecular weight of ether, calculated from the partial density of alcohol in its mixtures with ether, lies between the numbers 42–43 [$(C_2H_5)_2O$—74]. In order to obtain in these cases numbers corresponding to the chemical formulas, the corresponding association coefficients must be introduced into formula 62 bis. If such calculations are made for mixtures of acetic acid with benzene, it turns out that in these mixtures the association coefficient of acetic acid is expressed by the number 1.66; the association coefficient of alcohol, by the number 1.5–1.8; i.e., the association coefficient of acetic acid in its mixtures with benzene is expressed by the same number as for vaporous acetic acid (as is known, the molecular weight of acetic acid determined from the density of its vapor is equal to $60 \times 1.66 = 99$), while the association coefficient of alcohol proves to be the same as that given for liquid alcohol by Ramsay (1.80) and Traube (1.67).

The Molecular Weight of Iodine in Solutions of Iodine in Organic Solvents.

As is known, solutions of iodine in different solvents have different colors, varying from violet (solutions in carbon disulfide) to reddish-brown (solutions in ether). Solvents can be chosen such that the colors of the solutions form an entire scale, the colors of which begin with pure violet and, changing continuously, pass through cherry-red and claret-red into red-brown.

In investigating the reason for such different coloration of iodine solutions, the thought of investigators has followed two paths: 1) the different coloration of iodine solutions is due to different molecular states of iodine in different solvents; 2) the different coloration of iodine solutions is due to the formation of complexes of iodine with the solvent.

1) The first assumption was drawn from the observation that iodine vapors have a pure violet color, the same color as iodine solutions, for example, in carbon disulfide; while the reddish-brown color that is characteristic, for example, of iodine solutions in ether is possessed by solid iodine, if it is examined in thin plates. Since iodine in the vaporous state has a molecular weight corresponding to \(J_2\), hence the conclusion is that in solutions colored violet, iodine has the partial composition \(J_2\), while in solutions having a reddish-brown color, the partial composition of iodine is more complex, for example, \(J_4\), or in general \((J)_n\); in solutions having an intermediate coloration between violet and reddish-brown there is a mixture of various complexes of iodine atoms.^1)

Such an assumption apparently found support, on the one hand, in the observation of Wiedemann,^2) who showed that, on cooling with a mixture of ether and solid carbon dioxide, solutions of iodine in carbon disulfide, which have a violet color, pass into the reddish-brown color of solutions of iodine in ether; on the other hand, in the observation that the brown color of iodine solutions in such solvents as alcohol changes to violet upon heating.

There remained the methods of determining the molecular weights of dissolved substances to be applied to the detection of those complexes which iodine atoms form in solutions.

From the depression of the freezing temperature of the solutions, the following molecular weight of iodine was found in the following solvents:

Solvent	Molecular weight of iodine	Color of the solutions	Authors
in xylene	253–260	red	Beckmann und Stock;^3) Hertz
in ethylene bromide	225–257	red	Beckmann und Stock;^3) Hertz
in naphthalene	242–251	red	Beckmann und Stock;^3) Hertz
in acetic acid	249–264	red	Beckmann und Stock;^3) Hertz
in naphthalene	255–276	dark claret-red	Beckmann und Stock;^3) Hertz

Determinations of the molecular weight of iodine in solutions in benzene (Paterno et Nasini)^4) did not give satisfactory results, since it turned out that iodine forms solid solutions with benzene (Beckmann).^5)

1) Schultz Sellak, Pogg. Ann. 140, 334. 1870.
2) Wiedemann, Wied. Ann. 41, 299. 1890.
3) Beckmann und Stock, Zeitschr. phys. Chem. 17, 107. 1895.
4) Paterno et Nasini, Gazz. chim. ital. 18, 179, 1888; Paterno et Peratoner, Gazz. chim. ital. 21, 110, 1891.
5) Beckmann und Stock, Zeitschr. phys. Chem. 17, 107. 1895.

Thus, cryoscopic determinations of the molecular weight of dissolved iodine gave, identically, both in the case of solvents in which iodine dissolves with a red color (xylene, ethylene bromide, naphthalene), and in the case of solvents in which iodine dissolves with a brown color (acetic acid), numbers fluctuating around 254. Hence it follows that in all these solvents the iodine particle consists of two atoms \((J_2 = 254)\).

The cryoscopic method, however, could not provide material for a definitive conclusion, since for many solvents—among them carbon disulfide, in which iodine dissolves with the typical violet color—this method is not applicable.

More extensive and more complete material could be supplied by the ebullioscopic method, although here, too, a difficulty was encountered—namely, the considerable volatility of iodine at the boiling temperature of the solvents. In all cases it was necessary to determine the iodine content in the vapors and to make the corresponding corrections. This not only greatly complicated the measurements themselves, and not only limited the application of the method to solutions in the most volatile solvents, but also introduced a certain distrust of the results obtained, since there was no certainty that the correction had been made with complete accuracy; for Raoult’s law, even in approximate form, may be considered proved only for the case of solutions of nonvolatile bodies in volatile solvents.

In the literature we find a number of determinations of the molecular weight of iodine in its solutions in volatile solvents; in some cases a correction for the volatility of iodine was made, in others it was not. Namely, Beckmann¹), from the lowering of the boiling temperature of solutions of iodine in ether (the color of the solutions was brown), found the molecular weight of iodine to be 235–261. From the lowering of the boiling temperature of solutions of iodine in carbon disulfide (the color of the solutions was violet), he likewise found the molecular weight of iodine to be 263–272. In these determinations, no correction was made for the presence of iodine in the vapors.

In the following work Beckmann, already jointly with Stock²), made a whole series of carefully performed ebullioscopic measurements on solutions of iodine in various solvents. In calculating the molecular weight, a correction for the iodine content in the vapors was made. The results obtained by them are collected in the following table:

Solvents	Molecular weight of iodine from the lowering of the boiling temperature of the solution. Correction for the volatility of iodine not made.	Molecular weight of iodine from the lowering of the boiling temperature of the solution. Correction for the volatility of iodine made.
Carbon tetrachloride	370–382	233–241
Chloroform	325–316	237–238
Benzene	354–335	251–238
Ethyl alcohol	342	241
Methyl alcohol	261	193
Methylal	237	216
Acetone	225	213

¹) Beckmann, Zeitschr. phys. Chem. 5, 76. 1890.
²) Beckmann und Stock, Zeitschr. phys. Chem. 17, 107. 1895.

Similar measurements were also made by Oddo et Sera ¹). They obtained for iodine the following molecular weights, and they made a correction for the volatility of iodine.

Solvents:	Molecular weight of iodine:
carbon tetrachloride	382—394
carbon disulfide	235—252
benzene	273—279
ethyl alcohol	265—327

Loeb ²) measured the vapor pressure of solutions of iodine in carbon disulfide and ether and, from the lowering of the vapor pressure of these solutions, obtained the following numbers for the molecular weight of iodine: for solutions in ether—numbers 466—577, for solutions in carbon disulfide—numbers 264—326 ³).

Mikhailenko and Delyanov ⁴) measured the vapor pressure of solutions of iodine in ether, carbon disulfide, and chloroform. The measurements were carried out carefully at temperatures close to temp. 25°. At this temperature the vapor pressure of dissolved iodine is so small that it could not noticeably affect the observed value of the vapor pressure of the solution; in calculating the molecular weight from the lowering of the vapor pressure of the solutions, a correction for the volatility of iodine, therefore, was likewise not made. The following numbers were obtained: for solutions in carbon disulfide the molecular weight of iodine was found to be 283—305; for solutions in ether the molecular weight of iodine was found to be 237—250; finally, for solutions in chloroform the molecular weight of iodine was found to be 468—465 ⁵).

Nernst ⁶) made measurements of the molecular weight of substances dissolved in ether gel by the method of lowering of solubility; for solutions of iodine in ether by this method he obtained the numbers 222—239—281, i.e. numbers corresponding to the molecule $\mathrm{J}_2$.

Bringing together the results of all these measurements of the molecular weight of iodine in various solvents, it is necessary to conclude that in general they did not confirm the supposition that in solutions colored brown the iodine molecules are composed of four atoms ($\mathrm{J}_4$), while in solutions colored violet the iodine molecules consist of two atoms. And from this it follows that the different coloration of solutions of iodine in various solvents is, in all probability, due not to a difference in the molecular state of iodine in these solutions, but to other causes.

Despite these results, the idea that the different coloration of solutions of iodine is due to a different value of the molecular weight of iodine in these solutions was supported by Gautier and Charpy and by Krüss and Thiele.

Gautier et Charpy ⁷) based their opinion on the observation that the absorption spectrum of solutions of iodine in different solvents changes continuously, forming “une gamme continue de coloration, allant du violet au brun”.

¹) Oddo et Sera, Gazz. chim. ital. 21, 110. 1891.
²) Loeb, Zeitschr. phys. Chem. 2, 606. 1888.
³) The accuracy with which the vapor pressure of the solutions was measured, however, leaves much to be desired.
⁴) Chapter IV.
⁵) The calculations of the molecular weight of iodine from the lowering of the vapor pressure of its solutions in ether and carbon disulfide are given in Table LVI, p. 102.
⁶) Nernst, Zeitschr. phys. Chem. 6, 16.
⁷) Gautier et Charpy, Compt. rend. 110. 1890; 111, 646 1890.

In addition, they made the curious observation that, when a solution of iodine in various solvents is shaken with lead amalgam, solutions colored brown give yellow \(PbJ_2\), while solutions colored violet give a green mass \(Pb_2J_2\). With solutions of an intermediate color, a mixture of iodides of lead is obtained, the color of which changes continuously from yellow to green.

Krüss and Thiele \(^{1}\), and then Thiele alone \(^{2}\), investigated the absorption spectra of solutions of iodine in various solvents. In their opinion this different coloration is due to the formation in solution of complexes \((J_2)_n\), which they call physical molecular aggregates. In their opinion these aggregates cannot be detected by the methods of cryoscopy and ebullioscopy; just as, in general, such complexes cannot be detected by these methods when the molecular weights of their components are close to one another; for example, by the methods of cryoscopy and ebullioscopy it is not possible to detect complexes of picric acid with hydrocarbons.

2) The idea that the coloration of iodine solutions is caused by molecular compounds of iodine with the solvents was supported by Beckmann, Stock, and Vaubel.

Beckmann and Stock \(^{3}\) based themselves on the fact that their cryoscopic and ebullioscopic determinations of the molecular weight of iodine in solutions gave identical numbers, corresponding to the molecule \(J_2\), both for brown solutions and for violet solutions.

Vaubel \(^{4}\) draws attention to the fact that the solvents in which iodine dissolves with a brown color contain in their molecules either oxygen or nitrogen, i.e., elements capable of changing their atomicity to a higher one. In the first case oxonium compounds are obtained; in the second case, compounds containing pentavalent nitrogen. Vaubel substantiates these conclusions of his by data from observation of the spectra of iodine solutions.

Thus, the question of the state of iodine in solutions still remains open. Osmotic methods of determining the molecular weight of dissolved substances have not confirmed the existence of \(J_4\) molecules; but at the same time convincing evidence has not been given that these solutions contain molecular compounds of iodine with the solvent, nor have their composition and properties been determined.

Molecular weight of iodine in solutions from the partial density of the solvent of the solution.

In the course of my work on the relation between the partial density of the solvent in a solution and the osmotic pressure, among other things, I measured also the density of iodine solutions in various organic solvents (Chapter III). In addition, the vapor pressure of solutions of iodine in ether and in carbon disulfide was measured (Chapter IV). We used these data to calculate the molecular weights of iodine by formula (62 bis). These calculations are collected in Tables XXXVIII–XLVI. In addition, by comparing the quantities \(\frac{s_1}{s_0}\) and \(\frac{p_1}{p_0}\) for solutions of iodine in ether, the iodine–solvent complex contained in these solutions was calculated (Table XI). Now, in Table LVIII, we shall collect the results obtained and compare them with the results obtained by other authors and by other methods.

\(^{1}\) Krüss und Thiele, Zeitschr. für anorg. chem. 7, 52. 1894.
\(^{2}\) Thiele, Zeitschr. phys. Chem. 16, 177. 1895.
\(^{3}\) Beckmann und Stock, Zeitschr. phys. Chem. 17, 107. 1895.
\(^{4}\) Vaubel, Journ. für. pract. Chem. 63, 381.

Table LVIII.

Molecular weights of iodine in solutions in organic solvents.

Solvents	\(M\) from depression of the freezing point	\(M\) from elevation of the boiling point; nonisopr.	\(M\) from elevation of the boiling point; isopr.	\(M\) from depression of vapor pressure	\(M\) from depression of the partial density of the solvent
carbon disulfide	—	—	235–252	283–305	243–252
chloroform	—	325–316	237–231	468–465	343–315
carbon tetrachloride	—	370–382	233–241 (Beckm.) 382–394 (Oddo)	—	430–229
ethylene bromide	225–257 (Beckm.) 330–345 (Gautier)	—	—	—	346–349
benzene	—	354–335	251–238 (Beckm.) 273–279 (Oddo)	—	358–364
nitrobenzene	—	—	—	—	343–364
aniline	—	—	—	—	640–590
ether	—	235–261	—	237–250	499–567
acetic acid	249–264 (Beckm.) 330–345 (Gautier.)	—	—	—	350–343

Thus, in solutions in carbon disulfide (the color of the solutions is the typical violet) all the methods employed for the molecular weight of iodine agree in giving numbers corresponding to the molecule \(J_2\).

For the molecular weight of iodine dissolved in ether (the solutions are colored the typical brown color), the tonometric method gives numbers corresponding to the molecule \(J_2\); the densimetric method, however, gives numbers corresponding to the molecule \(J_4\). Comparison of the quantities of the relative partial density of the solvent in the liquid and vapor phases makes it possible to calculate that in these solutions the molecule of the solvent is bound in a complex with \(J_4\) (Table XI).

For solutions of iodine in aniline the densimetric method likewise gives values corresponding to \(J_4\). But here direct experiment has confirmed (Chapter III) that aniline interacts with iodine (there is no doubt that first a complex is formed, which then decomposes with formation of \(HJ\)).

For solutions of iodine in carbon tetrachloride the densimetric method gave numbers continuously decreasing from 430 to 229 as the concentration increases from 0.22% to 2.72%. There is no doubt that this phenomenon, too, is connected with the formation of complexes between iodine and \(CCl_4\).

For solutions in the other solvents listed in the table (the color of the solution is red, of various shades), for the molecular weight of iodine the densimetric method gave numbers corresponding to the molecule \(J_3\) or to a mixture of molecules \(J_2\) and \(J_4\).

Chapter III.

Experiments for determining the specific gravity of solutions.

Determinations of the specific gravity of solutions were undertaken with the aim of obtaining new experimental material for studying the relation between the density of solutions and the elasticity of their vapor¹.

Of the existing methods for determining the densities of liquids, the pycnometric method was chosen, as a very precise method and the most accessible under the conditions in which I had to work. As a model I chose Mendeleev’s work “Discourse on the Combination of Alcohol with Water,” 1865. Since the partial densities of the solvent change, in general, very little with changes in the concentration of the solution, and since it was desirable to investigate solutions that were also dilute and, moreover, in solvents that are often volatile, special efforts were applied to as accurate a determination of the specific gravities as possible.

The degree of accuracy of an individual pycnometric determination depends:

1) on the greater or lesser convenience of the chosen form of pycnometer;

2) on the perfection of filling the pycnometer (no bubbles adhering to the glass must remain) and on the degree of accuracy with which the volume is established;

3) on the degree of accuracy with which the temperature is measured;

4) on the degree of accuracy of the weighing;

5) on the degree of accuracy in determining the constants of the pycnometer;

6) on the degree of accuracy of the formula by which the calculation of the specific gravity is performed (whether corrections are introduced, or neglected);

7) finally, since the densities or specific gravities found refer to a definite substance or solution, the fidelity of the numbers also depends on how well the substance has been purified and how accurately the composition of the solution has been given.

Description of the pycnometer. All the most commonly used forms of pycnometers were tried by me, and the most suitable proved to be the pycnometer proposed by D. I. Mendeleev.

Mendeleev’s pycnometer, in the form in which it is described in the above-cited work, consists of an egg-shaped glass vessel with a thermometer sealed inside and with two lateral capillary tubes—

bottles serving for filling the pycnometer. These capillary tubes are graduated and are closed with ground glass stoppers. When the pycnometer is filled with liquid and the temperature has become established, the level of the liquid in both capillary tubes is measured and, since divisions have been marked on the tubes and the capacity of these divisions has been determined beforehand, all the data are available to determine precisely the volume of liquid in the pycnometer.

Mendeleev’s pycnometer has the following conveniences: 1) it is easy to fill and to wash; 2) the liquid in it does not evaporate, since it is closed with stoppers; 3) in it there is reserve space in case the solution expands.

The last two circumstances are especially important when working with volatile organic solvents. Namely, during the operation of wiping the pycnometer dry, the liquid filling the pycnometer, being heated by the warmth of the hands, expands rapidly and, if in doing so it manages to moisten the stoppers closing the pycnometer (and this often happens), there is no possibility of weighing the filled pycnometer, since strong evaporation of the liquid occurs around the stopper. For this reason pycnometers of the ordinary form, for example those of Sprengel and Ostwald, proved entirely unsuitable for determining the specific gravity of such volatile liquids as ether, benzene, and others.

In working with Mendeleev’s pycnometer, however, it turned out that the operations of graduating both capillary tubes and measuring the liquid levels in them are rather laborious; moreover, the walls of the tubes above the liquid level become coated with solution, the volume and concentration of which are unknown and cannot be determined; and it was not possible to wipe the tubes dry.

Therefore I preferred always to set one and the same level in one tube, namely the left one; the right-hand tube I filled entirely with solution and closed it quickly with a stopper so that no air bubbles remained. In order to avoid evaporation around the stopper, I further protected the stopper with a well-ground glass cap, as is shown in Fig. (12). Experiments showed that in this case, provided only that the grinding of the cap is not wetted in any way, evaporation, even in the case of such volatile liquids as ether and benzene, does not occur. Of course, it is necessary that the stopper and the cap be well ground.

One might fear that when the stopper is inserted it does not always enter one and the same place, so that the volume of the pycnometer, for different positions of the stopper, is not one and the same. Experiments, however, showed that there is no basis for fearing this. Indeed, the stopper is very small (diameter about \(1 \tfrac{1}{2}\) mm), and if it is well ground, then small differences in its position do not noticeably affect the volume of the pycnometer.

Although the second tube was graduated, nevertheless the level in this tube, for the reasons stated above, was always brought to a definite mark. The mark was located close to the widening of the capillary tube, and therefore it was always possible, with the aid of a twist of filter paper, to set the level precisely and to dry the walls above the level.

The pycnometers, made to special order by the firm “Dr. H. Geisler nachf. Franz Müller” in Bonn, were made of Jena glass, slightly hygroscopic. The glass stoppers and the cap were also...

carefully ground, as much as could be desired. The scales of the thermometers sealed into the pycnometers were divided into \(1/10\) of a degree. The work of determining the specific gravity with the pycnometer was carried out in the following manner.

Filling the pycnometer. At first the pycnometer was thoroughly washed with alcohol and ether and dried.

Drying was carried out by blowing through the pycnometer, with the aid of a bellows or by mouth, a stream of air well dried with calcium chloride.

Then the pycnometer was filled with the solution.

Filling was carried out either by sucking the solution into the pycnometer or, in the case of volatile liquids, by forcing the solution into the pycnometer. The latter manipulation was carried out as follows: the vessel containing the solution was closed with a stopper with two openings; through one opening passed a tube, connected by a ground joint with one of the side tubes (the right one) of the pycnometer (it was immersed in the solution and reached the bottom of the vessel); through the other opening passed a tube bent at a right angle, ending above the solution and connected with a bellows or with the mouth. With a slight excess of pressure in the vessel with the solution, the solution, without loss by evaporation, was slowly and uniformly transferred into the pycnometer.

Fig. 12.

With the aid of drying tubes filled with strong sulfuric acid and solid caustic potash, the solution under investigation was well protected from the sucking or blowing devices.

The operation of filling the pycnometer, despite all its apparent simplicity, nevertheless requires a certain skill.

The filled pycnometer was closed with stoppers and placed in the thermostat. When the temperature became established (which was judged by the thermometer of the pycnometer), the left tube was opened and the level of the liquid in it was brought up to the mark once and for all designated. This was done with the aid of a wick made of cigarette or blotting paper; with the same wick the walls of the tube above the mark were carefully dried of the solution,

with which they had previously been wetted. As soon as the level of the liquid in the side tube had been brought to the mark and its walls well dried, the tube was again closed with a stopper (this time as tightly as possible), the pycnometer was taken out of the thermostat, rinsed on the outside with alcohol and ether, carefully wiped first with blotting paper and then with chamois, and, after cooling to the temperature of the balance, weighed.

When wiping the pycnometer, special attention was paid to ensuring that the liquid filling the pycnometer, owing to the warmth of the hands, did not expand so much as to wet the stopper closing the left capillary tube of the pycnometer. Rinsing the pycnometer with ether was intended not only to wash the outside of the pycnometer, but also to lower its temperature sufficiently that subsequent warming of the pycnometer by the hands could not be dangerous.

The operation of washing the pycnometer on the outside and drying it is very important, since the success of the next weighing depends directly on the success of this operation.

Measurement of the temperature of the solution. The temperature of the solution was read from the pycnometer thermometer. The pycnometer thermometer was graduated in tenths of a degree; but with the aid of a magnifying glass it was easy to read hundredths of a degree.

The pycnometer thermometers were compared with a normal thermometer.

For this purpose the pycnometers were placed in a bath of a definite temperature and quickly filled with the bath water. After some time the temperature of the pycnometer and the temperature of the bath were read on the normal pycnometer. With this method of comparison, the separate observations agreed well with one another. The temperature measurement was made with an accuracy of \(\pm 0.05^\circ\).

The thermostat which I used was an Ostwald-type thermostat with a very sensitive temperature regulator (a U-shaped glass tube filled with kerosene), with a stirrer in the form of a mill driven by a gas burner. The thermostat was well wrapped in felt and, in addition, enclosed in an iron sleeve. The temperature of the room in which the determinations were made was adjusted so that it did not differ greatly from the temperature at which the determinations were being made.

Thus, all determinations of the specific gravity of solutions at \(15^\circ\) were made in a room whose temperature was kept within \(13^\circ\)—\(14^\circ\). Determinations of the density of solutions at \(25^\circ\) were made in a room whose temperature in winter varied within \(18^\circ\)—\(20^\circ\), and in summer \(22^\circ\)—\(24^\circ\).

Under these conditions it proved possible to maintain the temperature in the thermostat constant within \(\pm 0.02^\circ\)—\(0.05^\circ\).

The pycnometer was immersed in the water of the thermostat as deeply as possible, so that the entire main egg-shaped part of the pycnometer was in the water. The capillary tubes, however, protruded outward by approximately 10 mm. Since both these tubes, one completely and the other partly, were filled with solution that had the temperature not of the bath but of the air surrounding the bath, an error was introduced into the determination of the specific gravity. It proved negligible and could be disregarded.

Weighing. All weighings were carried out on short-arm Sartorius balances (the best model), with a maximum load of 200 grams. The balances were adjusted so that they showed, on average, a sensitivity of 2.5, i.e., with an overload of \(1\ mg.\), the deviation from the position of equilibrium was 2.5 scale divisions.

The ratio of the arms of the beam, calculated from extensive material of double weighings (with verification of the weights and constant dynamometers) according to the formula:

\[ \frac{R}{L}=1+\frac{l-r}{2p}, \tag{63} \]

where \(R\) is the length of the right arm of the beam, \(L\)—the length of the left, \(l\)—the additional weight for the load \(p\) on the left pan of the balance, \(r\)—the additional weight for the same load on the right pan of the balance¹, proved to be equal to:

\[ \frac{R}{L}=1-0.0000002. \]

In calculating the specific weights, no correction was made for the length of the arms of the beam.

The temperature of the air surrounding the balance was measured with a thermometer placed in the balance case. The degree of humidity was checked by a hygrometer, likewise placed in the balance case.

All weighings were carried out by the method of oscillations; ordinarily, three oscillations to the right and two to the left were observed; the sensitivity of the balance was determined for each individual weighing; the zero point was checked for each series of weighings.

In order to avoid error due to inaccuracy of the weights, a set of brass platinum-plated weights was specially ordered from the well-known firm Franz Rueprecht. Marks were made on weights of the same denomination (1 gram and 1 centigram), so that the individual weights could be distinguished from one another.

The weights were carefully compared with one another by double weighing, the sum of the weights being taken as equal to 100 grams.

So that one may judge the degree of accuracy of the weights sold, I give here a table of the corrections found.

\[ \begin{aligned} 100\ \mathrm{gr.} &= 100-0.00055\ \mathrm{gr.}\\ 50\ \text{”} &= 50-0.00018\ \text{”}\\ 20\ \text{”} &= 20-0.00022\ \text{”}\\ 10\ \text{”} &= 10-0.00003\ \text{”}\\ 10^*\ \text{”} &= 10+0.00001\ \text{”}\\ 5\ \text{”} &= 5-0.00042\ \text{”} \end{aligned} \]

\[ \begin{aligned} 2\ \mathrm{gr.} &= 2 - 0.00005\ \mathrm{gr.}\\ 1\ \text{″} &= 1 + 0.00004\ \text{″}\\ 1^{*} &= 1 - 0.00005\ \text{″}\\ 1^{**} &= 1 - 0.00001\ \text{″} \end{aligned} \]

For the platinum weights (fractions of a gram), the correction lay within the limits of sensitivity of the balances.

All weighings were corrected for loss of weight in air according to the following formula:

\[ M_1 = P_1 - \lambda\left(\frac{P_1}{8.4} - V_1\right) \tag{64} \]

In this formula the symbols denote:

\(M_1\)—the true weight of the body being weighed (weight in vacuum);
\(P_1\)—the weight of the body found by direct weighing in air;
\(V_1\)—the volume of the body being weighed;
\(\lambda\)—the density of air (relative to water at \(4^\circ\)) in the balance case during the weighing operation;
\(8.4\)—the density of the brass weights.

The loss of weight of the platinum weights in air (fractions of a gram) was not taken into account.

Thus, in order to make the correction for loss of weight in air, it is necessary to know \(V_1\)—the volume of the body being weighed, and \(\lambda\)—the density of the air during weighing.

\(V_1\)—the volume of the pycnometer—was determined for each pycnometer by a separate experiment. The methods of determination and the corresponding calculations will be given below.

\(\lambda\) was calculated by the formula:

\[ \lambda = \frac{0.001295}{1 + 0.004\,t^0}\times \frac{b}{760} \tag{65} \]

where: \(0.001295\)—the weight of one cubic cm of air under normal conditions of pressure and temperature;
\(b\)—the barometric pressure at the moment of weighing;
\(t^0\)—the temperature at the moment of weighing\(^1\).

This formula is derived on the assumption that the air is half-saturated with water vapor. In fact this is not so and, of course, with such a method of calculating the value \(\lambda\), an error is introduced. This error, however, proved possible to neglect. Namely, there were no desiccants in the balance case; therefore the humidity of the air in the balance case fluctuated within close limits around the value of 50%. Several control experiments calculating \(\lambda\), on the basis of data from an accurate measurement of the humidity in the balance case,

\(^1\) Kohlrausch. Guide to Practical Physical Measurements.

showed, indeed, that on the whole the error is not large and does not noticeably affect the final result.

Since it was difficult each time to calculate the quantity \(\lambda\), I have compiled a table once and for all. In view of the fact that in none of the reference books known to me did I find a table giving the values of \(\lambda\) (calculated by formula 65) for different values of temperature and pressure, I present my table, in the hope that it will save someone time.

Table LIX.

Values of \(\lambda\) (densities of air, half-saturated with water vapor, relative to water at \(4^\circ\)) for different values of \(t^\circ\) and pressure \(b\), calculated by the formula:

\[ \lambda=\frac{0.001295}{1+0.004t^\circ}\times\frac{b}{760}. \]

\(b\), mm.	\(\lambda\) at \(14^\circ\)	\(\lambda\) at \(15^\circ\)	\(\lambda\) at \(16^\circ\)	\(\lambda\) at \(17^\circ\)	\(\lambda\) at \(18^\circ\)	\(\lambda\) at \(19^\circ\)	\(\lambda\) at \(20^\circ\)	\(\lambda\) at \(21^\circ\)	\(\lambda\) at \(22^\circ\)	\(\lambda\) at \(23^\circ\)	\(\lambda\) at \(24^\circ\)	\(\lambda\) at \(25^\circ\)	\(b\), mm.
732	0.001181	1176	1172	1168	1163	1159	1155	1152	1146	1142	1138	1134	732
734	1185	1180	1175	1171	1166	1162	1158	1154	1149	1145	1141	1137	734
736	1188	1183	1179	1174	1170	1165	1161	1157	1153	1148	1144	1140	736
738	1191	1186	1182	1178	1173	1168	1164	1160	1156	1151	1147	1143	738
740	1194	1190	1185	1180	1176	1172	1167	1163	1159	1155	1151	1146	740
742	1198	1193	1188	1183	1179	1175	1171	1166	1162	1158	1154	1149	742
744	1201	1196	1191	1187	1182	1178	1174	1170	1165	1161	1157	1152	744
746	1204	1199	1195	1190	1186	1181	1177	1173	1168	1164	1160	1155	746
748	1207	1203	1198	1193	1189	1185	1180	1176	1172	1167	1163	1159	748
750	1210	1206	1201	1197	1192	1188	1183	1179	1175	1170	1166	1162	750
752	1214	1209	1204	1200	1195	1191	1187	1182	1178	1173	1169	1165	752
754	1217	1212	1207	1203	1198	1194	1190	1185	1181	1176	1172	1168	754
756	1220	1215	1211	1206	1202	1197	1193	1188	1184	1180	1175	1171	756
758	1223	1218	1214	1209	1205	1201	1196	1192	1187	1183	1178	1174	758
760	1226	1222	1217	1213	1208	1204	1199	1195	1190	1186	1181	1177	760

The number obtained in weighing depends not only on the equilibrium and sensitivity of the balance, on the correctness of the counterweights and the accuracy of the corrections, but also on that accidental state in which the object being weighed happens to be.

By an accidental state I mean here the following phenomenon.

It is known that when glass vessels are weighed, different results are obtained depending on whether the weighing was carried out immediately after wiping the vessel with a dry cloth, or after the object had been left standing for some time. With a large surface of the objects being weighed, these differences often reach very appreciable magnitudes.

This phenomenon is usually explained by the fact that a layer of atmospheric gases and water vapor condenses on the surface of the objects being weighed, a layer which is removed only with great difficulty in vacuo upon heating. The magnitude of this layer depends on the properties of the glass, on the pressure and humidity of the atmosphere, and, finally, on how soon the object is weighed after being wiped.

Since it is impossible to carry out all weighings under identical conditions, it would be necessary either to eliminate this condensation, or to introduce a correction, or, at the very least, to determine the magnitude of the error.

Ostwald proposes to eliminate the influence of condensation by carrying out all weighings at the maximum of the condensed layer. For this purpose he recommends wiping the glass vessel with a damp cloth before weighing.

An attempt to apply this proposal in practice, however, did not give me satisfactory results. And since, when wiping with a damp cloth, there always remained the doubt whether too much moisture had not been imparted to the vessel, I abandoned this method and settled on the following method of preparing the pycnometers for weighing.

My pycnometers, with an average capacity of about 25 cubic cm, were made of so-called Jena, non-hygroscopic glass. Before each weighing the pycnometer was thoroughly washed on the outside with alcohol and ether, and was wiped first with blotting paper and then finally with soft chamois or suede. In the balance case the pycnometer remained only as long as was necessary for it to assume the temperature of the surrounding air; it was then weighed.

It remained to determine experimentally how concordant the results obtained are when weighing pycnometers prepared in this way.

In the following table are given the figures for 12 weighings of empty working pycnometer No. 4, carried out over the course of 3 years, under different conditions of pressure and temperature. The total capacity of this pycnometer was 34.176 cubic cm; the internal capacity was 20.3079 cubic cm. Since the pycnometer was weighed empty, condensation could occur on the outer and inner walls of the pycnometer. All weighings were carried out on the same balance, with the same counterweights. During the weighing the temperature varied within the limits of 15°–24°, and the pressure within the limits of 736–753 mm.

The true weight (weight in vacuum) is calculated by formula (64).

Table LX.

	Temp.	Bar.	Weight in air, g	Weight in vacuum, g
1) December 18, 1899	15°	749 mm	24.89450	24.90723
2) 30 ” ”	15°	753 ”	24.89418	24.90699
3) January 10, 1900	18°	751 ”	24.89473	24.90736
4) May 20, 1900	22°	747 ”	24.89497	24.90737
5) 28 ” ”	24°	745 ”	24.89474	24.90701
6) 29 ” ”	22°	744 ”	24.89460	24.90695
7) June 14, 1900	19°	734 ”	24.89454	24.90684
8) February 3, 1902	14°	759 ”	24.89400	24.90670
9) March 24, 1902	17°	745 ”	24.89452	24.90725
10) November 3, 1902	15°	751 ”	24.89422	24.90715
11) March 11, 1903	18°	749 ”	24.89409	24.90683
mean				24.90706

From the data given, by the method of least squares, we find that the probable error of a single weighing is equal to ±0.00015. The probable error of the mean result is equal to ±0.00046.

I consider this accuracy of the weighings sufficient for investigations of this kind.

Calculation of the specific weight from experimental data. Density is the ratio

\[ \frac{M}{V}, \]

where \(M\) is the mass of the body under investigation, \(V\)—its volume.

The quantity \(M\), i.e. the mass of the solution in the volume of the pycnometer, is found from the equality

\[ M=M_2-M_1, \]

where \(M_1\)—the true weight of the unfilled pycnometer, \(M_2\)—the true weight of the pycnometer filled up to the mark.

The quantity \(V\) (the volume of the body under investigation) is equal to the capacity of the pycnometer up to the mark at the temperature of determination of the specific gravity.

The quantity \(M_1\)—the true weight (weight in vacuo) of the unfilled pycnometer—was calculated from the data of weighing the unfilled pycnometer in air by the formula:

\[ M_1=P_1+\left(V_0-V_1-V_2-\frac{P}{8.4}\right)\lambda \tag{66} \]

The quantity \(M_2\)—the true weight (weight in vacuo) of the pycnometer filled up to the mark—was calculated from the data of weighing in air the pycnometer filled up to the mark by the formula:

\[ M_2=P_2+\left(V_0-V_2-\frac{P_2}{8.4}\right)\lambda \tag{67} \]

Whence the density:

\[ S=\frac{P_2+\left(V_0-V_2-\frac{P_2}{8.4}\right)\lambda-M_1}{V_1} \tag{68} \]

In these formulas the symbols denote:

\(P_1\)—the weight of the unfilled pycnometer in air;
\(P_2\)—the weight of the pycnometer filled up to the mark in air;
\(V_0\)—the total air displacement of the pycnometer;
\(V_1\)—the capacity of the pycnometer up to the mark;
\(V_2\)—the capacity of the pycnometer tube from the mark to the stopper;
\(\lambda\)—the density of air during the weighing operation;
8.4—the specific gravity of the brass weights.

The quantities \(M_1\), \(V_0\), \(V_1\), and \(V_2\) for each given pycnometer are constant quantities. For each working pycnometer they were always determined from a series (never fewer than three) of observations.

Determination of the constants of the pycnometers. In my work on measuring the specific gravity of solutions I used 4 pycnometers of the described type. One of them had a capacity of about 10 cu. cm.; the capacity of the other three varied within the limits of 20–30 cu. cm.

My first measurements of specific gravity were made with the aid of the 10 cu. cm. pycnometer. In view of the comparatively small dimensions of the pycnometer, I considered it possible, in calculating the specific gravity from the data obtained in work with this pycnometer, to use the simplified formula (Kohlrausch), namely:

\[ S^{t_0}_{40}=\frac{P'_2}{P'_0}(D^t_0-0.0012)+0.0012 \tag{69} \]

where

\(P'_2\)—the weight of the solution in the volume of the pycnometer, found from the difference of two weighings in air;

$P'_0$ is the weight of water in the volume of the pycnometer at the temperature of determination of the specific gravity, found from the difference of two weighings in air;

$D_t$ is the density of water at the temperature of determination of the specific gravity;

0.0012 is the mean density (relative to water) of air.

All subsequent determinations of specific gravity (by far the greater part) were carried out with three other pycnometers. In calculating the specific gravity from the data obtained with these pycnometers, I used the exact formula (68) given above, and for all these pycnometers the constants could be determined with sufficient care: the weight of the empty pycnometer in vacuo ($M$), the air displacement of the pycnometer ($V_0$), the capacity of the pycnometer up to the mark ($V_1$), and the capacity from the mark to the stopper ($V_2$).

1) Determination of the air displacement of the pycnometer ($V_0$). By the air displacement of the pycnometer is meant the volume of air displaced by the pycnometer when one side tube of the pycnometer is closed with a stopper with a cap, and the other with a stopper.

The air displacement of the pycnometer was determined as follows.

Enough water was poured into the pycnometer so that it would sink in water; then the tubes of the pycnometer were closed with stoppers, and the pycnometer was weighed first in air and then on hydrostatic balances in water.

Let

the weight of the pycnometer in air be found to be $P_1$;

the weight of the pycnometer in water be found to be $P_2$;

the density of the air during weighing in air was $\lambda$;

the density of the water during weighing in water was $d$;

Then the air displacement of the pycnometer ($V_0$) is determined from the following expression:

\[ V_0 = \frac{ P_1 - P_2 - \dfrac{P_1 - P_2}{8.4}\lambda }{ d - \lambda } \ldots\ldots\ldots (70) \]

2) Determination of the capacity of the pycnometer up to the mark ($V_1$). The determination of the capacity of the pycnometer up to the mark, in view of the special importance of this constant, was carried out with particular care, observing all possible precautions. For this purpose the pycnometer was filled with water, placed in the thermostat, and, when exactly the temperature at which the determination of the specific gravity was being made had been established, the level was set to the mark. The pycnometer was then weighed.

The water for filling the pycnometer was prepared from ordinary distilled water—by redistilling the latter with potassium permanganate, first in acid and then in alkaline solution¹. The electrical conductivity

of the water prepared in this way fluctuated within the limits \(1.482 \times 10^{-6}\)—\(2.109 \times 10^{-6}\). Before filling the pycnometer, the water was boiled for some time under reduced pressure in a vessel of Jena glass, not corroded by water, acids, or alkalis, and was then cooled in a rarefied space.

From the weighing data the volume \(V_1\) was calculated as follows.

Let the weight in air of the unfilled pycnometer be found by weighing to be \(P_1\). Let us denote the density of the air during the weighing of the unfilled pycnometer by \(\lambda'\), the air displacement of the pycnometer by \(V_0\), and the volume from the mark to the stopper by \(V_2\). Then the true weight (weight in vacuum) of the unfilled pycnometer \((M_1)\) will be expressed as follows:

\[ M_1 = P_1 - \frac{P_1}{8.4}\lambda' + (V_0 - V_2)\lambda' - V_1\lambda'. \]

Let the weight in air of the pycnometer filled with water to the mark be found by weighing to be \(P_2\). Let us denote the density of the air during the weighing of the filled pycnometer by \(\lambda''\). The weight in vacuum of the pycnometer filled with water \((M_2)\) will then be expressed as follows:

\[ M_2 = P_2 - \frac{P_2}{8.4}\lambda'' + [V_0 - V_2]\lambda''. \]

But

\[ M_2 = M_1 + V_1 D_t, \]

where \(D_t\) is the density of water at the temperature of the experiment.

Consequently,

\[ P_2 - \frac{P_2}{8.4}\lambda'' + [V_0 - V_2]\lambda'' = P_1 - \frac{P_1}{8.4}\lambda' + [V_0 - V_2]\lambda' - V_1\lambda' + V_1D_t \]

Whence

\[ V_1 = \frac{ P_2 - P_1 + \frac{P_1}{8.4}\lambda' - \frac{P_2}{8.4}\lambda'' + (V_0 - V_2)(\lambda'' - \lambda') }{ D_t - \lambda' } \tag{71} \]

It was important to ascertain how large the actual error was in determining the volume \(V_1\). At the same time it would become clear to what extent the errors listed above had been committed and what their influence was on the accuracy of determining the specific weight.

Material for this may be provided by the following five experiments in determining \(V_1\) for pycnometer No. 2.

By weighing in air pycnometer No. 2, filled with water to the mark, the following data were obtained:

Table LXI.

Weighing temperature.	Bar.	Temperature of the pycnometer water.	Weight of the pycnometer in water.
18°	742.5 mm.	25.00°	45.11506
16°	744.5 ”	25.05°	45.11526
18°	751.0 ”	25.03°	45.11508
23°	747.0 ”	24.97°	45.11587
20.3°	747.0 ”	25.02°	45.11547

The data from weighing in air of pycnometer No. 2 when unfilled are given above. From these data, by formula (71), the following values for \(V_1\) are calculated:

\[ \begin{array}{r@{\ }l} 1)&20.2998\\ 2)&20.3003\\ 3)&20.3004\\ 4)&20.3009\\ 5)&20.3010 \end{array} \quad \left\} \quad \text{mean } \mathbf{20.30048} \right. \]

Applying the method of least squares, we find that the mean error of each separate observation is \(\pm 0.00048\), the mean error of the mean result is \(\pm 0.00021\), the probable error of a separate observation is \(\pm 0.00032\), and the probable error of the mean result is \(\pm 0.00014\).

I consider these results to be entirely consistent with that degree of accuracy with which I could carry out my weighings. Moreover, they convinced me that the errors enumerated above (inaccuracy in setting the level, air bubbles, nonuniformity of temperature, etc.) did not reach any considerable magnitude. Consequently, the chosen form of the pycnometer, the method of filling the pycnometer and setting the level to the mark, etc., achieved their purpose.

3) Determination of the volume from the mark to the stopper \((V_2)\).

The measurement of this volume was carried out in the following manner: the pycnometer was filled completely with water and closed with the stopper, so that there remained as much water as could fit with the stopper closed. Then the stopper was opened and, with the aid of absorbent paper, enough liquid was removed from the pycnometer for the level to come to rest at the mark. The quantity of water removed was determined from the gain in weight of the paper. The experiment was repeated several times and the mean was taken.

4) Determination of the true weight of the unfilled pycnometer (weight in vacuo) \(M_1\) was described above. It was made a rule, with each new series of determinations, to repeat the weighing of the unfilled pycnometers. Thus each pycnometer, under different conditions of pressure and temperature

was weighed many times. From a series of observations the mean was calculated. It was shown above that the probable error of the mean result was
\(\pm 0.000051\).

We give the table of constants for the three pycnometers with which the greatest number of determinations was made:

Pycnometer No. 2.
Air displacement \(V_0\) — 34.176 cu. cm.
Capacity up to the mark \(V_1\) — 20.30048 cu. cm.
Capacity of the tube from the mark to the stopper \(V_2\) — 0.075 cu. cm.
Weight when empty — \(M_1\) 24.90710 gr.

Pycnometer No. 4.
Air displacement \(V_0\) — 34.203 cu. cm.
Capacity up to the mark \(V_1\) — 20.67313 cu. cm.
Capacity of the tube from the mark to the stopper \(V_2\) — 0.0307 cu. cm.
Weight when empty \(M_1\) — 23.57870 gr.

Pycnometer No. 5.
Air displacement \(V_0\) — 38.885 cu. cm.
Capacity up to the mark \(V_1\) — 24.41702 “ ”
Capacity of the tube from the mark to the stopper \(V_2\) — 0.0307 “ ”
Weight when empty \(M_1\) — 25.50561 gr.

Calculation of the accuracy of the method. Apart from the determinations of specific gravity made with pycnometer No. 1 (capacity 10 cu. cm.), all the remaining determinations were calculated by the formula:

\[ S=\frac{P_2-M_1}{V_1}+ \frac{\left(V_0-V_2-\frac{P_2}{8.4}\right)\lambda}{V_1}, \qquad \ldots \ldots \ldots (72) \]

where

\(P_2\)—weight in air of the pycnometer filled to the mark with the solution;
\(M_1\)—weight when empty of the unfilled pycnometer;
\(V_0, V_1, V_2\) and \(\lambda\) have the same meaning as before.

The influence of observational errors on the specific gravity calculated by the formula will be found from the formula:

\[ F=f\frac{dX^{1)}}{dx}, \qquad \text{where} \qquad (73) \]

\(F\) — error of the result;
\(f\) — error in the determination of one or another observed quantity;
\(x\) — observed quantity;
\(X\) — result.

The following observed quantities enter into formula (72): \(P_2, M_1, V_1\) and \(\lambda\); we shall attempt to calculate the influence on the final result of the errors in determining these quantities.

1) Kohlrausch. Manual for the Practice of Physical Measurements.

1. The influence on the result of the error in determining the quantity \(P_2\), i.e., in determining the weight of the pycnometer filled with liquid.

Of the series of data at my disposal, the data from weighing pycnometer No. 5 with water may serve for this purpose.

In order to exclude the influence on the weighing of accidental pressure and temperature, we shall reduce the observed weights to vacuum and compare these reduced weights.

Table LXII.

Temperature of weighing	Bar.	Weight of pycnometer with water in air	Weight of pycnometer with water in vacuum
\(20^\circ\)	745 mm.	49,8106 gr.	49,8492
\(21^\circ\)	745 „	49,8102 „	49,8487
\(21^\circ\)	745 „	49,8105 „	49,8490
\(17^\circ\)	741 „	49,8099 „	49,8488
\(16^\circ\)	747 „	49,8091 „	49,8485
\(16^\circ\)	748 „	49,8094 „	49,8488

mean 49,84883

Calculating these data by the method of least squares, we find that the mean probable error of a single observation is \(\pm 0,00016\). We shall adopt the same error for the quantity \(P_2\).

This error includes not only the errors of the weighing itself, but also errors arising from the inaccuracy of setting the level in the pycnometer, from the nonuniformity of the temperature of the liquid filling the pycnometer (the pycnometer tubes protruded somewhat from the thermostat), from volatilization, from change of capacity with time, etc. Since all these sources of error are summed in determining the quantity \(P_2\), and since the error in the value \(P_2\) has been determined above experimentally, I did not consider it necessary to analyze each of the sources of error separately.

Thus, differentiating equation (72) with respect to \(P_2\), we obtain

\[ F_1=\frac{0,00016}{V_1}, \]

whence, for the pycnometer, for example No. 2, where \(V_1=20,3004\),

\[ F_1=0,000008 \]

for pycnometer No. 5, where \(V_1=24,4170\)

\[ F_1=0,000007. \]

1. The influence on the result of the error of observation of \(M_1\).

The quantity \(M_1\) was calculated for each pycnometer as the mean from an entire series of observations. On p. 121 it was found that the probable error of the mean result was \(\pm 0,000046\).

Differentiating equation (72) with respect to \(M_1\), we obtain:

\[ F_2=-\frac{0,000046}{V_1}. \]

For pycnometer No. 2, for which \(V_1\) is equal to 20.3004,

\[ F_2 = -0.000002. \]

3. Effect on the result of the error of observation of \(V_1\).
The quantity \(V_1\) for each pycnometer was likewise determined from a series of observations. On p. 125 it was found that the probable error of the mean result was equal to \(\pm 0.00014\).

Differentiating equation (72) with respect to \(V_1\), and disregarding the second term of equation (72), we obtain:

\[ F_3 = -0.00014\,\frac{P_2-M_1}{V_1^2} \]

The specific gravities of the liquids measured by me varied within the limits 0.7–2.0. For one limiting case the influence of errors in the determination of \(V_1\) on the final result will therefore be:

\[ F'_3 = -0.0000032 \]

For the other:

\[ F''_3 = -0.000014 \]

4. Effect on the result of the error in the determination of \(\lambda\).
The quantity \(\lambda\) was calculated by me from the temperature and pressure data, under the assumption that the air was half saturated with water vapor. In fact this was not the case; consequently, an error was admitted in such a calculation. An approximate estimate of the magnitude of the admitted error can be made on the basis of the following data. At a temperature of \(20^\circ\) and a barometric pressure of 750 mm, the weight of one cubic centimeter of dry air is equal to 0.001189 gr. At the same temperature and the same pressure, one cubic centimeter of air half saturated with water vapor weighs 0.001183 gr. Since, in assuming that the air was half saturated with water vapor, I could never have made an error in the content of water vapor even by 25%, I consider the magnitude of the error in the determination of \(\lambda\) to be no more than \(\pm 0.000002\).

In equation (72) \(\lambda\) is multiplied by the term

\[ \frac{V_0 - V_2 - \dfrac{P_2}{8.4}}{V_1}. \]

From the constants of my pycnometers given above it is seen that the magnitude of this number varies within the limits 1.5–1.7; consequently, the error in the result, owing to the error in the determination of \(\lambda\), will be expressed as:

\[ F_4 = \pm 0.000003. \]

Accuracy with which the specific gravities were measured. On the basis of the figures given above we find that, in normal cases, i.e., in the absence of accidental errors and with careful and accurate work, the errors of the method, in the most unfavorable case, for the lightest of the liquids investigated, should have been

\[ F_1 + F_2 + F'_3 + F_4 = \pm 0.000016; \]

for the heaviest,

\[ F_1 + F_2 + F''_3 + F_4 = \pm 0.000027; \]

while the probable ...

the error for the lightest of the liquids investigated should have been

\[ \pm \sqrt{F_1^2+F_2^2+F_3^2+F_4^2}=\pm 0.0000092, \]

for the heaviest—

\[ \pm \sqrt{F_1^2+F_2^2+F_3^2+F_4^2}=\pm 0.000016. \]

In reality, owing to the volatility of the liquids, owing to the mass of minor precautions whose observance fatigued the observer, owing to the impossibility of keeping the temperature strictly constant, owing to changes in the capacity of the pycnometers with time, owing to wear of the pycnometers themselves, and finally owing to chance occurrences in the work, the actual error was undoubtedly greater than the calculated one. In any case, as can be inferred from comparison of the many parallel determinations I have, it never exceeded the calculated error by a factor of three.

For example, with pycnometer No. 2 for ether the specific gravity was found to be

\[ S_{\frac{4^\circ}{}}^{25^\circ}=0.708122, \]

with pycnometer No. 4 the specific gravity of the same ether was found to be

\[ S_{\frac{4^\circ}{}}^{25^\circ}=0.708113. \]

The specific gravity of benzene with pycnometer No. 2 was found to be:

\[ S_{\frac{4^\circ}{}}^{25^\circ}=0.873531, \]

for the same benzene with pycnometer No. 5 the specific gravity was found to be

\[ S_{\frac{4^\circ}{}}^{25^\circ}=0.873502. \]

Six months earlier, for benzene of another preparation, the specific gravity was found:

\[ S_{\frac{4^\circ}{}}^{25^\circ}=0.873562. \]

The specific gravities determined with the small pycnometer, for which the corrections were made by the simplified formula, of course contained a larger error. The following data from determinations of the specific gravity of ether at \(15^\circ\) allow an approximate judgment of the magnitude of this error. These data refer to ether of different preparations and were obtained over a period of two years.

Specific gravity of ether at \(\dfrac{15^\circ}{4^\circ}\).		Difference from the mean result.
1) 0.71951		\(-0.00005\)
2) 0.71955		\(-0.00006\)
3) 0.71972		\(+0.00016\)
4) 0.71962		\(+0.00006\)
5) 0.71947	mean 0.71956	\(-0.00009\)
6) 0.71948		\(-0.00008\)
7) 0.71931		\(-0.00025\)
8) 0.71952		\(-0.00004\)
9) 0.71949		\(-0.00007\)

Preparation of the solutions and determination of their concentrations. In preparing the solutions two tasks were set: 1) to free the solutions, as far as possible, from gaseous bodies dissolved in them; 2) to determine the concentration of the solutions as accurately as possible.

1) To perform the first task, the solution (in the case where the dissolved substance was nonvolatile) or each of the liquids being mixed separately (if both of them were volatile) was boiled under ordinary or reduced pressure.

Boiling was carried out in short-necked flasks, of the kind used as Reinecke flasks for determining specific gravity, with a capacity between 75–100 cubic cm. To the neck of the flask there were ground in at the same time: an ordinary glass tube and a long glass tube intended to serve as a condenser. If necessary, a sleeve from a Liebig condenser was slipped over the tube. For boiling under reduced pressure a special apparatus was assembled.

After the boiling was finished, the tube-condenser was removed from the flask, the flask was closed with a ground glass stopper and left to stand for cooling to the balance temperature. After cooling the contents of the flask, owing to the fact that the air had been displaced from the flask by the vapors of the boiling liquid, the pressure in the flask was always below atmospheric, and, owing to the pressure of the outside air on the surface of the stopper, it was often very difficult to open the stopper. To avoid this inconvenience, the stopper that closed the flask was made hollow, and in the wall of the stopper, as well as in the wall of the neck of the flask, an opening was made. It was not difficult to turn the stopper so that both openings coincided and, consequently, to bring the inner space of the flask into communication with the outside air, even in the case where there was a strong rarefaction inside the flask.

2) The weighing of the solvent was always carried out in the same vessel in which the boiling was carried out. Solid substances were weighed in long glass tubes closed with ground glass stoppers. Liquids were weighed in pipettes closed at both ends with ground glass stoppers. In both cases the weight was determined from the difference between two weighings.

In the case where the dissolved substance was nonvolatile, the solution was prepared as follows: a weighed quantity of the substance intended for dissolution was placed in the flask, and so much solvent was poured in as to fill the flask by more than \(3/4\); the solution was boiled for some time, then, hermetically sealed, was cooled to the balance temperature; finally, it was weighed.

In the case where the dissolved substance was volatile, it was boiled and cooled in a closed space, as described above. After cooling, the necessary portion was withdrawn by means of an Ostwald pycnometer-type pipette, closed with ground stoppers, weighed together with the pipette, and transferred into the solvent, which had likewise been previously boiled and weighed. Weighing the emptied pipette gave the weight of the portion taken for dissolution. All weighings were carried out on ordinary analytical balances. Small weights (generally up to 50 gr.) were made with the usual accuracy, i.e. to tenths of a milligram. Weights of solvent (50–100 gr.) were made with an accuracy of 1–2 mgr. Corrections for loss of weight in air were always made. Since the specific gravity of the solution was determined immediately, there was full possibility of introducing these corrections according to the known formula:

\[ \frac{K}{1000}=0{,}0012\left(\frac{1}{S}-\frac{1}{8{,}4}\right)^{1}), \tag{74} \]

\(^{1}\) Kohlrausch, Guide to the Practice of Physical Measurements.

where

$S$ is the density of the body being weighed,

$8.4$ is the density of the brass weights,

$0.0012$ is the average weight of one cubic centimeter of air under ordinary conditions of pressure and temperature.

The concentration of the solutions was expressed by the content of dissolved substance (in general, substance $B$) in 100 parts by weight of solution.

If the weight of the first component of the mixture is denoted by $A$, then the content of the second component in the mixture ($\pi$) is expressed by the formula:

\[ \pi=\frac{B\times 100}{A+B}. \tag{75} \]

Formula (75) provides material for judging the accuracy with which the concentration of the solutions was determined.

Let us suppose that the weights of component $A$ were determined with an accuracy of $\pm 0.005$ gr.

Differentiating equation (75), according to the formulas on p. 126, with respect to $A$, we obtain:

\[ F_1=-0.005\times \frac{B\times 100}{(A+B)^2}. \]

For the case when $B$ is equal to 25 gr., and $A$ is equal to 75 gr., the error in determining the concentration ($\pi\%$), due to the error in the weight of $A$, will be:

\[ F_1=-0.00125 \]

The error in determining the magnitude $B$ was, let us suppose, $\pm 0.0005$ gr. Differentiating equation (75) with respect to $B$, we obtain:

\[ F_2=0.0005\times \frac{100}{A+B} \]

For the case when $B$ is equal to 25 gr., and $A$ is equal to 75 gr., the error in determining the concentration ($\pi\%$), due to the error in weighing substance $B$, will be:

\[ F_2=0.0005. \]

Liquids Mixing with One Another in All Proportions.

1. Ether and aniline.

The ether which I used in my experiments for determining the specific gravity and the vapor pressure of solutions was always prepared in the following manner.

Kahlbaum’s preparation, Ather über Natrium destill., was shaken, usually three times, in a separatory funnel with an equal volume of water—to remove traces of alcohol; it was then left for a day over CaCl₂ to remove water and was then distilled with a thermometer and a dephlegmator; the distilled, almost dry ether was further left for a day with metallic sodium and finally fractionated over sodium with Lebel’s compound dephlegmator, containing 9 bulbs.

The ether prepared by the method described above distilled almost entirely within 0.1°. For the experiments a fraction boiling within still narrower limits was collected.

For example, one preparation of ether yielded ether which distilled (about a liter) at 34.305°–34.310° at a pressure of 756.3 mm; another preparation yielded ether which distilled at 33.725°–33.737° at a pressure of 741.5 mm, etc.¹)

The specific gravity of this ether at 15°, as the mean of 9 determinations, was found (see p. 129) to be 0.71956.

The error of this mean result was ± 0.00004.²)

Aniline was prepared from Kahlbaum’s preparation: Anilin aus sulfat. After drying with solid caustic potash, this aniline was distilled, with almost all of it passing over within the limits 182.4°–182.6° at a pressure of 735.4 mm at 0°.³) For the experiments a fraction distilling within 0.1° was used.

The specific gravity of this aniline at 15° was found, as the mean of two determinations in very good agreement with one another, to be 1.02564.

Determinations of the specific gravities of mixtures of ether and aniline were made at 15°, with a 10 c.c. pycnometer.

¹) The temperature, both in this case and in all other cases of distillation, was always observed with shortened thermometers graduated to 0.1° or 0.2°, with the mercury column always in the vapors. Correction of the thermometer readings was always made by means of a capillary tube divided exactly as the thermometer tube in order to ensure that tenths of a degree were counted quite accurately. The proof of the purity of the liquids was their passing over during distillation within narrow temperature limits.

²) In the literature for the specific gravity of ether at 15° the following numbers are found: 0.72008 (Perkin) and 0.71908 (Squib).

³) The thermometer was not compared with the normal one.

Table LXIII.

Specific gravities of mixtures of ether and aniline at 15°.

% content of \(C_6H_5.NH_2\) in 100 parts by weight of the mixture	\(S \dfrac{15^\circ}{4^\circ}\) specific gravity at 15°
0	0.71956
1.54	0.7239
2.59	0.7267
12.46	0.7556
17.25	0.7698
24.86	0.7921
52.75	0.8752
72.64	0.9368
92.07	0.9991
98.78	1.0216
100	1.02564

2. Ether and nitrobenzene.

Nitrobenzene was prepared from Kahlbaum’s preparation, Nitrobenzol aus Benzol. cryst. The Kahlbaum preparation was subjected to triple freezing out, and then distilled. It boiled within the limits of 0.1°.

The specific gravity of this nitrobenzene at 15°, as the mean of two closely agreeing determinations, was found to be: 1.20851.

The specific gravities of mixtures of ether and nitrobenzene were measured at 15° with a pycnometer of 10 c.c.

Table LXIV.

Specific gravities of mixtures of ether and nitrobenzene at 15°.

% content of \(C_6H_5NO_2\) in 100 parts by weight of the mixture	\(S\frac{15^\circ}{4^\circ}\), specific gravity at 15°
0	0.71956
1.72	0.7254
9.70	0.7536
17.06	0.7808
22.33	0.8014
25.14	0.8099
49.82	0.9191
69.13	1.0181
74.12	1.0455
90.75	1.1460
98.86	1.2006
100.00	1.20851

3. Benzene and ethylene bromide.

The benzene used by me for the experiments to determine the specific gravities of solutions was prepared from Kahlbaum’s reagents: 1) Benzol Thiophenfrei; 2) Benzol aus anilinsulfat; 3) Benzol cryst. All these reagents were subjected to freezing until the freezing temperature became constant, then distilled over metallic sodium. The benzene obtained from these reagents passed almost entirely within the limits of 0.4° (for the experiments, fractions passing over within narrower limits were used). Its physical constants were as follows. The freezing temperature, determined in a Beckmann apparatus, lay close to 5.5°. The boiling temperature, for example, of one portion of benzene was 79.62°–79.80° at a pressure of 745.2 mm at 0°.

Determinations of the specific gravity at 25°, carried out at different times with different pycnometers and with portions of benzene of different preparation, gave the following results:

1) 0.87388
2) 0.87388 } Portion of the 1st preparation

3) 0.87380
4) 0.87381 } Portion of the 2nd preparation

5) 0.87376
6) 0.87375 } Portion of the 3rd preparation

7) 0.87353
8) 0.87350 } Portion of the 4th preparation.

} mean 0.87374.

The error of this mean result, calculated by the method of least squares, is ±0.00008.

In the literature we find the following data for the specific gravity of benzene at 25°: 0.87417 (Adrienz), 0.872627 (Pisoti and Paterno), 0.8707 (Janowsky), 0.87255 (Lachovicz). The disagreement among the data of different authors, as well as the comparatively too large error of my mean result, are due to the fact that benzene dissolves air, which can be removed only with great difficulty and which causes comparatively large differences in the specific gravity of portions of benzene of different preparations.

Ethylene bromide was obtained by me personally from ethylene and bromine. It was recrystallized many times and finally distilled.

The specific gravity of this ethylene bromide at 25°, as the mean of three determinations, was found to be: 2.16714.

The specific gravities of mixtures of benzene with ethylene bromide were determined at 25°, using a pycnometer of 10 cu. cm.

Table LXV.

Specific gravity of mixtures of benzene and ethylene bromide.

wt.% content of $C_2H_4Br_2$ in 100 parts by weight of mixture	$S \frac{25^\circ}{4^\circ}$ specific gravity at 25°
0	0.87374
0.982	0.8787
4.77	0.8989
8.02	0.9170
8.33	0.9188
19.51	0.9866
29.51	1.0586
35.39	1.1055
36.81	1.1176
47.23	1.2141
56.63	1.3165
69.56	1.4256
81.70	1.7022
88.99	1.8609
93.93	2.1346
100	2.16714

4. Benzene and chloroform.

The chloroform used by me for preparing mixtures with benzene was the ordinary Kahlbaum preparation. It was first shaken four times with an equal volume of water, then dried with calcium chloride, and finally distilled with a dephlegmator. It passed over within narrow temperature limits. The fraction passing over within \(0.1^\circ\) was used for the work.

The specific gravity of this chloroform, as the mean of 5 determinations very concordant with one another, was found to be 1.4797.

Subsequently, however, it turned out that chloroform prepared in this way from the ordinary Kahlbaum preparation contained some impurity, since, when iodine was dissolved in it, after some time a white precipitate was obtained. Therefore, for the later work (solutions of iodine in chloroform) a chloroform preparation made from chloral was used.

The specific gravities were determined with the aid of a pycnometer of 10 cu. cm.

Table LXVI.

Specific gravity of mixtures of benzene and chloroform.

\(\pi\%\) content of \(CHCl_3\) in 100 parts by weight of the mixture	\(S \dfrac{25^\circ}{4^\circ}\) specific gravity at \(25^\circ\)
0	0.87374
1.45	0.8789
7.07	0.8995
12.35	0.9198
20.31	0.9511
43.11	1.0595
61.60	1.1664
79.06	1.2899
88.65	1.3706
94.85	1.4277
98.04	1.4596
98.90	1.4682
100	1.4797

5. Benzene and chlorobenzene.

Chlorobenzene was a Kahlbaum preparation, which was washed with water, dried over calcium chloride, and distilled. The main fraction of this chlorobenzene passed over within the limits \(131.2^\circ\)—\(131.4^\circ\).¹

The specific gravity of this chlorobenzene at \(25^\circ\), as the mean of three determinations in very good agreement with one another, was found to be 1.10100.

The specific gravities were determined with large pycnometers, and all corrections were made.

Table LXVII.

Specific gravities of mixtures of benzene with chlorobenzene.

% content of \(C_6H_5Cl\) in 100 parts by weight of the mixture	\(S \dfrac{25^\circ}{4^\circ}\) specific gravity at \(25^\circ\)
0	0.87374
2.33	0.87794
4.90	0.88257
7.98	0.88826
24.12	0.91937
29.67	0.92831
36.83	0.94527
47.36	0.96811
60.48	0.99800
70.86	1.02310
79.99	1.04626
89.02	1.07019
95.22	1.08729
98.66	1.09703
100	1.10100

6. Benzene and bromobenzene.

Bromobenzene was a Kahlbaum preparation, which was washed with water, dried over calcium chloride, and then distilled. It passed over almost entirely within the limits \(154.6^\circ\)—\(154.8^\circ\).²

The specific gravity of this bromobenzene at \(25^\circ\) was found, as the mean of two mutually well-agreeing determinations, to be 1.48682.

The specific gravities of the mixtures were determined with large pycnometers, all corrections being made. The specific gravity for each concentration was determined twice with different pycnometers, so that in the following table the specific gravities are the means of two mutually well-agreeing determinations.

Table LXVIII.

% content of \(C_6H_5Br\) in 100 parts by weight of the mixture	\(S \dfrac{25^\circ}{4^\circ}\) specific gravity at \(25^\circ\)
0	0.87374
1.53	0.87930
4.29	0.88957
12.98	0.92322
18.32	0.94519
30.37	0.99890
41.09	1.05191
54.56	1.12034
63.70	1.18510
79.44	1.29936
88.95	1.38047
95.22	1.43865
99.01	1.47701
100	1.48682

7. Benzene and acetic acid.

The material for obtaining the preparation of acetic acid was Kahlbaum’s acid, Eisessig \(98\%—99\%\). More than 10 kilograms of this acid were taken and subjected to fractional freezing. After eight successive freezings, an acid was finally obtained whose melting point, determined in Beckmann’s apparatus, was \(16.55^\circ\). For completely anhydrous acid the following melting points are found in the literature: \(16.57^\circ\) (Rudorff); \(16.55^\circ\) (Petersson), \(17.5^\circ\) (Sanstadt).

Subsequently, when all determinations of the specific gravity of mixtures and solutions with acetic acid had already been made, attention was drawn to the fact that this acid contains, as an impurity, higher homologues of acetic acid. It remains unclear to me whether they could have been removed by the treatment described above.

Determinations of the specific gravity of this acetic acid at 25°, carried out at different times and with different pycnometers, gave the following results:

\[ \begin{array}{r@{\quad}l} 1) & 1{,}04368\\ 2) & 1{,}04367\\ 3) & 1{,}04391\\ 4) & 1{,}04379\\ 5) & 1{,}04370 \end{array} \left\} \quad \text{mean } \mathbf{1{,}04375} \right. \]

The specific gravities of mixtures of benzene with acetic acid were determined with the aid of large pycnometers, all corrections being made. The specific gravity for each concentration was determined twice with different pycnometers, so that in the following table each number for the specific gravity is the mean of two determinations that always agreed well with one another.

In storing the acetic acid and in filling the pycnometers, all precautions were taken against absorption of moisture.

Table LXIX.

Specific gravities of mixtures of benzene with acetic acid.

% content of $CH_3COOH$ in 100 parts by weight of mixture	$S \dfrac{25^\circ}{4^\circ}$ specific gravity at 25°
0	0,87374
2,04	0,87577
6,62	0,88101
10,62	0,88553
19,57	0,89634
30,76	0,91110
39,15	0,92317
56,31	0,95071
56,75	0,95144
80,06	0,99627
87,64	1,01320
95,95	1,03323
98,94	1,04091
100	1,04375

8. Carbon tetrachloride and aniline¹.

Carbon tetrachloride was prepared from Kahlbaum’s preparation. Kahlbaum’s preparation was washed with water, dried with calcium chloride, and distilled with a dephlegmator. Prepared in this way, the carbon tetrachloride distilled for the most part at \(75.7^\circ\)—\(76.8^\circ\) at 737.9 mm.; for the experiments, the portion passing over within the limits of \(0.1^\circ\) was taken. The specific gravity at \(25^\circ\) of this carbon tetrachloride, as the mean of three determinations, was found to be 1.58448.

The specific gravity of aniline at \(25^\circ\), as the mean of four determinations in excellent agreement with one another, was found to be 1.01694.

The specific gravities of mixtures of carbon tetrachloride and aniline were determined with large pycnometers, with all corrections being made.

TABLE LXX.

Specific gravities of mixtures of carbon tetrachloride and aniline.

% content of \(C_6H_5.NH_2\) in 100 parts by weight of mixture	\(S \dfrac{25^\circ}{4^\circ}\), specific gravity at \(25^\circ\)
0	1.58448
1.48	1.57176
5.80	1.53587
11.57	1.49073
20.24	1.42727
31.25	1.35339
37.46	1.31486
51.37	1.23535
56.46	1.20841
68.72	1.14789
83.29	1.08315
88.91	1.05999
94.52	1.03764
98.96	1.02074
100	1.01694

Iodine Solutions in Organic Solvents¹

The iodine preparation used was Jod. bis resublimatum Merck’a (garantirt reine Reagentien). Titration of various samples of this well-dried preparation with a \(1/10\)-normal solution of \(As_2O_3\) gave the following results:

Iodine taken:	Iodine found by titration:
1) 0.2533	0.2536
2) 0.2836	0.2841
3) 0.3955	0.3956
4) 0.3481	0.3487
5) 0.3374	0.3385

I considered these results satisfactory and, since, in addition, qualitative reactions for admixtures of chlorine and cyanogen also gave negative results, I confined myself only to drying the commercial preparation, without subjecting it to further purification.

9. Iodine Solutions in Benzene

The specific gravities were determined with large pycnometers, and all corrections were made.

Table LXXI.

Specific gravities of iodine solutions in benzene.

\(\pi^\circ/\%\) iodine content in 100 parts by weight of solution	\(S \dfrac{25^\circ}{4^\circ}\), specific gravity at \(25^\circ\)
0	0.87374
0.55	0.87698
0.87	0.87962
1.18	0.88028
2.27	0.88933
4.05	0.90222
6.02	0.91668
8.34	0.93452
9.40	0.94298
13.68	0.97811
saturated	solutions

10. Solutions of iodine in nitrobenzene.

Nitrobenzene was prepared from a Kahlbaum preparation and purified as described above (p. 133). The specific gravity of this nitrobenzene at \(25^\circ\), as the mean of two determinations, was found to be 1.19908.

The specific gravities were determined with the aid of large pycnometers, with all corrections being made.

Table LXXII.

Specific gravity of solutions of iodine in nitrobenzene.

% iodine content in 100 wt. parts of solution	\(S^{25^\circ}_{4^\circ}\) specific gravity at \(25^\circ\)
0	1.19908
0.49	1.20233
0.93	1.20575
1.87	1.21368
2.58	1.21963
3.46	1.22716
4.90	1.23935
saturated	solutions

11. Solutions of iodine in aniline.

In order to remove any gases that might be present in the solution, the solutions of iodine in aniline were heated for some time in a rarefied space. When the determinations of the specific gravities had been completed, it was noticed that, upon dilution of these solutions with ether, a yellow precipitate separated. On closer investigation it turned out that this precipitate is hydroiodide of aniline. Thus, in solutions of iodine in aniline, a substitution reaction of hydrogen by iodine occurs, with the formation of hydroiodic acid. I leave for the future the clarification of how far this reaction had proceeded and what influence it had on the specific gravity of the solutions. Here, for the present, I give the numbers that were obtained directly.

Table LXXIII.

Specific gravity of solutions of iodine in aniline.

% iodine content in 100 parts by weight of solution	$S^{25^\circ}_{4^\circ}$ specific gravity at $25^\circ$
0	1.01694
0.47	1.02105
2.45	1.03378
3.87	1.05172
7.15	1.08213

12. Solutions of iodine in chloroform.

Since it had been observed that chloroform prepared from the ordinary Kahlbaum preparation gave a precipitate when iodine was dissolved in it, on this occasion the chloroform was obtained from Merck’s preparation Chloroform aus Chloral. It was thoroughly washed with water, dried with calcium chloride, and finally distilled. Almost all of it distilled over within the limits of $60.4^\circ$–$60.6^\circ$, at a pressure of 741.5 mm. When iodine was dissolved in it, no precipitate formed. The specific gravity of this chloroform at $25^\circ$ was found to be 1.47896.

The specific gravities were determined by means of large pycnometers, with all corrections being made.

Table LXXIV.

Specific gravity of solutions of iodine in chloroform.

% iodine content in 100 parts by weight of solution	$S^{25^\circ}_{4^\circ}$ specific gravity at $25^\circ$
0	1.47896
0.782	1.48654
1.75	1.49536
2.79	1.50503

13. Solutions of iodine in carbon tetrachloride.

Carbon tetrachloride was prepared as described above, p. 140.

The specific gravities of the solutions were determined with the aid of large pycnometers, all corrections being made.

Table LXXV.

Specific gravities of solutions of iodine in carbon tetrachloride.

% iodine content in 100 parts by weight of mixture	$S\ \dfrac{25^\circ}{4^\circ}$ specific gravity at $25^\circ$
0	1,58448
0,218	1,58655
0,488	1,58916
0,508	1,58903
0,939	1,59331
1,438	1,59782
2,719	1,59859

14. Solutions of iodine in ethyl bromide.

Ethyl bromide was prepared by me personally from ethylene and bromine. Purified by freezing out, it was distilled, with almost all of it distilling over at $129^\circ$—$129{,}1^\circ$ at 737 mm pressure.

Its specific gravity at $25^\circ$, as the mean of three determinations in good agreement with one another, was found to be 2,16714.

The specific gravities were determined with large pycnometers, all corrections being made.

Table LXXVI.

Specific gravities of solutions of iodine in ethyl bromide.

% iodine content in 100 parts by weight of solution	$S\ \dfrac{25^\circ}{4^\circ}$ specific gravity at $25^\circ$
0	2,16714
0,907	2,17616
1,816	2,18546

15. Solutions of iodine in acetic acid.

The acetic acid was prepared as described above.
The specific gravities of the solutions were determined with large pycnometers, and all corrections were made.

Table LXXVII.

Specific gravities of solutions of iodine in acetic acid.

\(\pi\%\) iodine content in 100 parts by weight of solution	\(S\frac{25^\circ}{4^\circ}\) specific gravity at \(25^\circ\)
0	1.04375
0.61	1.04737
0.91	1.05052
1.35	1.05388
1.94	1.05829
2.45	1.06222
2.54	1.06294

16. Solutions of iodine in ether.

The ether was prepared as described above. The specific gravity of this ether at \(25^\circ\), as the mean of two determinations, was found to be 0.70812.

The specific gravities were determined with large pycnometers, and all corrections were made. For each concentration the specific gravity was determined twice with different pycnometers, so that all the numbers given in the following table represent the mean of two determinations, which always agreed well with one another.

Table LXXVIII.

Specific gravities of solutions of iodine in ether.

\(\pi\%\) iodine content in 100 parts by weight of solution	\(S\frac{25^\circ}{4^\circ}\) specific gravity at \(25^\circ\)
0	0.70812
0.7	0.71217
1.83	0.71988
3.10	0.72757
3.65	0.73090
4.82	0.73848
4.91	0.73912
6.13	0.74733
7.37	0.75504
8.03	0.76184

17. Solutions of Iodine in Carbon Disulfide

The carbon disulfide was prepared from Kahlbaum’s reagent. Kahlbaum’s reagent was shaken several times with mercury, then left for some time over sublimate, and finally distilled with a dephlegmator. Almost all of it passed over within the range \(46.2^\circ\)—\(46.4^\circ\) at \(751.5\ \mathrm{mm}\). For the experiments, the fraction was taken that passed over within still narrower temperature limits. The specific gravity of this carbon disulfide, measured at \(25^\circ\), gave the following figures:

\[ \begin{array}{r@{\ }l} 1) & 1.25592\\ 2) & 1.25590\\ 3) & 1.25586\\ 4) & 1.25588 \end{array} \quad\left\}\quad \text{mean } \mathbf{1.25589}. \]

The specific gravities were determined with large pycnometers, with all corrections being made. For each concentration the specific gravity was determined twice with different pycnometers, so that in the table below each number for the specific gravity is the mean of two determinations, which always agreed well.

TABLE LXXIX.

Specific gravities of solutions of iodine in carbon disulfide.

% content of iodine in 100 wt. parts of solution	\(S^{25^\circ}_{4^\circ}\) specific gravity at \(25^\circ\)
0	1.25589
0.60	1.26112
1.13	1.26574
2.02	1.27297
2.82	1.28096
3.34	1.28571
4.83	1.30003
5.85	1.30934
6.12	1.31199
6.48	1.31526
9.07	1.34088
11.85	1.36913

Separate determinations.¹

1. Solutions in benzene.

Boiling point of benzene \(80^\circ\)—\(82^\circ\). Specific gravity of benzene \(S \dfrac{25^\circ}{4^\circ}\) — 0.87431

1) Picric acid \(\left(c=\dfrac{0.7093}{43.221}\right)\)²; \(S \dfrac{25^\circ}{4^\circ}\) — 0.8803.

2) Naphthalene \(\left(c=\dfrac{0.6801}{41.690}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8611.

3) Dinitrobenzene \(\left(c=\dfrac{0.9588}{51.3620}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8787.

4) Azoxybenzene \(\left(c=\dfrac{0.9380}{31.026}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8800.

5) Nitrochlorobenzene \(\left(c=\dfrac{1.0578}{49.094}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8801.

6) Diphenylamine \(\left(c=\dfrac{0.8629}{46.700}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8767.

7) Quinone \(\left(c=\dfrac{0.8867}{27.124}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8806.

8) Benzil \(\left(c=\dfrac{0.9409}{99.234}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8754.

9) Benzophenone \(\left(c=\dfrac{0.9983}{52.816}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8770.

10) Isoamyl ether \(\left(c=\dfrac{0.5585}{40.8367}\right)\); \(S \dfrac{25^\circ}{4^\circ}\) — 0.8732.

2. Solutions in ether.

11) Benzoic ether \((\pi^0_0=22.84)\); \(S \dfrac{15^\circ}{4^\circ}\) — 0.7817.

12) Benzoic ether \((\pi^0_0=100)\) \(S \dfrac{15^\circ}{4^\circ}\) — 1.05105 (mean of two determinations).

13) α-Methyl-β-methyl-pseudobutyl-ethylenelactic acid

\[ \left(c=\frac{1.1052}{48.739}\right);\qquad S\frac{25^\circ}{4^\circ} — 0.7077. \]

3. Solutions in nitrobenzene.

14) Benzene \((\pi^{0}_{0}=1.188);\quad S\frac{15^\circ}{4^\circ} — 1.20786\) (average of two determinations).

4. Solutions in acetic acid.

15) Benzophenone \((\pi^{0}_{0}=2.07);\quad S\frac{25^\circ}{4^\circ} — 1.04534.\)

5. Solutions in ethyl iodide.

16) Iodine \((\pi^{0}_{0}—0.415);\quad S\frac{25^\circ}{4^\circ} — 1.9283.\)

17) Iodine \((\pi^{0}_{0}—0.651);\quad S\frac{25^\circ}{4^\circ} — 1.9342.\)

18) Iodine \((\pi^{0}_{0}—1.873);\quad S\frac{25^\circ}{4^\circ} — 1.94472.\)

Chapter IV.

Experiments on Measuring the Vapor Pressure of Solutions.

The measurements of the vapor pressure of solutions were undertaken with the aim of obtaining new experimental data for comparing the ratios $\dfrac{p_1}{p_0}$ and $\dfrac{s_1}{s_0}$.

Two series of measurements of the vapor pressure of solutions were carried out. The first series of measurements (of the vapor pressure of aqueous solutions of cane sugar) was made by me in Prof. G. Kahlbaum’s laboratory in Basel; the second series of measurements (of the vapor pressure of solutions in organic solvents) was made in Kiev in collaboration with student Tsel’tner.

The first series of measurements was made with Kahlbaum’s apparatus in the form in which this apparatus was used by Kahlbaum for measuring the vapor pressure of pure liquids¹. The second series of observations was made with Kahlbaum’s apparatus as well, but modified by me so as to provide a more convenient and at the same time more accurate measurement of pressure.

Method of measuring vapor pressure. Of all the existing methods for measuring vapor pressure, the boiling method was chosen, as sufficiently accurate and at the same time the simplest and more easily practicable than the others in the setting of an ordinary chemical laboratory.

The boiling method consists in boiling a liquid with a reflux condenser (or distilling it) in a closed space in which some specified pressure has previously been produced.

The pressure in the apparatus, measured by a manometer, is equal to the vapor pressure of the saturated vapor at the observed boiling temperature. By varying the pressure in the apparatus, one obtains a series of temperatures and, corresponding to these temperatures, a series of vapor pressures.

When applied to liquids whose vapor has the same composition as the liquid, the boiling method gives results identical with those obtained by the barometric method. This proposition was first put forward by Regnault’s classical experiments: “J’ai déjà fait voir, dans mon mémoire sur les forces élastiques de la vapeur aqueuse,” says Regnault, “que cette coïncidence est parfaite pour l’eau; les deux méthodes (statique et dynamique), donnant des valeurs identiques aux mêmes températures. Je mon-

...will show that the same is true for other volatile liquids, provided that they are in a state of perfect purity. But when a liquid contains a portion, even an extremely small one, of another volatile substance, the two methods give different values.... for the elastic forces of its vapor at the same temperature, is an extremely delicate method for judging the homogeneity of a volatile substance”¹.

Recently this proposition was challenged by Kahlbaum and defended by Ramsay and Young. In the course of the dispute it became clear that Regnault’s proposition, as Kahlbaum himself was obliged to confirm by his own experiments², is entirely correct.

Regnault’s proposition, however, could be considered proven only for liquids whose vapor has the same composition as the liquid. The boiling method was almost never applied to solutions. The measurements given below show that it is equally applicable to solutions as well. The theory of the boiling method is discussed below.

The boiling method is considerably simpler than the barometric method:

1) here there is no difficult manipulation of preparing a barometric vacuum and enclosing in it a substance free of air;

2) there is no need to take care of a bath with constant temperature.

Measurements of the Elasticity of the Vapor of Aqueous Solutions of Cane Sugar.

Description of the apparatus. The apparatus that I used for determining the elasticity of the vapor of aqueous sugar solutions consists of the following parts (Fig. 13):

1) a pear-shaped vessel \(B\) with an inverted condenser,

2) a reservoir \(V\), and 3) vacuum gauges \(Br\) and \(Bl\).

1) In vessel \(B\) the liquid was boiled.

In order to obtain uniform boiling and avoid superheating, the lower part of the vessel was filled with garnets. In addition, for the same purpose, dry air was introduced into the liquid through a capillary. The capillary tube supplying the air passes through a side tube into vessel \(B\) and reaches the bottom of the vessel. Air is drawn into the apparatus owing to the difference in pressures inside and outside the apparatus (in the apparatus the air is rarefied). The flow of air is regulated by a clamp. With the large capacity of the apparatus, the air introduced through the capillary changed the pressure in the apparatus very slowly.

2) Vessel \(V\), with a capacity of about 10 L., located between the right vacuum gauge and the boiling vessel, serves as a pressure regulator; i.e., it damps sudden small fluctuations of pressure, inevitable during the boiling of the liquid.

3) The vacuum gauges used were glass tubes \(Br\) and \(Bl\), graduated in millimeters (divisions on the glass), the free ends of which are immersed

into round reservoirs filled with mercury. These reservoirs were chosen to be of such a diameter that fluctuations in the height of the mercury column in the vacuum gauges would not noticeably affect the position of the mercury level in the reservoirs. With such an arrangement it was possible to avoid reading the lower level of the mercury at each separate observation—it was sufficient to make one or several careful readings for an entire series of observations. As is known, it is rather difficult to make these readings accurately. The vacuum gauges hung freely. Particular attention was paid to their vertical position, which was often checked by means of two plumb lines situated in mutually perpendicular planes.

Fig. 14.

By means of the three-way stopcock \(D\) (Fig. 13), the apparatus could be connected either with the outside air or with a water or mercury pump.

The principal parts of the apparatus were connected to one another by means of glass ground joints with mercury seals, examples of which are shown in Figure 14. In those places where vapors of the liquid could not penetrate, thick-walled rubber was used for the connection.

Course of observations. Work with the apparatus was carried out as follows.

1) The apparatus was assembled in the form in which it is presented in Figure (13), and was thoroughly dried.

The drying was performed as follows. In the apparatus, by means of a pump, rarefaction was first produced, and then well-dried air, i.e. air passed through a dryer, was slowly admitted. This operation was repeated several times.

2) When the apparatus had been well dried, the liquid under investigation was poured into vessel \(B\) in such a way that the level of the liquid was approximately two centimeters above the surface of the garnets.

3) Into the same vessel \(B\), as shown in Figure (13), two thermometers with shortened scales were placed so that one of them was immersed in the liquid—its bulb almost touched the garnets; the other was placed in the vapor several millimeters above the level of the liquid. The mean of the readings of the one and the other thermometer was taken as the boiling temperature.

Both thermometers had a shortened scale divided into \(0.2^\circ\). They were carefully compared with one another and verified at the Reichsanstalt. After the completion of the experiments they were sent a second time to the Reichsanstalt and checked once again, so that no doubt could remain as to the correctness of their readings.

4) Heating of vessel \(B\) was carried out on an asbestos dish with a Bunsen burner, reducing the flame as much as possible. To avoid heat losses by radiation, vessel \(B\) was wrapped to the top with asbestos cord, insofar as this did not interfere with observation of the thermometer scale.

5) When the apparatus had been finally prepared for the experiments, mercury was poured into the traps and the desired rarefaction was produced by means of the pump. Having turned cock \(D\) so as to disconnect the apparatus from the pump, and having loosened clamp \(K\) sufficiently for a weak current of air to be established into vessel \(B\) (the air had previously been passed through a bottle with a strong solution of caustic potash), vessel \(B\) was carefully heated.

6) When the liquid boiled with a key, the readings were taken in the following order:

1) the upper and lower levels of mercury in the right-hand vacuum gauge \(Br\) were read; 2) the temperature of both thermometers in vessel \(B\); 3) the upper and lower levels of mercury in the left-hand vacuum gauge \(Bl\); 4) the barometer, showing the atmospheric pressure and placed in the same room where the experiments were performed; 5) the upper and lower levels of mercury in vacuum gauge \(Br\); 6) the readings of both thermometers in vessel \(B\); 7) the upper and lower levels of mercury in vacuum gauge \(Bl\).

Thus the pressure in the apparatus was measured four times and the temperature twice (four readings). Since the pressure in the apparatus, owing to the fact that air entered through the capillary, slowly but continuously increased, all the readings differed somewhat from one another—they gave a picture of the relation between temperature and pressure for a certain interval of time. To obtain the final number, I took the arithmetical mean of all the observations. In this way the separate observations supplemented one another and there was assurance that the mean number was close to the truth.

I made the readings of the mercury levels in the tubes by the naked eye or with the aid of a magnifying glass, the tenths of a millimeter being estimated by eye. It was not possible to measure the mercury column more accurately, for example with a cathetometer, since the mercury column was continuously falling and, owing to the shocks of boiling, oscillated up and down. The comparative inaccuracy of the individual readings was compensated for by their number.

It goes without saying that all heights of mercury columns were reduced to \(0^\circ\).

The temperature readings were likewise made by the naked eye or with the aid of a magnifying glass. These readings could be made only with an accuracy of \(0.1^\circ\), since the temperature rose comparatively rapidly and continuously.

7) When all seven readings had been made, dry air was admitted into the apparatus, by means of the three-way cock \(D\), until a new pressure was established in the apparatus; when the liquid again began to boil, a series of readings was made in the previous order, air was again admitted into the apparatus, etc.

8) When the series of observations of the vapor pressure at different temperatures for the given solution had been completed, I disassembled the apparatus, assembled it again, charged it with a solution of another concentration, and made a new series of observations.

Measurement of the vapor pressure of water. In order to test the apparatus, i.e. to make sure whether it had been well assembled and whether it worked correctly, a series of measurements of the vapor pressure of water was made.

The water used for the experiment was purified by the method of Harry C. Jones and Mackay¹, which, because of its simplicity and expediency, can be especially

recommend the following. Ordinary distilled water was boiled in a flask, to which a small quantity of potassium permanganate and sulfuric acid had been added. The vapors were led into an inverted retort containing caustic potassium hydroxide and a little potassium permanganate. In the neck of the retort was placed a stopper made of platinum mesh, serving as a drop-catcher. This stopper was held in place by a constriction made in the neck of the retort. Into the same neck of the retort, by means of asbestos paper, the tin tube of the condenser was tightly fitted. Before use this tube had been thoroughly steamed with hot steam from distilled water, generated in a separate boiling flask. The first and last thirds of the distillate were discarded. The collected distillate was kept in a bottle made of a special sort of glass not attacked by water (Resistenzglas).

Water purified in this way had an exactly neutral reaction, and in solution contained neither mineral nor organic substances, nor carbon dioxide. Its electrical conductivity, determined by me many times, varied within the limits:

\[ 1.482 \times 10^{-6} \text{--} 2.109 \times 10^{-6}. \]

The results of observations of the elasticity of the vapor of this water, carried out in the apparatus described, are given in Tables LXXX--LXXXII.

In Table LXXX the observations are given in the order in which they were made.

In the columns under the symbols \(V_{\mathrm{abs.}}\ R\), \(V_{\mathrm{abs.}}\ L\), are given the heights of mercury in the right and left tubes which served for measuring the pressure in the apparatus. Under the symbol Bar. Athm. are the heights of the barometer that measured the atmospheric pressure at the moment of the experiment. All readings of the heights of mercury are reduced to \(0^\circ\).

Under the symbols \(t^0\) liquid, \(t^0\) vapor are given the readings of two thermometers: one in the liquid, the other in the vapor. The readings of both thermometers are corrected according to the certificate of the Reichsanstalt.

Under the symbols \(t^0\) mean, Pressure mean are given the arithmetic means of the temperature and pressure.

Table LXXX.

Boiling temperatures of water at pressures of 88.5--146.9 mm.

\(V_{\mathrm{abs.}}\ R\)	\(t^0\) liquid	\(t^0\) vapor	\(V_{\mathrm{abs.}}\ L\)	\(V_{\mathrm{abs.}}\ R\)	\(t^0\) liquid	\(t^0\) vapor	\(V_{\mathrm{abs.}}\ L\)	Bar. Athm.	\(t^0\) mean	Pressure mean
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	mm.
658,9	48,9	49,0	658,3	657,9	49,2	49,2	657,2	746,4	49,07	88,5
654,1	50,0	50,0	653,5	653,4	50,2	50,2	653,4	746,4	50,1	92,61
652,0	50,6	50,5	650,6	651,0	50,8	50,7	650,2	746,7	50,65	95,75
647,2	51,55	51,6	646,0	646,7	51,65	51,7	645,5	746,7	51,62	100,35
642,2	52,4	52,3	642,2	640,2	52,5	52,4	641,2	746,2	52,4	104,7
640,6	52,8	52,7	639,8	640,1	52,8	52,75	639,4	746,4	52,8	106,4
637,1	53,2	53,2	637,1	636,2	53,4	53,4	636,2	746,1	53,3	109,4

Vac. R	\(t^0\) liquid	\(t^0\) vapor	Vac. L	Vac. R	\(t^0\) liquid	\(t^0\) vapor	Vac. L	Bar. Atm.	\(t^0\) mean	Pressure, mean
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	mm.
636,0	53,6	53,6	635,2	635,8	53,6	53,7	635,0	746,2	53,6	110,7
632,3	54,3	54,3	632,3	632,0	54,4	54,4	631,1	746,1	54,35	114,1
628,2	54,9	54,9	628,1	627,2	55,0	55,1	—	745,9	55,0	118,2
623,2	55,4	55,4	623,2	622,8	55,5	55,6	622,8	744,4	55,5	121,4
623,5	55,8	55,7	623,3	622,8	55,85	55,9	622,3	746,0	55,8	123,0
619,0	56,3	56,2	618,1	618,0	56,4	56,3	617,2	744,2	56,3	126,1
617,6	56,65	56,7	617,4	617,1	56,8	56,8	617,0	745,9	56,8	128,6
612,2	57,45	57,45	611,7	612,0	57,45	57,45	611,2	744,2	57,45	132,4
612,1	57,55	57,55	612,1	611,3	57,7	57,65	611,1	745,8	57,6	134,1
608,0	58,05	58,05	607,2	607,3	58,15	58,05	606,7	744,1	58,1	136,8
606,6	58,45	58,45	606,3	606,2	58,5	58,5	606,2	745,8	58,5	139,5
603,7	58,65	58,65	602,8	602,8	58,75	58,75	602,3	743,8	58,7	140,9
602,2	59,15	59,15	602,0	602,2	59,15	59,15	602,0	745,8	59,2	143,7
600,5	59,15	59,15	590,7	600,1	59,15	59,2	599,2	743,7	59,2	143,8
599,7	59,55	59,55	599,0	598,9	59,65	59,65	598,2	745,8	59,6	146,9

In Tables LXXXI and LXXXII the results obtained are compared with the values of the vapor pressure of water according to Regnault, taken from the Physikalisch-Chemische Tabellen, Landolt und Börnstein.

In Table LXXXI the pressures corresponding to the observed temperatures are compared.

In Table LXXXII the temperatures corresponding to the observed pressures are compared¹.

Comparison of experimentally found values of the vapor pressure of water with Regnault’s data.

Table LXXXI.

Vapor temperature	Our data	Regnault’s data	Difference
°C.	mm.	mm.	mm.
49,1	88,5	87,93	+0,57
50,1	92,7	92,44	+0,26
50,65	95,7	94,99	+0,71
51,2	98,5	97,63	+0,9
51,6	100,3	94,99	+0,87
52,4	104,6	103,57	+1,03
52,8	106,4	105,62	+0,78
53,3	109,4	108,23	+1,17
53,6	110,7	109,82	+0,80
54,35	114,1	113,88	+0,22
55,0	118,2	117,52	+0,68
55,5	121,4	120,37	+1,03
55,8	123,0	122,12	+0,9
56,3	126,1	125,07	+1,03
56,8	128,6	128,07	+0,53
57,45	132,4	132,10	+0,30
57,6	134,1	133,04	+0,96
58,1	136,8	136,2	+0,6
58,5	139,5	138,8	+0,7
58,7	140,9	140,1	+0,8
59,2	143,7	143,43	+0,27
59,2	143,8	143,43	+0,37
59,6	146,9	146,14	+0,76

Table LXXXII.

Pressure	Vapor temperature observed by us	Vapor temperature according to Regnault	Difference
mm.	°C.	°C.	°C.
88,5	49,1	49,25	−0,15
92,7	50,1	50,15	−0,05
95,7	50,65	50,8	−0,15
98,5	51,2	51,4	−0,2
100,3	51,6	51,75	−0,15
104,6	52,4	52,6	−0,2
106,4	52,8	52,95	−0,05
109,6	53,3	53,55	−0,25
110,8	53,6	53,75	−0,05
114,1	54,35	54,4	−0,05
118,2	55,0	55,15	−0,15
121,4	55,5	55,67	−0,12
123,0	55,8	55,95	−0,15
126,1	56,3	56,47	−0,17
128,6	56,8	56,9	−0,10
132,4	57,45	57,5	−0,05
134,1	57,6	57,75	−0,05
136,8	58,1	58,2	−0,10
139,5	58,5	58,63	−0,13
140,9	58,7	58,83	−0,13
143,7	59,2	59,25	−0,05
143,8	59,2	59,25	−0,05
146,9	59,6	59,7	−0,10

To clarify how, in general, the observations of different observers on the vapor pressure differ from one another, and consequently also for a comparative evaluation of the results obtained by me, Tables LXXXIII and LXXXIV give and compare with one another the old observations on the vapor pressure of water by Wüllner¹) and the more recent ones by D. Konovalov.²)

Both observers worked by the barometric method.

Table LXXXIII.

Vapor pressure of water according to Wüllner’s experiments.

Temperature	Pressure	Pressure	Difference
°C.	Wüllner, mm.	Regnault, mm.	mm.
19,9	16,69	17,28	−0,59
24,2	22,25	22,46	−0,21
29,9	30,66	31,36	+0,30
35,0	41,49	41,72	−0,23
40,9	57,61	57,61	−0,00
44,8	70,49	70,67	−0,18
48,4	84,62	84,36	+0,26
49,8	90,14	91,00	+0,14
52,5	103,56	104,49	−0,93
54,1	110,61	112,39	−1,78
57,9	134,24	134,72	−0,48
61,2	156,61	157,29	−0,68
68,7	219,89	220,28	−0,39
72,2	257,00	256,30	+0,70
82,3	391,90	389,12	+2,78

Table LXXXIV.

Vapor pressure of water according to D. Konovalov’s experiments.

Temperature	Pressure	Pressure	Difference
°C.	Konovalov, mm.	Regnault, mm.	mm.
16,5	13,7	13,9	−0,2
26,4	25,4	25,5	−0,1
40,4	56,5	56,0	+0,5
50,25	92,9	93,1	−0,2
59,2	142,8	143,4	−0,6
70,7	239,8	240,5	−0,7
80,25	359,4	361,4	−2,0
90,0	523,4	525,5	−2,1
91,25	549,9	551,4	−1,5

The comparison presented permits the conclusion that the numbers obtained by me lie within the limits of the errors generally inherent in observations—

¹) Wüllner, Pogg. Ann. 13, 541. 1858.
²) Konovalov, Zh. R. Phys.-Chem. Soc. 21, 31. 1889.

of this kind, and agree with the numbers found by the barometric method.

Interpolation of the experimental data. In order to smooth the errors of individual observations and to obtain a probable mean, the data obtained, both in this and in all other cases, were adjusted by graphical interpolation according to the method developed by Prof. Kohlbaum¹.

This method consists in the following. The numerical data are plotted on paper with a millimeter grid. Pressures \((p)\) are laid off along the abscissa axis, and temperatures along the ordinate axis. From a whole group of curved rulers prepared in advance, each about one meter long², one is selected whose curvature would fit the assumed curve. The ruler is applied so that the direction of its curvature coincides with the direction of the course of the greatest possible number of points plotted on the paper. Then the curve is drawn with a very fine pencil.

When such a curve has been drawn, a single glance is enough immediately to see gross errors of observation and to assess the accuracy of the method. Indeed, if the observations have been made well, the marked points lie either on the curve itself or very close to it, on one side or the other of the curve. Gross errors lie far outside the curve. Finally, the greater or lesser distance of the observation points from the curve assesses the accuracy of the observations and the accuracy of the method employed.

In Table LXXXV the elasticities found experimentally and the elasticities read from the curve are compared for the same temperatures.

Table LXXXV.

Comparison of the experimental data with the numbers read from the curve.

Temperature, °C	Pressure — Experiment, mm	Pressure — On the curve, mm	Difference, mm
49,07	88,5	88,5	0
50,1	92,6	93,1	+0,5
50,65	95,75	95,5	+0,25
51,62	100,35	100,4	−0,05
52,4	104,7	104,4	+0,3
52,8	106,4	106,4	0
53,3	109,4	109,1	+0,3
53,6	110,7	110,7	0
54,35	114,1	113,9	+0,3
55,0	118,2	118,2	0
55,5	121,4	121,1	+0,3
55,8	123,0	122,8	+0,2
56,3	126,1	125,7	+0,4
56,8	128,6	128,7	−0,1
57,45	132,4	132,4	0
57,60	134,1	133,7	−0,5
58,1	136,8	137,0	−0,2
58,5	139,5	139,7	−0,2
58,7	140,9	150,0	−0,1
59,2	143,7	144,2	−0,5
59,2	143,8	144,2	−0,5
59,6	146,9	147,0	−0,1

As we see, the observations lie on both sides of the curve and at the same time are very close to the curve. The difference of 0.1–0.5 mm lies within the limits of the error in reading the temperature, since at the temperature at which the observations were made (50°–60°), a difference in pressure of 0.5 mm corresponds to a temperature difference of 0.1°.

In Table LXXXVI the numerical values of the vapor pressure obtained by me, interpolated for whole degrees from the plotted curve, are compared with the values of the vapor pressure of water taken, for the same temperatures, from the Tabellen of Landolt and Börnstein.

Table LXXXVI.

Comparison of the interpolation data with Regnault’s figures.

Temperature	Pressure	Pressure	Difference
°C.	According to my curve, mm.	According to the tables, mm.	mm.
49,0	88,1	87,488	+0,6
49,5	90,4	89,709	+0,7
50,0	92,6	91,978	+0,6
50,5	95,0	94,297	+0,7
51,0	97,4	96,664	+0,8
51,5	99,9	99,08	+0,8
52,0	102,3	101,55	+0,8
52,5	104,9	104,078	+0,8
53,0	107,5	106,65	+0,9
53,5	110,0	109,286	+0,7
54,0	112,8	111,973	+0,9
54,5	115,5	114,76	+0,8
55,0	118,2	117,516	+0,7
55,5	121,0	120,375	+0,6
56,0	124,0	123,292	+0,7
56,5	126,9	126,270	+0,6
57,0	130,0	129,310	+0,7
57,5	133,0	132,411	+0,6
58,0	136,3	135,57	+0,7
58,5	139,6	138,8	+0,8
59,0	142,9	142,09	+0,8

Table LXXVI clearly proves that the curve I have plotted runs parallel to the actual (according to Regnault) curve of the vapor pressure of water, only somewhat higher. The pressures read from my curve are always higher, and moreover always by almost one and the same amount, on average 0.7 mm.

Obviously, a systematic error had crept into my experiments. The source of the error could not have been the thermometers, since they had been carefully calibrated. Nor could it have been the barometer that measured the atmospheric pressure, since it had been carefully compared with the barometer of the Physical Institute. Only the scale marked on the vacuometric tubes that served for measuring the pressure in the apparatus had not been checked. It is possible that the source of the error must be sought here.

Since the same error also occurred in measuring the vapor pressure of solutions, I considered it unnecessary to introduce the corresponding correction.

Measurement of the vapor pressure of aqueous sugar solutions. From the example of the measurement of the vapor pressure of water it is evident that the apparatus gives satisfactory results when working with pure liquids. The measurements below will show that the same results are obtained for solutions as well.

In order to reduce to the smallest possible minimum the error from a change in the concentration of the solution owing to the fact that part of the solvent passes into the vapor state, rather large quantities of solution were taken for each experiment, namely 150–200 g each time. With such a comparatively large mass of solvent, the concentration of the solution, as a consequence of evaporation, could not change appreciably, and it could be hoped that this change in concentration would not noticeably affect the observed pressure. The comparison given below of the numbers obtained with those of other authors did indeed show that the error due to the change in concentration of the solution during the experiment does not exceed the other errors of the method, and there is no real need to analyze the solution during or after the experiment.

The material for the investigation, cane sugar \(C_{12}H_{22}O_{11}\), was obtained from the firm C. A. F. Kahlbaum in Berlin.

It was purified in the following way: a strong aqueous solution of sugar was poured into absolute alcohol. On the following day a very fine powder precipitated, which was filtered off and dried in a desiccator. It contained no ash. The water was purified by the method described above.

The solutions were prepared by weighing sugar and water in flasks with ground-glass stoppers. A correction was made for the loss of weight in air.

The results of the measurements are presented in the form of tables. In table \(A\), for each solution, the direct experimental data are summarized, i.e. the observed boiling temperatures at the observed pressure. Table \(B\) contains: 1) the values of the pressure read from the interpolation curve, plotted as described above; 2) the ratio \(\frac{p_1}{p_0}\), where \(p_1\) is the vapor pressure of the solution, \(p_0\) the vapor pressure of pure water; the value \(p_1\) was read from the interpolation curve for the solution, \(p_0\) from the interpolation curve constructed by me with the same apparatus for water; 3) the difference between the found value \(\frac{p_1}{p_0}\) and the arithmetic mean of all values of \(\frac{p_1}{p_0}\) found for the given solution.

The concentration of the solution is expressed by the content of sugar in 100 parts by weight of the solution (%).

Table LXXXVII A.

Boiling temperatures of a 4.478% sugar solution at pressures of 98.3–151.5 mm.
(experimental data).

Vac. R	\(t^0\) liq.	\(t^0\) vap.	Vac. L	Vac. R	\(t^0\) liq.	\(t^0\) vap.	Vac. L	Bar. Atm.	\(t^0\) mean	Pressure mean
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	mm.
646,1	51,2	51,2	646,6	645,7	51,4	51,4	645,5	744,3	51,3	98,3
638,6	52,7	52,7	639,0	638,4	52,9	52,8	638,4	744,3	52,77	105,7
632,8	53,8	53,9	632,9	632,0	54,0	54,0	632,4	744,3	53.92	111.8
627,4	54,6	54,7	627,9	626,6	54,9	54,9	627,0	744,2	54,77	117,0
621,6	55,8	55,7	621,9	621,4	55,8	55,9	621,4	744,2	55,80	122,65
614,3	56,9	56,8	614,3	613,8	57,0	56,9	613,8	743,1	56,90	129,15
607,4	58,05	58,05	607,5	606,7	58,05	58,05	607,1	743,2	58,05	136,05
601,3	58,95	58,95	601,3	600,3	59,05	59,05	600,7	743,4	59,00	142,50
596,1	59,65	59,65	596,1	595,6	59,70	59,75	595,6	743,3	59,68	147,55
592,3	60,25	60,25	592,3	591,4	60,35	60,45	591,6	743,3	60,30	151,5

Table LXXXVII B.

Vapor pressure of a 4.478% sugar solution at temperatures of 51°–58° C.
(interpolated data).

Temperature	Pressure	\(\dfrac{p_1}{p_0}\)	Difference
°C.	mm.	—	—
51,0	96,8	0,998	0
51,5	99,4	0,996	−0,002
52,0	102,0	0,998	0
52,5	104,5	0,997	−0,001
53,0	107,0	0.997	−0,001
53,5	109,7	0,996	−0,002
54,0	112,5	0,997	−0,001
54,5	115,2	0,996	−0,002
55,0	117,8	0,998	0
55,5	120,9	0,997	−0,001
56,0	123,8	0,998	0
56,5	126,8	0,998	0
57,0	129,8	0,999	+0,001
57,5	132,9	0,999	+0,001
58,0	136,0	0,999	+0,001
		mean. 0,998

Table LXXXVIII A.

Boiling temperatures of an 11.50% sugar solution at pressures of 83.8–141.4 mm.

(experimental data).

Vessel R	\(t^0\) liq.	\(t^0\) vapor	Vessel L	Vessel R	\(t^0\) liq.	\(t^0\) vapor	Vessel L	Bar. Atm.	\(t^0\) mean	Mean pressure
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	mm.
660,6	48,0	—	660.6	660,4	48,0	—	660,4	744,3	48,0	83,8
653,8	49,6	49,6	653,5	653,0	49,7	49,7	652,8	744,3	49,6	91.05
645,5	51,4	51,4	645,6	644,3	51,6	51,6	644,6	744,2	51,5	99.2
633,4	53,8	53,8	633,3	632,3	54,0	53,9	632,3	744,0	53.9	111,0
623,3	55,6	55,6	623,4	622,3	55,8	55,7	622,4	743,9	55,7	121,1
612,2	57,55	57,45	612,0	610,8	57,65	57,55	610,9	744,0	57,55	132.5
602,7	58,95	58,85	602,7	601,2	58,95	58,95	601,3	746,3	58,95	141,4

Table LXXXVIII B.

Vapor tension of an 11.50% sugar solution at temp. 49°–53.5° C.

(interpolated data).

Temperature	Pressure	\(\dfrac{p_1}{p_0}\)	Difference	Temperature	Pressure	\(\dfrac{p_1}{p_0}\)	Difference
°C.	mm.	—	—	°C.	mm.	—	—
49,0	88,0	0,998	+0,006	54,0	111,7	0,990	—0,002
49,5	90,2	0,998	+0,006	54,5	114,3	0,989	—0,003
50,0	92,5	0,998	+0,006	55,0	117,0	0,992	0
50,5	94,6	0,996	+0,004	55,5	119,8	0,989	—0,003
51,0	96.9	0,995	+0,003	56,0	122,6	0,988	—0,004
51,5	99,2	0,994	+0,002	56,5	125,5	0,989	—0,003
52,0	101,5	0,993	+0,001	57,0	128,6	0,991	—0,001
52,5	104,0	0,992	0	57,5	131,8	0,993	+0,001
53,0	106,5	0,993	+0,001		mean	0,992
53,5	109,0	0,990	+0,002

Table LXXXIX A.

Boiling temperatures of a 14.14% sugar solution at pressures of 85.6–143.8 mm.

(Experimental data).

Vac. R	\(t^\circ\) liq.	\(t^\circ\) vapor	Vac. L	Vac. R	\(t^\circ\) liq.	\(t^\circ\) vapor	Vac. L	Bar. Atm.	\(t^\circ\) mean	Vapor pressure
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	mm.
656,8	48,6	48,55	655,6	—	—	—	—	738,7	48,57	85,6
648,5	49,7	49,7	648,1	648,0	49,8	49,8	647,6	738,6	49,75	90,25
644,9	50,5	55,5	644,4	644,4	50,5	50,5	644,0	738,4	50,5	94,2
640,8	51,35	51,35	639,9	640,1	51,4	51,4	639,8	738,5	51,37	98,7
636,6	52,2	52,2	636,1	635,8	52,25	52,25	635,7	738,5	52,22	102,9
629,8	53,50	53,5	629,6	629,7	53,60	53,6	629,0	738,5	53,55	109,35
626,8	53,9	54,0	626,3	626,3	54,0	54,1	625,8	738,0	54,0	111,7
622,8	54,6	54,55	622,4	622,6	54,7	54,75	621,8	737,9	54,67	115,5
620,2	55,1	55,1	619,8	619,8	55,1	55,1	619,8	738,0	55,1	118,0
615,8	55,9	55,9	615,3	615,3	55,95	56,0	615,0	737,9	55,93	122,55
609,7	57,0	57,0	609,3	609,4	57,05	57,1	609,0	737,9	57,04	128,55
603,8	57,95	57,95	603,6	603,7	57,95	57,95	602,9	738,0	57,95	134,50
597,9	58,85	58,85	597,4	597,7	58,9	58,85	597,1	738,0	58,85	140,5
594,7	59,35	59,25	594,1	594,2	59,45	59,35	593,9	738,0	59,35	143,8

Table LXXXIX B.

Vapor pressure of a 14.14% sugar solution at temp. 49°—58° C.
(interpolated data).

Temperature	Pressure	$\dfrac{p_1}{p_0}$	Difference
°C.	mm.	—	—
49.0	87.4	0.991	0
49.5	89.5	0.990	−0.001
50.0	91.85	0.990	−0.001
50.5	94.1	0.990	−0.001
51.0	96.6	0.992	+0.001
51.5	98.9	0.992	+0.001
52.0	101.4	0.992	+0.001
52.5	103.9	0.992	+0.001
53.0	106.6	0.994	+0.003
53.5	109.2	0.992	+0.001
54.0	111.9	0.992	+0.001
54.5	114.8	0.993	+0.002
55.0	116.9	0.991	0
55.5	119.8	0.989	−0.003
56.0	122.8	0.990	−0.001
56.5	125.6	0.989	−0.002
57.0	128.7	0.990	−0.001
57.5	131.8	0.991	0
58.0	135.0	0.992	+0.001
		avg. 0.991

Table XC A.

Boiling temperatures of a 21.06% sugar solution at pressures
89.45–147.80 mm.

(experimental data).

Vac. R	t° liquid	t° vapor	Vac. L	Vac. R	t° liquid	t° vapor	Vac. L	Bar. Atm.	t° mean	Mean pressure
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	mm.
653,2	49,4	49,5	652,1	652,2	49,6	49,6	651,3	742,0	49,52	89,45
646,3	51,0	51,0	645,2	645,4	51,15	51,15	644,9	741,8	51,10	96,4
641,0	52,1	52,05	640,2	640,7	52,1	52,05	640,2	741,6	52,07	101,1
635,2	53,1	53,2	635,0	635,1	53,2	53,3	634,2	741,5	53,2	106,6
629,3	54,0	54,1	628,7	628,9	54,1	54,2	628,2	740,3	54,1	111,5
623,1	55,1	55,1	622,4	622,9	55,2	55,3	621,9	740,3	55,2	117,75
617,0	56,1	56,1	616,5	616,5	56,2	56,2	615,9	739,8	56,15	123,35
610,0	57,25	57,3	609,8	609,8	57,3	57,3	609,4	739,8	57,3	130,05
603,9	58,25	58,25	603,8	603,9	58,25	58,25	603,8	739,7	58,25	135,9
601,1	58,65	58,75	600,4	600,8	58,75	58,85	600,0	739,8	58,75	139,25
695,2	59,55	59,55	594,8	595,0	59,55	59,65	594,5	739,8	59,60	144,95
592,0	59,95	59,95	591,8	592,0	59,95	59,95	591,8	739,7	59,95	147,80

Table XC B.

Vapor pressure of a 21.06% sugar solution at temperatures 49°–58° C.
(interpolated data).

Temperature	Pressure	$\dfrac{r_1}{r_0}$	Difference
°C	mm.	—	—
49,0	87,0	0,986	+0,003
49,5	89,1	0,986	+0,003
50,0	91,3	0,985	+0,002
50,5	93,6	0,985	+0,002
51,0	95,85	0,984	+0,001
51,5	98,2	0,984	+0,001
52,0	100,5	0,984	+0.001
52,5	103,0	0,984	+0,001
53,0	105,5	0,984	+0,001
53,5	108,0	0,981	−0,002
54,0	110,8	0,981	−0,002
54,5	113,35	0,980	−0,003
55,0	116,1	0,984	+0,001
55,5	119,0	0,982	−0,001
56,0	121,8	0,981	−0,002
56,5	124,6	0,981	−0,002
57,0	127,7	0,982	−0,001
57,5	130,3	0,980	−0,003
58,0	134,4	avg. 0,983

Table XCI A.

Boiling temperatures of a 38.84% sugar solution at pressures of
94.55–137.55 mm.

(experimental data).

Vac. R, mm.	\(t^\circ\) liquid, °C	\(t^\circ\) vapor, °C	Vac. L, mm.	Vac. R, mm.	\(t^\circ\) liquid, °C	\(t^\circ\) vapor, °C	Vac. L, mm.	Bar. Atm., mm.	\(t^\circ\) mean, °C	Mean pressure, mm.
649,2	50,0	50,05	649,0	648,7	50,1	50,15	648,5	738,3	—	—
643,9	51,2	51,2	643,4	643,4	51,25	51,3	643,3	738,1	51,23	94,55
641,1	51,8	51,8	640,8	640,6	51,85	51,9	640,6	738,0	51,83	97,25
635,7	52,85	52,9	635,7	635,3	53,0	53,0	635,4	738,0	52,94	102,5
632,3	53,4	53,4	631,7	631,3	53,5	53,5	631,2	736,8	53,45	105,2
625,4	54,6	54,55	624,9	625,4	54,6	54,6	624,9	736,5	54,60	111,25
620,2	55,5	55,5	619,8	619,8	55,6	55,5	619,8	736,3	55,52	116,45
614,2	56,6	56,6	613,7	613,7	56,6	56,7	613,4	736,2	56,62	122,45
611,1	57,1	57,15	610,3	610,7	57,2	57,2	609,9	736,2	57,16	125,75
607,3	57,85	57,85	606,3	606,5	57,85	57,85	606,0	736,1	57,85	129,6
603,4	58,35	58,35	602,7	603,3	58,4	58,35	602,7	736,1	58,36	133,15
599,4	59,05	59,05	598,4	598,6	59,15	59,05	597,9	736,1	59,10	137,55

Table XCI B.

Vapor pressure of a 38.84% sugar solution at temp. 50°–59° C.
(interpolated data).

Temperature	Pressure	$\dfrac{p_1}{p_0}$	Difference
°C.	mm.	—	—
50.0	89.0	0.960	+0.001
50.5	91.1	0.959	0
51.0	93.5	0.960	+0.001
51.5	95.8	0.960	0
52.0	98.2	0.961	+0.002
52.5	100.6	0.960	0
53.0	103.1	0.961	+0.002
53.5	105.7	0.960	+0.001
54.0	108.3	0.959	0
54.5	110.9	0.959	0
55.0	113.5	0.962	+0.003
55.5	116.2	0.959	0
56.0	118.9	0.958	−0.001
56.5	121.8	0.958	−0.001
57.0	124.6	0.959	0
57.5	127.5	0.959	0
58.0	130.2	0.957	−0.002
58.5	133.6	0.963	+0.004
59.0	136.7	0.959	0
		avg. 0.959

Table XCII A.

Boiling temperatures of a 46.74% sugar solution at pressures of 83.15–138.5 mm.

(experimental data).

Vac. R	\(t^\circ\) liq.	\(t_0\) vapor	Vac. L	Vac. R	\(t^\circ\) liq.	\(t^\circ\) vapor	Vac L	Bar. Atm.	\(t^\circ\) mean	Pressure mean
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	mm.
655,5	48,8	48,8	655,1	655,3	48,9	48,9	655,4	738,2	48,85	83,15
649,3	50,4	50,4	648,1	648,8	50,5	50,5	648,1	738,2	50,45	89,6
644,5	51,4	51,4	644,3	644,5	51,5	51,5	644,1	738,4	51,45	94,05
640,4	52,4	52,4	639,7	640,0	52,5	52,5	639,3	738,6	52,45	98,15
636,5	53,2	53,2	636,4	636,4	53,3	53,3	636,3	738,7	53,25	102,35
633,4	53,85	53,9	633,3	633,0	54,0	54,0	632,8	738,8	53,94	105,7
629,5	54,8	54,7	629,3	629,4	54,85	54,8	628,8	740,0	54,79	110,5
624,9	55,65	55,7	624,4	624,4	55,7	55,7	624,3	740,0	55,71	115,55
621,5	56,2	56,2	621,2	621,3	56,3	56,3	620,7	740,1	56,25	118,95
610,8	57,05	57,15	616,4	616,5	57,15	57,25	616,0	740,2	57,15	123,8
613,6	57,70	57,75	613,0	613,1	57,85	57,85	612,6	740,2	57,79	127,15
610,2	58,30	58,30	609,4	609,2	58,45	58,45	608,9	740,2	58,37	130,3
605,1	59,25	59,25	604,2	604,5	59,25	59,25	608,8	740,2	59,25	135,7
601,7	—	59,65	601,7	601,7	—	59,65	601,75	740,2	59,65	138,5

Table XCII B.

Vapor pressure of a 46.74% sugar solution, at temp. 49°–59° C.

(interpolated data).

Temperature	Pressure	$\dfrac{p_1}{p_0}$	Difference
°C	mm.	---	—
49.0	83.6	0.948	+0.006
49.5	85.6	0.948	+0.006
50.0	87.6	0.945	+0.003
50.5	90.0	0.948	+0.006
51.0	91.8	0.942	0
51.5	94.0	0.942	0
52.0	96.2	0.942	0
52.5	98.4	0.939	−0.003
53.0	101.0	0.941	−0.001
53.5	103.5	0.940	−0.002
54.0	106.0	0.939	−0.003
54.5	108.5	0.939	−0.003
55.0	111.1	0.941	−0.001
55.5	114.1	0.941	−0.001
56.0	117.1	0.944	+0.002
56.5	119.5	0.940	0
57.0	122.2	0.940	−0.002
57.5	125.0	0.940	−0.002
58.0	128.0	0.941	−0.001
58.5	131.0	0.945	+0.003
59.0	134.3	0.942	0
		mean 0.942

Table XCIII A.

Boiling temperatures of a 52.31% sugar solution at pressures of 85.80–129.50 mm.

(experimental data).

Vac. R	\(t^\circ\) liq.	\(t^\circ\) vapor	Vac. L	Vac. R	\(t^\circ\) liq.	\(t^\circ\) vapor	Vac. L	Bar. Atm.	\(t^\circ\) mean	Mean pressure
mm.	°C.	°C.	mm.	mm.	°C.	°C.	mm.	mm.	°C.	°C.
657,0	50,0	50,0	656,1	656,5	50,05	50,05	656,0	742,2	50,02	85,80
652,4	51,05	51,0	652,0	652,3	51,10	51,10	651,6	742,2	51,05	90,10
647,3	52,0	52,0	647,0	647,2	52,1	52,1	636,9	742,2	52,05	95,15
644,6	52,7	52,7	644,2	644,4	52,7	52,7	644,0	742,2	52,7	97,90
638,2	53,7	53,8	637,6	637,9	53,8	53,9	637,5	741,0	53,80	103,2
634,1	54,6	54,6	631,3	633,6	54,6	54,6	633,3	741,0	54,6	107,45
630,6	55,3	—	630,1	630,1	55,3	—	629,9	741,1	55,3	110,95
625,9	56,1	56,1	625,4	625,6	56,1	56,1	625,3	741,0	56,1	115,5
622,4	56,6	—	622,4	622,4	56,65	56,7	622,3	741,0	56,61	118,65
619,2	57,2	—	618,9	619,2	57,2	—	618,8	740,8	57,2	121,8
615,4	57,85	57,85	614,8	615,2	57,85	57,85	614,8	740,7	57,85	125,65
611,3	58,55	58,55	611,2	611,3	58,55	58,55	611,0	740,7	58,55	129,5

Table XCIII B.

Vapor pressure of a 52.31% sugar solution at temp. 50°—57.5 C°.

(interpolated data).

Temperature	Pressure	$\dfrac{p_1}{p_0}$	Difference
°C	mm.	--	—
50.0	85.8	0.926	+ 0.001
50.5	87.9	0.925	0
51.0	90.1	0.925	0
51.5	92.3	0.925	0
52.0	94.6	0.926	+ 0.001
52.5	96.9	0.925	0
53.0	99.4	0.926	+ 0.001
53.5	101.8	0.925	0
54.0	104.4	0.925	0
54.5	106.9	0.925	0
55.0	109.5	0.928	+ 0.003
55.5	112.0	0.924	− 0.001
56.0	114.9	0.926	+ 0.001
56.5	117.8	0.927	+ 0.002
57.0	120.8	0.929	+ 0.004
57.5	123.8	0.930	+ 0.005
		avg. 0.925

The vapor pressure of stronger solutions was not measured, since it was observed that the solution containing 60.30% sugar changed during the experiment, namely, it turned yellow and precipitated a sediment. I considered it superfluous to present the data obtained for this solution. Less concentrated solutions apparently do not change during the time over which the experiment continues.

From the measurement results given above it is evident that the ratio $\dfrac{p_1}{p_0}$, i.e. the relative magnitude of the vapor pressure of the solution, for different temperatures within the limits of $50^\circ$–$60^\circ C$ of the experiment, fluctuates very little to one side or the other around a certain mean value. With the accuracy with which the observations were made, these fluctuations must be regarded as the result of observational errors, and the ratio $\dfrac{p_1}{p_0}$ may be taken as independent of temperature. Consequently, Babo’s law is, of course with a certain approximation, confirmed also for aqueous sugar solutions.

I took the ratio $\dfrac{p_1}{p_0}$ to be independent of temperature and used this quantity for characterizing the vapor pressure of sugar solutions.

In Table XCIV the concentrations of sugar solutions are compared with the values $\dfrac{p_1}{p_0}$ obtained directly by experiment. From these data a curve was constructed.

In Table XCV the concentrations of sugar solutions are compared with the corresponding values $\dfrac{p_1}{p_0}$ read from the curve.

The concentrations are expressed by the content of grams of sugar in 100 grams of solution ($\pi\%$) and by the number of gram-molecules of sugar in 1000 grams of water ($n$).

Table XCIV.

Vapor pressure of aqueous sugar solutions, referred to the vapor pressure of water at the same temperature.

(experimental data).

Concentration	Concentration	$\dfrac{p_1}{p_0}$
$\pi\%$	$n$	—
4,478	0,1370	0,998
11,50	0,3800	0,992
14,14	0,4817	0,991
21,06	0,7801	0,983
38,84	1,856	0,959
46,74	2,566	0,942
52,31	3,207	0,925

Table XCV.

Vapor pressure of aqueous sugar solutions, referred to the vapor pressure of water at the same temperature.

(interpolated data).

Content of grams of sugar in 100 grams of solution.	$\dfrac{p_1}{p_0}$	Content of gram-molecules of sugar per 1000 g of water.	$\dfrac{p_1}{p_0}$
$\pi_{0}^{0}$	—	$n$	—
0	1,000	0	1,000
5	0,997	0,4	0,992
10	0,994	0,8	0,984
15	0,990	1,2	0,976
20	0,986	1,6	0,966
25	0,980	2,0	0,955
30	0,974	2,4	0,945
35	0,967	2,8	0,935
40	0,95	3,20	0,925
45	0,946
50	0,932

If the composition of the solution is expressed in weight percentages, i.e., as the number of grams of sugar in 100 g of solution, then the curve expressing the dependence between the composition of the solution (concentration) and its vapor pressure proves to be convex and descends steeply downward as the concentration increases.

If the composition of the solution is expressed as the number of gram-molecules of sugar contained in 1000 grams of water, then the same curve is almost a straight line.

Both curves pass almost exactly through the points of observation; only 2 observations lie somewhat outside the curve.

Comparison of the results obtained with data from other authors. The results obtained were compared with data known in the literature. In doing so, the aim was:

1) to find out how much these data differ from one another;

2) to have the possibility of drawing a conclusion on the suitability of the method used and the degree of its accuracy;

3) from all the known numerical data for the vapor pressure of sugar solutions, to derive a probable mean.

We know of direct measurements of the vapor pressure of sugar solutions, carried out by Wüllner, Dieterici, and Smits.

The measurements of Wüllner¹ were carried out by the barometric method. Table XCVI gives the results of these measurements. The concentration is expressed by the ratio of the mass of sugar to the mass of water, taken as 100.

Table XCVI.

Vapor pressure of aqueous sugar solutions according to Wüllner’s observations.

Temperature	Vapor pressure of pure water	Observed lowering of vapor pressure for solutions of concentration: \(50/100\)	Observed lowering of vapor pressure for solutions of concentration: \(100/100\)	Observed lowering of vapor pressure for solutions of concentration: \(150/100\)
°C.	mm.	mm.	mm.	mm.
29.2	30.13	1.49	2.68	3.97
42.7	63.35	2.28	4.76	7.10
47.2	79.91	2.97	6.24	9.41
56.0	123.24	5.04	9.75	15.04
66.8	202.60	7.01	13.93	21.54
73.1	266.29	8.98	16.99	26.67
80.4	360.49	11.85	24.05	37.85
83.6	409.81	13.30	26.90	40.78
90.9	543.72	16.43	34.14	51.85
96.7	674.60	21.12	43.73	68.31

The observations of Dieterici² were carried out by a differential method specially developed by him.

The difference was measured between the vapor pressure of pure water and the vapor pressure of the solution. The manometer was an elastic membrane separating two vessels, in one of which was the solution, in the other—pure water. The bending of the membrane was transmitted by means of levers to a mirror, whose deflections were measured on a scale. According to Dieterici, his method makes it possible to measure the difference of pressures with an accuracy of 0.001 mm of mercury. All Dieterici’s observations were carried out at \(0^\circ\).

The numbers obtained by Dieterici at different times are combined in Table XCVII. The concentration of the solutions is expressed by the number of gram-molecules of sugar \((n)\) per 1000 g of water. The vapor pressure of pure water at \(0^\circ\) is taken as equal to 4.62 mm. The lowering of the vapor pressure is expressed in mm of mercury.

Table XCVII.

Vapor pressure of aqueous sugar solutions according to Dieterici’s observations.

$n$	Observed lowering	$n$	Observed lowering
—	mm	—	mm
0.116	0.0078	0.506	0.0405
0.1506	0.0127	0.604	0.0250
0.193	0.0136	0.991	0.0874
0.255	0.0199	1.0016	0.0894
0.2653	0.0223	1.0122	0.0916
0.319	0.0250	2.00	0.181
0.4993	0.0433

Smits’s observations¹) were carried out by the boiling method. The manometer with which he measured the pressure was filled with two immiscible liquids, namely aniline and water. By means of such a manometer he could read differences of pressure with an accuracy of 0.00024 mm of mercury. The measurements were made at 0°.

The data obtained by Smits are given in Table XCVIII.

The concentration of the solutions is expressed by the number of gram-molecules of sugar ($n$) per 1000 g of water. The lowering of the vapor pressure is calculated in mm of mercury. The vapor pressure of water at 0° is taken to be equal to 4.62 mm.

Table XCVIII.

Vapor pressure of sugar solutions according to Smits’s observations.

n	Observed lowering
—	mm.
1.8821	0.17453
0.77912	0.06485
0.28340	0.02366
0.17287	0.01439
0.08488	0.00705
0.04630	0.00388
0.02138	0.00178

¹) Smits, Zeitschr. phys. Chem. 25, 574. 1898.

In order to compare the numbers of all these observers, I found it convenient to compare not the absolute values of the vapor pressures at some selected temperature, but the ratios \(\frac{p_1}{p_0}\), i.e. the vapor pressure of the solution \((p_1)\) referred to the vapor pressure of pure water \((p_0)\) at the same temperature. The ratio \(\frac{p_1}{p_0}\), insofar as has been clarified up to now, may be regarded, at least practically, i.e. within the limits of the observational error, as independent of temperature. For each series of observations a separate curve was constructed.

In Table XCIX the values of \(\frac{p_1}{p_0}\), read from these curves for various concentrations, are compared. The concentration is expressed by the number of gram-molecules of sugar per 1000 grams of water \((n)\).

Table XCIX.

Vapor pressure of aqueous sugar solutions.

Concentration	Wüllner	Dieterici	Smits	Mikhailenko	Probable mean
\(n\)	\(\dfrac{p_1}{p_0}\)	\(\dfrac{p_1}{p_0}\)	\(\dfrac{p_1}{p_0}\)	\(\dfrac{p_1}{p_0}\)	\(\dfrac{p_1}{p_0}\)
0		0,9962	0,9962	0,996	0.9961
0,200		0,9924	0,9924	0,993	0,9925
0,400		0,9888	0,9888	0,989	0.9888
0,600		0,9849	0,9848	0,984	0,9846
0,800		0,9810	0,9810	0,980	0,9812
1,000		0,9772	0,9770	0,976	0.9770
1,200		0,9732	0,9732	0,971	0,9720
1,400	0,965	0,9692	0,9694	0,966	0,9678
1,600	0,960	0,9650	0,9654	0,961	0,9635
1,800	0,955	0,9610		0,955	0 9578
2,000	0,951			0,950	0,9487
2,200	0,946			0,946	0,9443
2,400	0,941			0,941	0,9393
2,600	0,936			0,935	0,9333
2,800	0,931			0,930	0,9287
3,000	0,926

The results of the comparison made are as follows: all vapor-pressure values for sugar solutions, despite the fact that the measurements were carried out by heterogeneous methods, are in general agreement; the observations of Dieterici and Smits gave almost identical values; Wüllner’s values are somewhat lower than those of Dieterici and Smits for concentrations less than \(2n\), and agree quite well with those obtained by me for concentrations greater than \(2n\); the values obtained by me agree very well with those of Dieterici and Smits for weak concentrations and with Wüllner’s values for stronger concentrations.

It follows from this that the accuracy of the results obtained by the boiling method must be regarded as sufficiently satisfactory for solutions as well. Better results, taking into account the shortcomings of the method, could not have been expected.

In order to obtain a probable mean for the vapor pressure of sugar solutions, the observations cited above were weighted as follows. Since Wüllner made observations for only three concentrations, and the observations themselves (in view of the fact that the ratio \(\frac{p_1}{p_0}\), calculated from his experiments, fluctuates strongly with temperature, which should not be the case) must be considered comparatively insufficiently accurate, Wüllner’s observations were assigned the weight 1. I assigned my own observations the weight 2. Finally, the observations of Dieterici and Smits I assigned, each, the weight 4. The mean thus obtained is given in the last column of Table XCIX.

Measurement of the Vapor Pressure of Solutions in Organic Solvents.

Description of the apparatus. Measurements of the vapor pressure of solutions in organic solvents were made with an apparatus that was the Calbaum apparatus described earlier, in which certain modifications had been made. These modifications were intended to achieve greater rapidity in operation and greater accuracy in the measurement of pressure. They consisted of the following:

1) the pressure was measured by means of a manometer constructed by me, which made it possible to measure the pressure in the apparatus quickly and accurately;

2) the reservoir, which damped pressure fluctuations in the apparatus, had a capacity of about 50 liters;

3) the design of the vessel in which the solution was boiled was modified so that it became possible, without letting air into the apparatus, to change the concentration of the solution under investigation;

4) all the separate parts of the apparatus were connected to one another by means of ground-glass tubes fitted to one another, with mercury stopcocks, which made it possible to maintain any desired pressure in the apparatus for as long as desired.

1) The manometer consisted of a barometer \(B\) (Fig. 15) and a vacuum-gauge tube \(C\), immersed in one and the same reservoir of mercury. Between the tubes there was a brass silver-plated scale, along which two verniers could move up and down, with devices allowing the mercury level in both tubes to be measured with an accuracy of 0.1 mm.

On the vacuumetric tube there was a cock \(A\) with a mercury seal. The original purpose of placing this cock was that, during the measurement of the height of the mercury column in tube \(C\), this tube could be disconnected from the apparatus, on the assumption that fluctuations of pressure in the apparatus due to the jolts of the boiling liquid would cause fluctuations of the mercury level in tube \(C\). In practice, however, it turned out that, owing to the large capacity of the vessel \(V\), which regulated the pressure, this did not occur; the mercury level in tube \(C\) moved uniformly upward or downward until

Fig. 15.

a pressure was established in the apparatus, and then remained exactly (so far as the means at my disposal for observing the level allowed one to notice) at one and the same height. Owing to the perfection of the mercury seals used in joining the separate parts of the apparatus, the entry of even a negligible amount of external air into the apparatus was absolutely excluded.

Tube \(C\) was connected with the vessel \(V\), which regulated the pressure, and through it, consequently, with the apparatus in which the boiling of the solution was produced. The difference of the levels in tubes \(B\) and \(C\) directly measured the pressure in the apparatus.

The advantages of measuring the pressure with this manometer are obvious. With the previously described method of measuring pressure, it was necessary each time to read off the atmospheric pressure and the heights of the upper and lower levels

mercury in the right and left vacuometric tubes (Fig. 13), to correct all the heights obtained for the expansion of mercury due to heat, and then to find the desired value by subtraction. It is impossible to measure the atmospheric pressure only once for an entire series of experiments, since it, as I had occasion to convince myself many times, can change appreciably even over a short interval of time, i.e., within tenths of a millimeter.

The readings of the manometer described, however, do not depend on atmospheric pressure.

Another advantage of this manometer consists in the fact that, when working with it, one has to read only the upper levels of the mercury, i.e., the levels of the mercury in the tubes. The readings of the lower levels of the mercury, i.e., of the levels of the mercury in the wide vessels, which formerly had to be made and whose execution was associated with such labor and errors, are here completely eliminated.

Finally, the immobility of the mercury levels and the presence of verniers made it possible to measure the pressure not only rapidly, but also accurately.

The barometer was filled under my direct observation in the following manner. From the barometric tube, carefully washed and dried, the air was pumped out by means of a mercury pump to the rarefaction of Röntgen rays; the tube was then thoroughly heated from top to bottom in order to remove the last traces of moisture and gases condensed on the walls of the tube. Then the barometric tube was connected with an apparatus for distilling mercury, and mercury, carefully purified and previously distilled, was distilled directly into the barometric tube; throughout the operation the tube was heated and the pressure in the apparatus, by means of the mercury pump, was kept close to zero.

With this method of filling there was complete assurance that in the barometric vacuum there remained the minimum amount of gaseous residue that can in general remain with the most careful filling of a barometer. Since I did not have at my disposal a barometer in which I could fully have confidence, I considered the barometer I had prepared to be normal. Measurements of the vapor elasticity of ether made with this manometer, and comparison of the numbers obtained with those of other observers, did indeed show that, in making this assumption, I had not made any appreciable error.

The barometric tube had, at a height of one third from the base, a constriction with a narrow tube sealed into it. This protected the barometric vacuum from the entrance into it of air that might be carried along with the mercury when the mercury level in the barometer changed as a result of changes in atmospheric pressure or changes in the mercury level in the wide vessel into which the barometer and the vacuometric tube were lowered.

The vessel into which both tubes of the manometer were lowered was glass. Its lower half, throughout its width and length, was occupied by a marble insert cemented to the bottom and sides, with two deep sockets that served as beds for both tubes. On the lid closing the vessel there was a device in the form of a wide bolt (it is not shown in the drawing), which could be raised and lowered by means of a screw and served to bring the level of mercury in the vessel to the point of the scale. This latter de—

device had the aim of making it possible to compare the barometer of the apparatus with a normal one and, in general, to use the apparatus as a barometer¹.

2) The pressure-regulating reservoir was a glass vessel of 50 liters. It was placed between the manometer and the boiler and was located in a wooden box, the walls of which, in accordance with the practice adopted in the Main Chamber of Weights and Measures for the construction of heat-impermeable partitions, were first covered with sheet iron and then with thick cardboard. The space remaining unoccupied in the box was filled with cotton wool. All these arrangements were intended to protect the reservoir from temporary and accidental changes of temperature during work with the apparatus. At the bottom of the reservoir there was a certain quantity of calcium chloride, which kept the walls of the reservoir in a dry state.

3) The boiler was in general left in its former form. Only its dimensions were increased, so that it normally held 200–300 cubic centimeters of the liquid under investigation; moreover, the rod on which the thermometers were attached was made of a hollow, thick-walled glass tube, so that this rod could be used to admit air into the apparatus. The side opening could then serve for introducing into the apparatus new portions of the dissolved substance. Usually one and the same portion of solvent served me for preparing three solutions of increasing concentrations.

Having completed these three series of determinations, I unloaded the apparatus and charged it with a new portion of solvent.

4) The condenser was left as before. In all cases cooling was carried out with a mixture of snow and salt. While working with the apparatus it was easy to observe that the principal mass even of such a volatile liquid as ether condensed considerably below the coil of the condenser.

5) The temperature was measured by means of short thermometers graduated in 0.1°. The divisions were large enough to allow hundredths of a degree to be observed with the naked eye. All the thermometers were furnished with certificates of the Physikalisch-Technische-Reichsanstalt-Charlottenburg. One thermometer, as before, was placed in the liquid, the other—in the vapors. To protect the thermometers and the vapor from heat loss by radiation, the upper part of the bulb of the boiler was wrapped in tin foil, and the neck of the boiler was enclosed in a cardboard case, covered inside with tin foil and, in addition, lined with fur. At the moment when it was necessary to observe the thermometers, the case was opened, the thermometer readings were recorded, and then the case was closed again. The two thermometers did not read alike; specifically, the thermometer in the liquid always read higher than the thermometer in the vapors, and the higher the

the more concentrated solution was. The readings of one and the other thermometer were recorded separately.

6) Heating was carried out by means of a water bath, into which the lower end of the vessel containing the solution was immersed. The temperature of the bath was kept \(1^\circ\)–\(2^\circ\) above the boiling temperature of the solution.

Drying of the apparatus. First of all the apparatus was dried. I considered the drying operation, when working with nonaqueous solutions, to be especially important, and used every effort to ensure that this operation was performed as thoroughly and perfectly as possible.

The drying was carried out as follows. The apparatus, the separate parts of which had previously been well washed with water and dried with alcohol and ether, was assembled, as shown in Fig. 15, and the air was pumped out of the apparatus. Then the apparatus was connected with a powerful drying apparatus of the kind used in organic analysis, and through it was slowly filled with dry air. After some time, sufficient for the air to become saturated with the vapors of the remaining moisture, the air was again pumped out of the apparatus, dry air was again admitted, and so on up to five times. Then the apparatus was taken apart, filled with garnets and the solution under investigation, and assembled again, this time already for observations.

The garnets with which the boiler was filled to one-third in order to facilitate boiling were carefully freed from foreign impurities, boiled with water, alcohol, ether, and the solvent with which the investigation was being carried out, and finally ignited and cooled in a desiccator.

Course of observations. When the apparatus had been charged and assembled, the desired rarefaction was produced in it by means of a suction pump; the water bath surrounding the boiler was heated; and, when the liquid under investigation began to boil and the temperature became constant, readings were taken in the following order: 1) the readings of both thermometers were read; 2) the mercury levels in the barometric and vacuum tubes were read; 3) after 5 minutes the readings of both thermometers were again read; 4) the mercury levels in the barometric and vacuum tubes were again read. Thus the pressure was measured twice each time, and the temperature four times. Although air was continuously being sucked out of the apparatus, the pressure inside the apparatus, owing to the large capacity of the pressure-regulating reservoir, changed only insignificantly during the five-minute interval between each two analogous readings, as can readily be seen in the experimental protocols given below; correspondingly, the temperature also changed only insignificantly. From each pair of analogous readings the mean was taken. The temperatures of the thermometers in the liquid and in the vapor were recorded separately. As was mentioned above, their readings always differed from one another, and in this series of experiments, carried out very carefully and with more sensitive thermometers than in the first series, I no longer found it possible to ignore this difference and to take as the boiling temperature of the solution the mean of the readings of the thermometers—in the liquid and in the vapor.

When all the records had been made, a certain amount of air was admitted into the apparatus through the drying tube; as soon as a new boiling temperature was established, new readings were taken, and so on.

When one series of measurements (with solutions of three concentrations) was completed, the apparatus was taken apart, charged with a new solution, and a new series of measurements was begun.

Measurement of the elasticity of the vapor of pure ether. Since ether belongs to the number of substances which are more readily than others obtained in the pure state, and since the elasticity of ether vapor has already repeatedly been measured by observers of high authority, the measurement of the elasticity of ether vapor was undertaken first of all, with the aim of checking the accuracy and distinctness of the operation of the apparatus.

The ether taken for the experiments was purified with special care, as was described above, p. 132.

In Tables C, CI, CII, and CIII are given the records of four series of observations in the order in which the observations were made. In these tables \(t^0\) liquid denotes the temperature of the thermometer whose bulb was in the liquid; \(t^0\) vapor denotes the temperature of the thermometer placed in the vapors; under the sign Barom. are placed the readings of the mercury levels in the barometric tube; under the sign Vacuum are placed the readings of the mercury levels in the vacuumetric tube; \(T^0\) denotes the temperature in the room; \(t^0\) liquid mean is the mean of the observed temperatures of the boiling liquid; \(t^0\) vapor mean is the mean of the observed vapor temperatures; \(p_0\) is the mean observed pressure, expressed in millimeters of mercury at \(0^\circ\).

Table C.

Boiling temperatures of pure ether at pressures of 395.51—442.63 mm.

(experimental data; first series of observations).

\(t^0\) liquid	\(t^0\) vapor	Diff.	Barom.	Vacuum	\(T^0\)	\(t^0\) liquid mean	\(t^0\) vapor mean	\(p_0\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17.40	17.20	0.2	147.9	544.4	16	17.4	17.2	395.51
17.40	17.20	0.2	147.8	544.4	16	17.4	17.2	395.51
18.39	18.20	0.19	147.9	560.9	17	18.4	18.21	411.92
18.41	18.22	0.19	147.9	561.0	17	18.4	18.21	411.92
19.23	19.04	0.19	147.9	574.7	17	19.23	19.04	425.75
19.23	19.04	0.19	147.9	574.7	17	19.23	19.04	425.75
20.19	20.02	0.17	147.9	591.7	17	20.185	20.02	442.63
20.18	19.95	0.16	147.9	591.7	17	20.185	20.02	442.63

Table CI.

Boiling temperatures of pure ether at pressures of 402.29–478.4 mm.
(experimental data; second series of observations).

$t^0$ liquid, °C	$t^0$ vapor, °C	Difference, °C	Barometer	Vacuum	$T^0$, °C	$t^0$ liquid, mean, °C	$t^0$ vapor, mean, °C	$p_0$, mm
17,88	17,65	0,23	145,8	549,2	17	17,88	17,65	402,29
17,88	17,65		145,8	549,2
18,72	18,49	0,23	145,7	563,2	17	18,72	18,49	416,29
18,72	18,49	0,23	145,7	563,1
19,74	19,52	0,22	145,5	580,2	17	19,74	19.52	433,46
19,74	19,52	0,22	145,5	580,1
20,66	20,44	0,22	145,2	596,1	17	20,66	20,44	449,65
20,66	20,44	0,22	145,2	596,1
21,30	21,08	0,22	144,9	607,7	17	21.305	21,09	461,49
21,31	21,10	0,21	144,9	607,7
22,24	22,01	0,23	144,6	624,3	17	22,245	22,015	478,4
22,25	22,02	0,23	144,6	624,3

Table CII.

Boiling temperatures of pure ether at pressures of 392.19–460.66 mm.
(third series of observations; experimental data).

$t^0$ liquid, °C	$t^0$ vapor, °C	Difference, °C	Barometer	Vacuum	$T^0$, °C	$t^0$ liquid, mean, °C	$t^0$ vapor, mean, °C	$p^0$, mm
17,26	17.00	0,26	145,3	538,5	17′	17,26	17.00	392.19
17,26	17.00	0,26	145,2	538,7
18,35	18,10	0,25	145,2	556,1	17°	18,35	18,10	409 76
18,35	18,10	0,25	145,2	556,1
19,25	19,01	0,24	144,0	570,4	17′	19.255	19,02	425,16
19,26	19,03	0,23	144,1	570,4
20,25	20,03	0.22	143,8	587,4	18′	20,26	20,035	442,45
20,27	20,04	0.23	143,6	587,5
21,25	21,06	0,19	143,3	605,1	18′	21,26	21,055	460,55
21,27	21,05	0,22	143,2	605,2

Table CIII.

Boiling temperatures of pure ether at pressures of 407.76–467.79 mm.

(fourth series of observations; experimental data).

\(p\) liquid, °C	\(p\) vapor, °C	Difference, °C	Barom.	Vacuum	\(T^0\), °C	\(p\) liquid, mean, °C	\(p\) vapor, mean, °C	\(p_0\), mm
18.15	17.95	0.20	157.5	566.4	17	18.16	17.96	407.76
18.17	17.98	0.19	157.5	566.4	17	18.16	17.96	407.76
18.87	18.62	0.25	157.5	577.3	17	18.87	18.62	418.64
18.87	18.62	0.25	157.5	577.3	17	18.87	18.62	418.64
19.48	19.26	0.22	157.5	587.6	17	19.48	19.26	428.91
19.48	19.26	0.22	157.5	587.6	17	19.48	19.26	428.91
20.07	19.85	0.22	157.3	598.0	17	20.08	19.86	439.48
20.09	19.87	0.22	157.3	598.0	17	20.08	19.86	439.48
20.87	20.64	0.12	157.0	611.9	17	20.87	20.645	453.60
20.87	20.65	0.12	157.2	612.0	17	20.87	20.645	453.60
21.65	21.44	0.21	156.9	626.0	17	21.65	21.44	467.79
21.65	21.43	0.22	156.9	626.0	17	21.65	21.44	467.79

For each series of observations its own curve was drawn, and from this curve the observations of each series were interpolated within the limits \(17^\circ\)–\(22^\circ\) at intervals of \(0.5^\circ\). Since the temperatures of the boiling liquid and of its vapor are different, different vapor pressures correspond to one and the same temperature, depending on whether the temperature is referred to the liquid or to the vapor. In Table CIV are collected the interpolation data for the case when the temperature was measured in the liquid; in Table CV—for the case when the temperature was measured in the vapors.

Table CIV.

Vapor pressure of pure ether (temperature measured in the vapors).

(interpolated data).

\(t^0\) vapor, °C	1st series \(p_0\), mm	2nd series \(p_0\), mm	3rd series \(p_0\), mm	4th series \(p_0\), mm	Mean \(p_0\), mm
17.0	392.5	—	392.2	—	392.35
17.5	400.3	—	400.1	—	400.20
18.0	408.4	408.15	408.25	408.45	408.22
18.5	416.55	416.50	416.40	416.70	416.53
19.0	425.10	424.70	424.90	424.85	424.89
19.5	433.45	433.20	433.30	433.20	433.29
20.0	442.20	441.85	442.00	442.00	442.02
20.5	—	450.80	450.65	450.90	450.78
21.0	—	459.70	459.70	460.20	459.87
21.5	—	468.90	—	469.90	469.40
22.0	—	478.40	—	—	478.40

Table CV.

Vapor pressure of pure ether (temperature measured in the liquid).

(interpolated data).

\(t^\circ\) liquid	1st series \(p_0\)	2nd series \(p_0\)	3rd series \(p_0\)	4th series \(p_0\)	mean \(p_0\)
°C.
17.0	—	—	388.40	—	388.40
17.5	397.10	—	397.60	—	397.35
18.0	405.25	404.40	404.10	—	404.91
18.5	413.50	412.65	412.40	413.00	412.87
19.0	421.80	420.90	420.80	420.85	421.09
19.5	430.35	429.25	429.40	429.40	429.60
20.0	438.20	437.95	438.00	437.20	437.83
20.5	—	446.85	446.80	446.90	446.85
21.0	—	456.00	455.75	456.10	455.92
21.5	—	465.05	—	465.80	465.82
22.0	—	474.10	—	—	474.10

Tables CIV and CV, establishing the mean values of the vapor pressure of ether for temperatures 17°–22°, values that will subsequently have to be used constantly, at the same time aim to provide material for estimating the degree of accuracy of the method employed. To make this estimate, let us compare the vapor pressures of the different series of observations for some arbitrarily chosen temperature, e.g. 20°, and, by the method of least squares, determine the probable error of each individual observation and of the mean result. Doing this, we find that the probable error of each individual observation is ±0.066 mm, and the probable error of the mean result is ±0.033 mm. This calculation was made for those data in which the temperature was measured in the vapor. Approximately the same results are also obtained for those data in which the temperature was measured in the boiling liquid¹, and likewise not only for temp. 20°, but also for data at any other temperature.

If one takes into account the comparative simplicity of the apparatus and manipulations and the speed of the work, the results must be recognized as more than satisfactory.

For an absolute evaluation of the results yielded by the method and the apparatus, the mean values obtained for the vapor pressure of ether were compared with the numerical values found by other authors, namely, Regnault, Ramsay and Young, and Battelli. To obtain the values of the vapor pressure of ether

within the temperature range \(17^\circ\)—\(22^\circ\), the observations of all these authors were interpolated by the formula:

\[ \Log p_0 = a - b\alpha^\theta - c\beta^\theta, \tag{76} \]

where the numerical values of the constants varied according to the indications of each individual author. Namely, for the constants of equation (76), Regnault \(^{1}\) gives the following values: \(a=5{,}0286298\); \(b=-0{,}0002284\), \(c=3{,}1906390\); \(\log \alpha=0{,}0145775\); \(\log \beta=\overline{1}, 9968777\); \(\theta=(t^\circ+20)\); Ramsay and Young \(^{2}\)—the following: \(a=5{,}9834771\); \(\log b=0{,}5240258\); \(\log c=\overline{1}, 5733238\); \(\log \alpha=\overline{1}, 99827459\); \(\log \beta=\overline{1}, 99130336\); \(\theta=t^\circ\); Battelli \(^{3}\)—the following: \(a=5{,}981578\); \(b-3{,}337745\); \(c=0{,}382505\); \(\log \alpha=\overline{1}, 9982801\); \(\log \beta=\overline{1}, 9910451\); \(\theta=t^\circ\).

Regnault’s measurements were made partly by the barometric method, partly by the boiling method; the measurements of Ramsay and Young and the measurements of Battelli were made by the method of observing isotherms.

The comparison is made in Table CVI.

Table CVI.

Comparison of the numerical values of the vapor pressure of ether obtained by different authors and by different methods.

(interpolated data).

\(t^\circ\)	Regnault \(p_0\)	Battelli \(p_0\)	Ramsay and Young \(p_0\)	Mikhailenko and Thermom. in vapors \(p_0\)	Zeltner Thermom. in liquid \(p_0\)
°C.	mm.	mm.	mm.	mm.	mm.
17,0	383,69	390,61	392,86	392,35	388,40
17,5	391,56	398,76	400,21	400,20	397,35
18,0	399,53	406,98	408,23	408,22	404,91
18,5	407,65	415,37	416,55	416,53	412,87
19,0	415,89	423,88	425,03	424,89	421,09
19,5	424,25	432,61	433,63	433,29	429,60
20,0	432,78	441,32	442,19	442,02	437,83
20,5	441,43	450,11	451,23	450,78	446,85
21,0	450,23	459,32	460,24	459,87	455,92
21,5	459,28	468,53	469,39	469,40	465,82
22,0	468,27	477,80	478,69	478,40	474,10

A comparison of the numerical values collected in Table CVI leads to the following conclusions.

1) The observations of Ramsay and Young almost coincide with my observations (for the case when the thermometer was placed in the vapors), and

\(^{1}\) Regnault, Mem. de l’Acad. 26, 339, 1862.
\(^{2}\) Ramsay and Young, Phil. Trans. London 178, 57, 1887.
\(^{3}\) Battelli, Mem. Ac. di Torino (2) 60 1891; Ann. de chim. phys. (6) 25, 38, 1892.

this agreement is so close that it may be considered exceptional for investigations of this kind in general, and in particular for the present case, where a difference in temperature of \(0.1^\circ\) corresponds to a difference in vapor pressure of \(1.47—1.86\) mm.; to this it must further be added that the two series of observations were made by different methods.

2) The observations of Ramsay and Young, Battelli, and my own may be considered in agreement, since the differences between these observations do not exceed the usual differences between analogous observations made by different authors—the measurement of vapor pressure belongs among the most difficult physical manipulations.

3) Regnault’s observations differ sharply from the observations of Ramsay and Young, Battelli, and my own.

There can hardly be any doubt that Regnault’s numbers are incorrect. The reason for this is that the ether with which Regnault made his measurements was not a pure preparation. Regnault himself pointed out this circumstance; namely, he noted that the ether prepared by him underwent, with time, some changes of itself, which affected the magnitude of its vapor pressure.

Meanwhile, in all reference books, such as, for example, the well-known “Physikalisch-Chemische Tabellen” von Landolt und Börnstein 1894, “Physico-Chemical Tables” by John Castell—Evans 1902, “Handbuch der Physik” Winkelmann, and others, Regnault’s data are everywhere given alongside the data of other authors, and in those cases where, besides the data of Regnault and of Ramsay and Young, no others are given (as is the case in Landolt’s “Tables”), the user of the Tables has absolutely no grounds for making one or another choice. I think that at the present time, despite all the quite deserved authority enjoyed by Regnault’s observations, his observations on the vapor pressure of ether have only historical significance, and they should be excluded from the “Tables” and other reference publications of the present day.

4) The boiling method gives values of pressure that agree with the values obtained by the barometric method only in the case when the observed pressure is referred to the temperature of the vapor, and not of the liquid.

5) The apparatus was assembled and functioned quite correctly. With this apparatus the following measurements of the vapor pressure of solutions were also made.

I. Mixtures of ether and nitrobenzene.

The measurement of the vapor pressure of mixtures of ether and nitrobenzene was undertaken in order to check Raoult’s data,¹) the accuracy of which was called into question by me for the following reason.

While searching in the literature for experimental material to verify the equality

\[ \frac{s_1}{s_0} = \frac{p_1}{p_0} \]

on various examples, among other things, I also turned to measurements of the vapor pressure of ethereal solutions made by Raoult and, since there were no data for the specific gravity, I myself measured the specific gravity of mixtures of ether and aniline and of mixtures of ether and nitrobenzene. It turned out that the relation \(\frac{s_1}{s_0} = \frac{p_1}{p_0}\) was satisfied comparatively well for mixtures

¹) Raoult, Ann. de chim. et phys. (6) 15, 375. 1888.

ether with aniline, but poorly for mixtures of ether with nitrobenzene. I therefore decided to verify Raoult’s data.

Ether and nitrobenzene were carefully purified, as described above (pp. 132–133). The results of the measurements are brought together in Tables CVII–CXX; each table A is a record of observations and of the mean quantities derived from these observations; each table B contains the vapor pressures of the solutions, obtained by graphical interpolation of the experimental data in table A. The purpose of the graphical interpolation was to smooth out the errors of individual observations and to make it possible to judge the regularity of the given series of observations.

The notation in the tables is the same as before. New notation:

\(p_1\) liquid, \(p_1\) vapor, \(\dfrac{p_1}{p_0}\) liquid and \(\dfrac{p_1}{p_0}\) vapor denote the absolute and relative vapor pressures of the solution, referred to the temperature measured in the liquid and in the vapors. In addition, in the series \(\dfrac{p_1}{p_0}\) liquid and \(\dfrac{p_1}{p_0}\) vapor the mean values are given (they are printed in bold type), and the mean error of each mean result is calculated.

The composition of the mixture is expressed by the content of nitrobenzene in 100 parts by weight of the mixture.

Table CVII A.

Boiling temperatures of a mixture of ether and nitrobenzene, 3.94%, at pressures 394.82–455.07 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\nu\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17.91	17.89	0.02	142.5	538.2	15	17.91	17.89	394.82
17.91	17.89		142.4	538.3
18.64	18.63	0.01	142.2	549.5	15	18.64	18.63	406.3
18.64	18.63		142.2	549.5
19.38	19.36	0.02	142.2	562.0	15	19.385	19.365	418.78
19.39	19.37		142.2	562.0
20.03	20.01	0.03	142.2	572.9	15	20.04	20.015	429.65
20.05	20.02		142.2	572.9
20.68	20.59	0.18	142.1	584.1	16	20.69	20.595	440.98
20.70	20.60		142.1	584.2
21.48	21.35	0.13	141.9	598.1	16	21.485	21.355	455.07
21.49	21.36		141.9	598.1

Table CVII B.

Vapor pressure of a mixture of nitrobenzene and ether, 3.94%, at temp. 18°—21.5°.
(interpolated data).

\(t'\)	\(p_1\), liquid	\(p_1\), vapor	\(\dfrac{p_1}{p_0}\), liquid	\(\dfrac{p_1}{p_0}\), vapor
°C.	mm.	mm.
18.0	396.10	396.55	0.9784	0.9712
18.5	403.90	404.30	0.9784	0.9707
19.0	412.15	412.55	0.9786	0.9707
19.5	420.75	421.05	0.9790	0.9716
20.0	429.0	429.5	0.9799	0.9719
20.5	437.55	439.05	0.9793	0.9736
21.0	446.35	448.45	0.9788	0.9750
21.5	455.6	458.20	0.9781	0.9763
			0.9788 ± 0.0002	0.9726 ± 0.0008

Table CVIII A.

Boiling temperatures of a mixture of ether and nitrobenzene, 7.63%, at pressures 402.86—445.45 mm.
(experimental data).

\(t^0\) liquid	\(t'\) vapor	Diff.	Barom.	Vacuum.	\(T'\)	\(t^0\) liquid, mean	\(t^0\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
19.12	18.69	0.44°	149.5	553.3	16	19.12	18.68	402.86
19.12	18.67		149.4	553.4
19.67	19.22	0.45°	149.2	561.8	16.5	19.67	19.225	411.53
19.67	19.23		149.2	561.8
20.25	19.77	0.48°	149.0	571.5	17	20.255	19.77	421.39
20.26	19.77		149.0	571.6
20.98	20.49	0.48°	148.8	583.7	17	20.98	20.50	433.86
20.98	20.51		148.6	583.8
21.65	21.10	0.54°	148.3	595.0	17	21.65	21.11	445.45
21.65	21.12		148.3	595.0

Table CVIII B.

Vapor pressure of a mixture of ether and nitrobenzene, 7.63%, at temp. 19°–21.5°.

(interpolated data).

$t'$	$p_1$ liquid	$p_1$ vapor	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor
°C.	mm.	mm.
19.0	401.0	407.75	0.9521	0.9594
19.5	408.90	416.45	0.9517	0.9609
20.0	417.15	425.20	0.9526	0.9621
20.5	425.70	433.90	0.9528	0.9625
21.0	434.30	443.25	0.9526	0.9636
21.5	442.90	---	0.9508	---
			0.9521 ± 0.0002	0.9617 ± 0.0006

Table CIX A.

Boiling temperatures of a mixture of ether and nitrobenzene, 9.95%, at pressures 395.05–444.34 mm.

(experimental data).

$t^0$ liquid	$t'$ vapor	Diff.	Barom.	Vacuum.	$T^0$	$t^0$ liquid, mean	$t^0$ vapor, mean	$p_1$
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.57	18.15	0.41	136.3	527.3	16	18.58	18.175	395.05
18.59	18.18		136.3	527.4		18.58	18.175	395.05
19.38	18.96	0.42	136.1	539.3	16	19.38	18.96	402.21
19.38	18.96		136.0	539.3		19.38	18.96	402.21
20.07	19.66	0.40	135.8	550.3	16	20.07	19.67	413.43
20.07	19.68		135.8	550.3		20.07	19.67	413.43
20.94	20.53	0.41	135.6	564.7	16	20.945	20.53	428.08
20.95	20.53		135.5	564.8		20.945	20.53	428.08
21.90	21.45	0.45	135.2	580.7	16	21.91	21.46	444.34
21.92	21.47		135.2	580.7		21.91	21.46	444.34

Table CIX B.

Vapor pressure of a mixture of ether and nitrobenzene 9.95% at temp. 18.5°—22.0°.
(interpolated data).

$t'$	$p_1$ liquid	$p_1$ vapor	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor
°C.	mm.	mm.
18.5	388.00	394.95	0.9419	0.9482
19.0	396.40	402.85	0.9412	0.9480
19.5	404.20	410.65	0.9408	0.9475
20.0	412.35	418.95	0.9417	0.9478
20.5	420.55	427.55	0.9412	0.9462
21.0	428.95	436.15	0.9408	0.9482
21.5	437.35	445.20	0.9389	0.9486
22.0	446.10	—	0.9408	—
			0.9409	0.9477 ± 0.0002

Table CX A.

Boiling temperatures of a mixture of ether and nitrobenzene 15.96%
at pressures 376.61 and 429.41 mm.
(experimental data).

$t^\circ$ liquid	$t^\circ$ vapor	Diff.	Barom.	Vacuum	$T^\circ$	$t^\circ$ liquid, mean	$t^\circ$ vapor, mean	$p_1$
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.63	18.31	0.33	130.2	507.8	16	18.64	18.315	376.61
18.65	18.32		130.2	507.8		18.64	18.315	376.61
19.62	19.26	0.36	130.1	522.7	16	19.63	19.27	391.56
19.64	19.28		130.1	522.7		19.63	19.27	391.56
20.40	20.02	0.39	129.7	534.4	16	20.395	20.00	403.64
20.39	19.98		129.7	534.5		20.395	20.00	403.64
21.18	20.76	0.42	129.5	547.5	16	21.18	20.76	416.94
21.18	20.76		129.4	547.5		21.18	20.76	416.94
21.96	21.51	0.46	128.9	559.5	17	12.96	21.50	429.41
21.96	21.49		128.9	559.5		12.96	21.50	429.41

Table CX B.

Vapor pressure of a mixture of ether and nitrobenzene 15.96%, at temp. 18°—22.0°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18.0
18.5	374.60	379.45	0.9074	0.9110
19.0	381.95	387.30	0.9068	0.9114
19.5	389.55	395.40	0.9066	0.9124
20.0	397.45	403.60	0.9076	0.9133
20.5	405.45	412.25	0.9074	0.9143
21.0	413.70	420.90	0.9076	0.9152
21.5	422.10	429.40	0.9061	0.9150
22.0	430.05	—	0.9070	—
			0.9070 ± 0.0002	0.9132 ± 0.0006

Table CXI A.

Boiling temperatures of a mixture of ether and nitrobenzene 20.81%,
at pressures 365.92—425.73 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum.	\(T\)	mean \(t^\circ\) liquid	mean \(t^\circ\) vapor	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.60	18.11	0.49	128.9	495.7	15	18.60	18.11	365.92
18.60	18.11		128.9	495.7		18.60	18.11	365.92
19.63	19.07	0.59	129.0	510.8	15	19.63	19.065	380.97
19.63	19.06		128.9	510.9		19.63	19.065	380.97
20.64	20.02	0.62	128.8	525.9	15.5	20.64	20.02	396.12
20.64	20.02		128.8	525.9		20.64	20.02	396.12
21.55	20.86	0.70	128.9	541.3	16	21.56	20.86	411.43
21.57	20.86		128.8	541.4		21.56	20.86	411.43
22.44	21.54¹	0.75	128.8	555.7	16	22.44	21.69	425.73
22.44	21.84		128.9	555.7		22.44	21.69	425.73

¹ It was observed that when the bath temperature was raised, the temperature \(t^\circ\) vapor rose, namely to 21.84°, while the temperature \(t^\circ\) liquid remained unchanged.

Table CXI B.

Vapor pressure of a mixture of ether and nitrobenzene, 20.81%, at temperatures 18°–22°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18.0	—	364.15		0.8919
18.5	364.50	372.10	0.8829	0.8935
19.0	371.55	380.00	0.8823	0.8943
19.5	378.95	387.95	0.8819	0.8952
20.0	386.35	395.90	0.8823	0.8958
20.5	393.95	404.70	0.8817	0.8976
21.0	401.85	413.50	0.8813	0.8991
21.5	410.05	422.40	0.8802	0.8999
22.0	418.35	—	0.8823
			0.8818 ± 0.0003	0.8959 ± 0.0003

Table CXII A.

Boiling temperatures of a mixture of ether and nitrobenzene, 25.39%, at pressures 353.22–413.53 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.44	17.90	0.54	132.4	486.5	15	18.44	17.90	353.22
18.44	17.90		132.4	486.5
19.41	18.97	0.51	132.4	500.3	15.5	19.41	18.90	367.02
19.41	18.97		132.4	500.3
20.47	19.99	0.54	132.3	516.3	16	20.52	19.985	383.01
20.47	19.98		132.3	516.3
21.54	20.99	0.58	132.2	532.1	16	21.54	20.99	399.01
21.54	20.99		132.1	532.1
22.48	21.84	0.64	131.9	546.5	16	22.485	21.845	413.53
22.49	21.85		131.9	546.5

Table CXII B.

Vapor pressure of a mixture of ether and nitrobenzene, 25.39%, at temp. 17.5°–22.5°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p^0}\) vapor
°C	mm.	mm.
17.5	—	354.50		0.8684
18.0	354.10	361.30	0.8576	0.8676
18.5	361.05	367.00	0.8572	0.8638
19.0	368.25	375.70	0.8570	0.8670
19.5	375.30	383.30	0.8572	0.8672
20.0	382.75	391.05	0.8566	0.8674
20.5	390.35	399.20	0.8561	0.8680
21.0	398.35	407.70	0.8551	0.8686
21.5	406.05	—	0.8562	—
22.0	413.90	—
22.5			0.8566 ± 0.0002	0.8676 ± 0.0006

Table CXIII A.

Boiling temperatures of a mixture of ether and nitrobenzene, 30.56%, at pressures 342.37–403.97 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.48	17.94		134.0	477.1	15	18.48	17.94	342.37
18.48	17.94	0.54	133.9	477.2
19.65	19.12		134.0	493.5	15	19.65	19.12	358.62
19.65	19.12	0.53	134.0	493.5
20.67	20.17		134.1	508.3	15	20.67	20.17	373.32
20.67	20.17	0.50	134.1	508.4
21.70	21.12		134.1	523.6	15	21.705	21.125	398.57
21.71	21.13	0.58	134.1	523.6
22.72	22.08		134.0	538.9	15	22.72	22.065	403.97
22.72	22.05	0.66	134.0	539.0

Table CXIII B.

Vapor pressure of a mixture of ether and nitrobenzene, 30.56%, at temp. 17.5°—22.5°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
17.5	—	343.20		0.8406
18.0	342.70	350.00	0.8300	0.8404
18.5	349.45	356.80	0.8297	0.8397
19.0	356.45	363.85	0.8295	0.8393
19.5	363.55	370.75	0.8302	0.8387
20.0	370.85	378.50	0.8299	0.8397
20.5	378.10	386.65	0.8293	0.8406
21.0	385.55	394.75	0.8276	0.8410
21.5	393.10	403.20	0.8291	0.8428
22.0	400.80	—
22.5			0.8294±0.0003	0.8403±0.0003

Table CXIV A.

Boiling temperatures of a mixture of ether and nitrobenzene, 35.26%,
at pressures of 330.17—395.92 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.40	17.81		140.8	471.8	14.5	18.405	17.815	330.17
18.41	17.82	0.59	140.8	471.8
19.70	19.05		140.6	488.8	14.5	19.70	19.055	347.47
19.70	19.06	0.65	140.6	488.8
20.78	20.09		140.6	503.9	14.5	20.78	20.09	362.47
20.78	20.09	0.69	140.5	503.9
21.93	21.20		140.3	520.4	14.5	21.935	21.205	379.17
21.94	21.21	0.73	140.3	520.4
23.08	22.29		140.0	536.9	14.5	23.08	22.30	395.92
23.08	22.31	0.78	140.1	537.0

Table CXIV B.

Vapor pressure of a mixture of ether and nitrobenzene 35.26% at temp. 17.5°–23.0°
(interpolated data).

$t^\circ$	$p_1$ liquid	$p_1$ vapor	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor
°C.	mm.	mm.
17.5	—	333.05		0.8156
18.0	331.35	340.10	0.8024	0.8166
18.5	337.95	347.25	0.8024	0.8171
19.0	344.75	354.40	0.8022	0.8179
19.5	351.65	361.25	0.8030	0.8171
20.0	358.60	368.50	0.8026	0.8173
20.5	365.60	376.15	0.8019	0.8177
21.0	372.95	383.85	0.8006	0.8177
21.5	380.35	391.55	0.8020	0.8183
22.0	387.45	398.85
22.5	394.80	—
23.0			0.8021±0.0002	0.8172±0.0003

Table CXV A.

Boiling temperatures of a mixture of ether and nitrobenzene 40.01%
at pressures 321.68–390.52 mm.
(experimental data).

$t^\circ$ liquid	$t^\circ$ vapor	Diff.	Barom.	Vacuum	$T^\circ$	$t^\circ$ liquid avg.	$t^\circ$ vapor avg.	$p_1$
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.61	17.92		144.1	466.5	14	18.615	17.915	321.68
18.62	17.91	0.70	144.1	466.5
19.74	19.00		144.0	481.0	15	19.74	19.00	336.22
19.74	19.00	0.73	143.9	481.0
21.25	20.46		141.8	499.7	14.5	21.25	20.46	357.07
21.25	20.46	0.79	141.7	499.7
22.52	21.73		141.7	517.3	14.5	22.52	21.735	374.67
22.52	21.72	0.79	141.7	517.3
23.60	22.82		141.5	533.1	14.5	23.60	22.81	390.52
23.60	22.80	0.79	141.4	533.0

Table CXV B.

Vapor pressure of a mixture of ether and nitrobenzene 40.01% at temp. 18.0°—23.5°.
(interpolated data).

$t^\circ$	$p_1$ liquid	$p_1$ vapor	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor
°C.	mm.	mm.
18.0	—	322.85		0.7907
18.5	320.45	329.45	0.7761	0.7909
19.0	326.55	336.65	0.7755	0.7921
19.5	333.10	343.10	0.7754	0.7918
20.0	339.70	350.25	0.7759	0.7923
20.5	346.50	357.60	0.7755	0.7932
21.0	353.55	364.30	0.7754	0.7921
21.5	360.45	341.20	0.7737	0.7909
22.0	367.25	378.35	0.7745	0.7907
22.5	374.30	385.70
23.0	381.60	393.30
23.5	389.15	—
			0.7752±0.0002	0.7916±0.0003

Table CXVI A.

Boiling temperatures of a mixture of ether and nitrobenzene 44.85%
at pressures 315.23—379.15 mm.
(experimental data).

$t^\circ$ liquid	$t^\circ$ vapor	Diff.	Barom.	Vacuum.	$T^\circ$	$t^\circ$ liquid, mean	$t^\circ$ vapor, mean	$p_1$
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.94	18.33		138.9	454.8	14	18.94	18.33	315.23
18.94	18.33	0.61	138.8	454.8
20.26	19.63		138.7	471.2	14.5	20.26	19.63	331.72
20.26	19.63	0.64	138.7	471.3
21.46	20.81		138.9	487.7	15	21.46	20.81	347.97
21.46	20.81	0.65	139.0	487.8
22.53	21.90		138.9	502.6	15	22.53	21.895	362.87
22.53	21.89	0.64	138.9	502.7
23.63	22.98		138.9	518.0	16	23.64	22.98	379.15
23.65	22.98	0.66	138.9	518.1

Table CXVI B.

Vapor pressure of a mixture of ether and nitrobenzene, 44.85%, at temp. 18.5°–23.5°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18.5	—	317.35		0.7619
19.0	315.95	323.55	0.7501	0.7614
19.5	322.05	330.05	0.7495	0.7616
20.0	328.45	336.65	0.7501	0.7616
20.5	334.95	343.50	0.7495	0.7619
21.0	341.60	350.50	0.7492	0.7621
21.5	348.50	357.35	0.7482	0.7612
22.0	355.35	364.45	0.7494	0.7617
22.5	362.35	371.75
23.0	369.60	379.40
23.5	377.05	—
			0.7494 ± 0.0002	0.7616 ± 0.0001

Table CXVII A.

Boiling temperatures of a mixture of ether and nitrobenzene, 50.74%, at pressures 306.22–360.26 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum.	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
19.46	18.70		139.1	442.0	15	19.46	18.70	306.22
19.46	18.70	0.76	139.2	442.2		19.46	18.70	306.22
20.41	19.62		139.1	457.6	15	20.435	19.64	317.72
20.46	19.68	0.79	139.1	457.6		20.435	19.64	317.72
21.67	20.86		139.1	473.3	15	21.675	20.86	333.42
21.68	20.86	0.80	139.0	473.3		21.675	20.86	333.42
22.49	21.65		139.0	483.8	16	22.495	21.65	343.95
22.50	21.65	0.88	138.9	483.8		22.495	21.65	343.95
23.72	22.77		138.7	499.7	16	23.72	22.79	360.26
23.72	22.81	0.93	138.7	500.1		23.72	22.79	360.26

Table CXVII B.

Vapor pressure of a mixture of ether and nitrobenzene, 50.74%, at temp. 18.5°—28.5°.

(interpolated data).

\(t^0\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18.5	—	303.90	0.7138	0.7296
19.0	—	309.80	0.7138	0.7291
19.5	306.70	315.95	0.7130	0.7290
20.0	312.55	322.20	0.7122	0.7290
20.5	318.50	328.60	0.7106	0.7290
21.0	324.75	335.15	0.7119	0.7286
21.5	331.05	341.90		0.7285
22.0	337.50	348.85		0.7291
22.5	343.95	356.05
23.0	350.50	363.40
23.5	357.25	—
			0.7125±0.0005	0.7289±0.0001

Table CXVIII A.

Boiling temperatures of a mixture of ether and nitrobenzene, 60.04%, at pressures 270.64—328.27 mm.¹

(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Difference	Barom.	Vacuum	\(Z^0\)	\(t^0\) liquid, mean	\(t^0\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.49	18.03		150.3	421.4	15	18.50	18.00	270.64
18.51	18.03	0.50	150.3	421.8
19.82	19.26		150.6	436.0	15	19.82	19.255	284.74
19.82	19.25	0.57	150.7	436.2
21.33	20.66		151.1	454.0	16	21.34	20.68	302.22
21.35	20.70	0.66	151.1	454.2
22.45	21.68		151.2	467.3	16	22.46	21.68	315.36
22.47	21.68	0.78	151.2	467.5
23.45	22.60		151.2	480.1	15	23.465	22.60	328.27
23.48	22.60	0.86	151.2	480.3

¹ Until now the apparatus had not been shielded from heat radiation. Beginning with this experiment and in all subsequent ones, the boiler was protected from heat radiation by the moss box described above.

Table CXVIII B.

Vapor pressure of a mixture of ether and nitrobenzene 60.04% at temp. 18°–23°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18.0	—	270.35	0.6554	0.6621
18.5	270.60	276.00	0.6552	0.6627
19.0	275.95	281.80	0.6545	0.6631
19.5	281.25	287.65	0.6548	0.6637
20.0	286.70	293.75	0.6545	0.6645
20.5	292.45	300.00	0.6540	0.6654
21.0	298.20	306.40	0.6527	0.6662
21.5	304.05	313.00	0.6536	0.6668
22.0	309.95	319.75		0.6682
22.5	315.95	326.90
23.0	322.20	—
			0.6543±0.0003	0.6647±0.0006

Table CXIX A.

Boiling temperatures of a mixture of ether and nitrobenzene 70.24%
at pressures 233.85–293.90 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum.	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_0\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18.77	18.10		154.1	388.6	16	18.78	18.12	233.85
18.79	18.16	0.66	154.2	388.6
20.13	19.44		153.9	400.9	17	20.135	19.42	246.40
20.14	19.45	0.69	153.9	401.0
21.63	20.82		153.8	415.3	17	21.64	20.86	260.97
21.65	20.91	0.78	153.7	415.6
23.24	22.34		153.3	431.6	17	23.25	22.36	277.62
23.26	22.38	0.89	153.3	431.8
24.71	23.66		153.0	447.6	17	24.72	23.665	293.90
24.73	23.67	1.06	152.8	447.6

Table CXIX B.

Vapor pressure of the mixture of ether and nitrobenzene, \(70.24\%\), at temp. \(18^\circ\)—\(24.5^\circ\).

(interpolated data).

\(t'\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18.0	—	232.55		0.5695
18.5	—	237.45		0.5700
19.0	235.75	242.40	0.5598	0.5704
19.5	240.45	247.25	0.5595	0.5704
20.0	245.20	252.25	0.5600	0.5706
20.5	249.95	257.40	0.5594	0.5710
21.0	254.75	262.60	0.5586	0.5710
21.5	259.65	268.00	0.5573	0.5710
22.0	264.70	273.50	0.5583	0.5717
22.5	269.80	279.25
23.0	275.00	285.50
23.5	280.35	291.75
24.0	285.80	—
24.5	291.40	—
			0.5589 ± 0.0003	0.5706 ± 0.0002

Table CXX A.

Boiling temperatures of the mixture of ether and nitrobenzene, \(78.86\%\), at pressures \(198.38\)—\(256.76\) mm.

(experimental data).

\(t^\circ\) liquid	\(t'\) vapor	Difference	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_0\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
19.80	18.59		151.2	351.1	17	19.80	18.59	198.38
19.80	18.59	1.21	151.1	350.0
22.14	20.86		151.4	368.1	16	22.15	20.885	216.20
22.16	20.91	1.27	151.4	368.2
23.73	22.44		151.0	381.2	16	23.735	22.45	229.60
23.74	22.46	1.28	151.0	381.2
25.12	23.76		151.0	394.1	17	25.12	23.76	242.41
25.12	23.76	1.36	151.0	394.1
26.59	25.10		151.0	408.4	17	26.59	25.08	256.76
26.59	25.06	1.51	151.0	408.5

Table CXX B.

Vapor pressure of a mixture of ether and nitrobenzene, 78.86%, at temp. 18.5°—25.5°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18.5	—	197.70		0.4747
19.0	—	201.45		0.4740
19.5	—	205.30		0.4738
20.0	198.85	209.15	0.4540	0.4732
20.5	203.65	213.05	0.4557	0.4725
21.0	207.45	217.0	0.4549	0.4721
21.5	211.35	221.30	0.4536	0.4715
22.0	215.30	225.65	0.4540	0.4715
22.5	219.35	230.05
23.0	223.40	234.90
23.5	227.55	239.85
24.0	231.95	244.90
24.5	236.55	250.25
25.0	241.30	255.80
25.5	246.05	—
			0.4544 ± 0.0004	0.4729 ± 0.0004

Discussion of the results.

A comparison of the results of measuring the vapor pressure of mixtures of ether and nitrobenzene makes it possible to state the following.

1) The temperature of the boiling solution is always higher than the temperature of the vapor, and the more concentrated the solution, the higher it is.

2) The vapor-pressure curves of the solutions represent parts of parabolas; they appear parallel to the vapor-pressure curve of the pure liquid.

3) The vapor-pressure curves corresponding to the temperature measured in the liquid have the same form as the vapor-pressure curves corresponding to the temperature measured in the vapors. Both curves run one above the other, but not in parallel, gradually diverging.

4) The vapor-pressure curves corresponding to the temperature measured in the vapors proceed less regularly than the vapor-pressure curves corresponding to the temperature of the boiling liquid.

5) The ratios \(\dfrac{p_1}{p_0}\) are calculated differently depending on whether \(p_1\) and \(p_0\) are referred to the temperature of the vapor or to the temperature of the boiling liquid.

6) For a solution of a definite concentration, the ratio \(\dfrac{p_1}{p_0}\), both in one series and in the other, i.e. \(\dfrac{p_1}{p_0}\) liquid and \(\dfrac{p_1}{p_0}\) vapor, may be considered un-

dependent on temperature, of course within the limits of that temperature interval for which the measurements were made. This ratio fluctuates to one side and the other around a certain mean value. True, there are several exceptions where this ratio continuously increases or decreases, but there is no doubt that this is the result of an irregular course of the curve, owing to errors of observation¹. Raoult, who made analogous experiments, incidentally also with ethereal solutions of nitrobenzene, arrived at exactly the same conclusion².

In order to judge the degree of approximation to the true mean conclusion of the ratios \(\frac{p_1}{p_0}\) liquid and \(\frac{p_1}{p_0}\) vapor, and also in order to estimate numerically the degree of accuracy of the method and the degree of regularity of the elasticity curve of one or another series (\(p_1\) vapor and \(p_1\) liquid), for each series \(\frac{p_1}{p_0}\) the mean error of the mean conclusion was calculated by the method of least squares. This mean error is given in each separate table and added to the mean conclusion.

For greater clarity these quantities are compared in the following table.

Table CXXI.

Mean error of the mean conclusion of the ratios \(\frac{p_1}{p_0}\) for mixtures of ether and nitrobenzene.

\(\pi^\circ/\%\)	\(\frac{p_1}{p_0}\) liquid	\(\frac{p_1}{p_0}\) vapor	\(\pi^\circ/\%\)	\(\frac{p_1}{p_0}\) liquid	\(\frac{p_1}{p_0}\) vapor
3,94	\(\pm 0{,}0002\)	\(\pm 0{,}0008\)	35,26	\(\pm 0{,}0002\)	\(\pm 0{,}0003\)
7,63	\(\pm 0{,}0002\)	\(\pm 0{,}0006\)	40,01	\(\pm 0{,}0002\)	\(\pm 0{,}0003\)
9,95		\(\pm 0{,}0002\)	44,85	\(\pm 0{,}0002\)	\(\pm 0{,}0001\)
15,96	\(\pm 0{,}0002\)	\(\pm 0{,}0006\)	50,74	\(\pm 0{,}0005\)	\(\pm 0{,}0001\)
20,81	\(\pm 0{,}0003\)	\(\pm 0{,}0003\)	60,64	\(\pm 0{,}0003\)	\(\pm 0{,}0006\)
25,39	\(\pm 0{,}0002\)	\(\pm 0{,}0006\)	70,24	\(\pm 0{,}0003\)	\(\pm 0{,}0002\)
30,56	\(\pm 0{,}0003\)	\(\pm 0{,}0003\)	78,86	\(\pm 0{,}0004\)	\(\pm 0{,}0004\)

Thus, the mean error of the mean derivation of the ratios \(\frac{p_1}{p_0}\) liquid fluctuates, in the majority of cases, between the limits \(\pm 0.0001\)—\(\pm 0.0003\) (only one case \(\pm 0.0004\) and one case \(\pm 0.0005\)); the mean error of the mean derivation of the ratios \(\frac{p_1}{p_0}\) vapor fluctuates, in the majority of cases, within the limits \(\pm 0.0003\)—\(\pm 0.0006\) (only one case \(\pm 0.0009\)). If these errors are expressed in millimeters of mercury, then for temperatures within the limits of the plotted curve they will lie: for \(\frac{p_1}{p_0}\) liquid, between \(\pm 0.038\) mm and \(\pm 0.131\) mm; for \(\frac{p_1}{p_0}\) vapor, between \(\pm 0.114\) mm and \(\pm 0.282\) mm.

These results, obtained by the method employed, I consider more than satisfactory.

The numerical values given in Table CXXI, moreover, clearly illustrate the fact that the vapor-pressure curves corresponding to temperatures measured in the vapor run less smoothly than the vapor-pressure curves corresponding to temperatures measured in the liquid.

Finally, it is also evident from Table CXXI that the method is suitable not only for dilute solutions but also for very concentrated solutions of nonvolatile substances. At least, the mean error of the mean derivation of the ratios \(\frac{p_1}{p_0}\) liquid and \(\frac{p_1}{p_0}\) vapor does not noticeably increase with increasing concentration.

Relation between the vapor pressure of a solution and its concentration

Since the ratio \(\frac{p_1}{p_0}\) may be considered independent of temperature, at least within the limits of experimental error, the mean values \(\frac{p_1}{p_0}\) liquid and \(\frac{p_1}{p_0}\) vapor may serve as characteristics of the vapor pressure of a given solution. I used these quantities to establish the relation between the change in the vapor pressure of a solution and its concentration. For this purpose, along the abscissa axis were plotted the quantities \(\%\) (content of nitrobenzene in 100 parts by weight of the mixture), and along the ordinate axis—the mean values \(\frac{p_1}{p_0}\) liquid and \(\frac{p_1}{p_0}\) vapor. The plotted curves represented the law of variation of the vapor pressure of the mixtures with variation of concentration; they also served for interpolation (I never allowed myself to resort to extrapolation).

Both curves represented a concave curve, whose concavity is at first scarcely noticeable, but then, with increasing concentration of the solution, the concavity increases very strongly, and the curve turns sharply upward.

If the concentration of the mixture is expressed by the content of nitrobenzene in 100 volumetric parts of ether, curves plotted in the same manner represent uniformly convex curves.

Table CXXII is a summary of the mean values \(\frac{p_1}{p_0}\) found experimentally, which served as material for constructing the curves.

Table CXXIII gives the values of \(\frac{p_1}{p_0}\) read from the plotted curves at a concentration interval of 5%.

Table CXXII.

Relative vapor pressure of mixtures of ether and nitrobenzene within the concentration limits 3.94%—78.86%
(experimental data).

$\pi\%$	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor	$\pi\%$	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor
3.94	0.9788	0.9726	35.26	0.8021	0.8172
7.63	0.9521	0.9617	40.01	0.7752	0.7916
9.95	0.9409	0.9477	44.85	0.7494	0.7616
15.96	0.9070	0.9132	49.99	0.7125	0.7289
20.81	0.8818	0.8959	60.04	0.6543	0.6647
25.39	0.8566	0.8676	70.24	0.5589	0.5706
30.56	0.8282	0.8403	78.86	0.4544	0.4729

Table CXXIII.

Relative vapor pressure of mixtures of ether and nitrobenzene within the concentration limits 0%—100%.
(interpolated data).

$\pi\%$	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor	Note	$\pi\%$	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor	Note
0	1.000	1.000	According to observations by Mikhailenko and Zellner.	80	—	0.452	According to observations by L. Konovalov.
5	0.967	0.974	According to observations by Mikhailenko and Zellner.	85	—	0.374	According to observations by L. Konovalov.
10	0.941	0.949	According to observations by Mikhailenko and Zellner.	90	—	0.283	According to observations by L. Konovalov.
15	0.914	0.924	According to observations by Mikhailenko and Zellner.	95	—	0.155	According to observations by L. Konovalov.
20	0.987	0.998	According to observations by Mikhailenko and Zellner.	100	—	—	According to observations by L. Konovalov.
25	0.860	0.872	According to observations by Mikhailenko and Zellner.
30	0.832	0.845	According to observations by Mikhailenko and Zellner.
35	0.804	0.818	According to observations by Mikhailenko and Zellner.
40	0.775	0.791	According to observations by Mikhailenko and Zellner.
45	0.748	0.763	According to observations by Mikhailenko and Zellner.
50	0.718	0.733	According to observations by Mikhailenko and Zellner.
55	0.687	0.703	According to observations by Mikhailenko and Zellner.
60	0.653	0.666	According to observations by Mikhailenko and Zellner.
65	0.611	0.623	According to observations by Mikhailenko and Zellner.
70	0.562	0.576	According to observations by Mikhailenko and Zellner.
75	0.518	0.532	According to observations by Mikhailenko and Zellner.

When the measurements of the vapor pressure of mixtures of ether and nitrobenzene had been completed, a work by D. Konovalov appeared in print, “The Critical Region of Solutions and the Phenomena of Opalescence,”^1) in which, among other things, there were also data on measurements of the vapor pressure of mixtures of ether and nitrobenzene obtained by the method which I had mentioned in my description “Methods for Determining the Vapor Pressure of Solutions,”^2) namely, by the “density” method. Thus, in the literature there proved to be three series of measurements of the vapor pressure of mixtures of ether and nitrobenzene, carried out by three different procedures: 1) Raoult’s,^3)—carried out by the barometric method; 2) D. Konovalov’s,—carried out by the density method; and 3) Mikhailenko and Zeltner’s—carried out by the boiling method. An opportunity presented itself, one not very often encountered in the literature on the vapor pressure of solutions, to compare results obtained by different methods, and in this way to make a comparative evaluation of these methods. This comparison is made in Table CXXIV, where Raoult’s figures and D. Konovalov’s figures, again the quantities $\frac{p_1}{p_0}$, are compared with the quantities $\frac{p_1}{p_0}$ liq. and $\frac{p_1}{p_0}$ vapor, obtained by me and calculated from the curves drawn by me.

TABLE CXXIV.

Comparison of the values of the relative vapor pressure of mixtures of ether and nitrobenzene according to the observations of Raoult, D. Konovalov, Mikhailenko and Zeltner.

$n\%$	Raoult $\frac{p_1}{p_0}$	Mikhailenko and Zeltner $\frac{p_1}{p_0}$ liq.	Mikhailenko and Zeltner $\frac{p_1}{p_0}$ vapor	$n\%$	Konovalov $\frac{p_1}{p_0}$	Mikhailenko and Zeltner $\frac{p_1}{p_0}$ liq.	Mikhailenko and Zeltner $\frac{p_1}{p_0}$ vapor
9,6	0,945	0,943	0,951	24,0	0,869	0,865	0,877
26,7	0,858	0,850	0,863	52,9	0,713	0,700	0,716
47,2	0,744	0,735	0,749	63,3	0,633	0,626	0,639
65,4	0,620	0,607	0,620	70,6	0,562	0,555	0,569
80,9	0,444	—	—	74,6	0,522	0,511	0,525
88,5	0,355	—	—	76,8	0,493	0,483	0,499
				83,3	0,403	—	—
				84,1	0,390	—
				91,7	0,239	—	—
				97,9	0,144	—	—

^1) D. Konovalov. Zh. R. F. Kh. O. 34 (1), 738. 1902.
^2) Ya. I. Mikhailenko. Methods for Determining the Vapor Pressure of Solutions. Kiev. 1901.
^3) Raoult, Zeitschr. phys. Ch. 2, 1888; Ann. de chim. et de phys. (6), 15, 375. 1888.

A comparison of the numbers in Table CXXIV leads to the conclusion that all three series of observations may be regarded as agreeing in magnitude, if only, from my observations, one takes for comparison the series \(\frac{p_1}{p_0}\) vapor. Indeed, the difference between the corresponding values of these three series fluctuates within the limits \(0.003\)—\(0.008\), and the largest differences, \(0.008\), occur only once each; if this difference is expressed in mm of mercury, then for the temperature \(18.1^\circ\), at which D. Konovalov’s measurements were made, it will have the magnitude: \(1.239\) mm—\(3.308\) mm; and for the temperature \(16^\circ\), at which Raoult’s measurements were made, it will have the magnitude \(1.122\) mm—\(2.712\) mm. These differences do not exceed the usual differences between the values for vapor pressure given by different authors, even in the case where the measurements were made by one and the same method, and even, as examples of this are found in this chapter, for pure liquids as well.

Table CXXIV also confirms the conclusion that the boiling method is suitable, and, apparently, to the same degree, for measuring the vapor pressure of both pure and strong solutions; at least, the differences between the values obtained by this method and the values obtained by other methods do not increase with increasing concentration.

Since I avoided extrapolating my experimental data, in Table CXXIII within the concentration limits \(80\%\)—\(100\%\) the interpolation was performed from D. Konovalov’s data, and the numerical values \(\frac{p_1}{p_0}\) thus obtained were entered in the column \(\frac{p_1}{p_0}\) vapor, since the comparison made in Table CXXIV showed that vapor pressures observed by the barometric method and by the density method (in both cases the vapor and liquid have one and the same temperature) agree with the pressure found by the boiling method (the vapor and the boiling liquid have different temperatures) only in the case when the vapor pressure is referred to the temperature of the vapor, and not of the liquid.

Solutions of iodine in organic solvents.

Measurements of the vapor pressure of solutions of iodine in organic solvents were made with the aim of obtaining for these solutions the values \(\frac{p_1}{p_0}\) and comparing them with the values \(\frac{s_1}{s_0}\), calculated on the basis of measurements of specific gravity made earlier by me jointly with Jaworski and Schelter.

The vapor pressure of solutions of iodine in ether, carbon disulfide, and chloroform was measured at various concentrations, extending up to the saturation concentration. The temperature interval was chosen so that the temperature \(25^\circ\), namely, the temperature at which the determinations of specific gravity were made, lay either in the middle of this interval or close to it. The solvents were carefully purified as described above (Chapter III). The iodine was analyzed (see p. 141).

The results of the measurements are brought together in tables compiled according to the same system as before. The designations are everywhere the same as before. The concentration of the solutions is determined by the content of iodine in 100 parts by weight of the solution (\(n\%\)).

2. Solutions of iodine in ether.

The vapor pressure of 9 solutions of iodine in ether was measured. The solutions were prepared by dissolving dry iodine in ether and immediately, in order to avoid the formation of \(HJ\), were subjected to investigation. The results of the measurements are given in Tables CXXV—CXXXIII.

Table CXXV A.

Boiling temperatures of a 3.02% solution of iodine in ether
at pressures of 382.10—442.90 mm.
(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
16,80	16,64		141,0	524,1	17
16,81	16,64	0,16	140,8	524,2		16,805	16,64	382,10
18,29	18,08		140,6	547,0	18
18,29	18,09	0,21	140,7	547,0		18,29	18,085	405,18
19,28	19,04		140,6	563,7	18
19,28	19,04	0,24	140,6	563,7		19,28	19,04	421,85
20,41	20,14		140,4	583,3	18
20,40	20,15	0,26	140,4	583,3		20,405	20,145	442,90

Table CXXV B.

Vapor pressure of a 3.02% solution of iodine in ether at temp. 17°—20.5°.
(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
17,0	385,00	387,70	0,9913	0,9883
17,5	392,60	395,60	0,9883	0,9886
18,0	400,00	403,90	0,9881	0,9895
18,5	408,60	412,35	0,9897	0,9899
19,0	417,00	421,15	0,9901	0,9911
19,5	425,85	430,35	0,9911	0,9931
20,0	435,05	440,10	0,9936	0,9959
20,5	444,95	—	0,9959
			0,9910±0,0009	0,9909±0,0010

Table CXXVI A.

Boiling temperatures of a 5.56% solution of iodine in ether at pressures of
386.83–464.45 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Difference	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17.28	17.15	0.14	140.8	528.7	18	17.285	17.14	386.83
17.29	17.13		140.8	528.8
18.49	18.30	0.19	140.5	547.2	18	18.49	18.30	405.93
18.49	18.30		140.5	547.1
20.22	19.98	0.24	139.5	574.9	18	20.22	19.98	434.23
20.22	19.98		139.5	575.1
20.99	20.74	0.24	139.3	588.3	18	20.995	20.75	447.73
21.00	20.76		139.2	588.3
21.94	21.65	0.28	138.9	604.6	18	21.945	21.66	464.45
21.95	21.67		138.8	604.7

Table CXXVI B.

Vapor pressure of a 5.56% solution of iodine in ether at temp. 17.5°–22.0°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
	mm.	mm.
17.5	390.10	392.55	0.9820	0.9806
18.0	397.95	400.75	0.9829	0.9815
18.5	406.10	409.15	0.9836	0.9822
19.0	414.25	417.25	0.9836	0.9817
19.5	422.15	425.85	0.9824	0.9827
20.0	430.45	434.75	0.9831	0.9836
20.5	439.00	443.55	0.9827	0.9838
21.0	448.00	452.20	0.9827	0.9831
21.5	456.50	461.40	0.9799	0.9831
22.0	—	—
			0.9825 ± 0.0004	0.9824 ± 0.0004

Table CXXVII A.

Boiling temperatures of a 6.35% solution of iodine in ether at pressures of 383.78–463.45 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum.	T	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17,15	16,99		141,4	526,3	18	17,15	16,99	383,78
17,15	16,99	0,16	141,4	526,3
18,12	17,95		141,2	541,1	18	18,12	17,955	398,70
18,12	17,96	0,17	141,3	541,1
19,18	19,98		141,2	558,2	18	19,18	18,98	415,70
19,18	19,98	0,20	141,3	558,2
20,29	20,06		141,0	576,7	18	20,29	20,065	434,40
20,29	20,07	0,23	141,0	576,6
21,87	21,60		140,8	604,2	19	21,875	21,605	463,45
21,88	21,61	0,27	140,8	604,3

Table CXXVII B.

Vapor pressure of a 6.35% solution of iodine in ether at temperatures 17.0°–21.5°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
17,0	—	383,95		0,9787
17,5	388,95	391,55	0,9788	0,9781
18,0	396,55	399,45	0,9793	0,9784
18,5	404,40	407,55	0,9795	0,9784
19,0	412,60	416,15	0,9797	0,9793
19,5	420,95	424,55	0,9797	0,9795
20,0	429,45	433,30	0,9808	0,9804
20,5	438,15	442,20	0,9806	0,9808
21,0	447,05	451,55	0,9804	0,9817
21,5	456,40	461,40	0,9797	0,9831
			0,9798 ± 0,0002	0,9798 ± 0,0004

Table CXXVIII A.

Boiling temperatures of an 8.33% solution of iodine in ether at pressures
379.33–455.38 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17,00	16,82		142,3	522,8	18	17,00	16,82	379,33
17,00	16,82	0,18	142,3	522,7
18,30	18,11		142,2	542,9	18	18,305	18,11	399,53
18,31	18,11	0,19	142,2	542,9
19,48	19,25		142,0	561,8	18	19,48	19,25	418,51
19,48	19,25	0,23	142,1	561,8
20,39	20,16		141,9	577,6	18	20,39	20,16	434,48
20,39	20,16	0,23	141,9	577,7
21,51	21,32		141,7	598,4	18	21,57	21,325	455,38
21,57	21,33	0,25	141,7	598,4

Table CXXVIII B.

Vapor pressure of an 8.33% solution of iodine in ether at temp. 17.0°–21.5°.

(interpolated data).

\(t_0\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
17,0	379,30	382,05	0,9766	0,9739
17,5	386,70	389,70	0,9734	0,9736
18,0	394,50	397,75	0,9743	0,9743
18,5	402,45	405,80	0,9748	0,9743
19,0	410,50	413,95	0,9748	0,9741
19,5	418,85	422,50	0,9748	0,9750
20,0	427,50	431,50	0,9763	0,9763
20,5	436,40	440,35	0,9768	0,9766
21,0	445,00	449,40	0,9761	0,9770
21,5	454,15	—	0,9750
			0,9753 ± 0,0003	0,9750 ± 0,0004

Table CXXIX A.

Boiling temperatures of a 10.49% solution of iodine in ether at pressures of
385.04–444.03 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Difference	Barom.	Vacuum	\(T^\circ\)	mean \(t^\circ\) liquid	mean \(t^\circ\) vapor	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17,55	17,36	0,18	139,1	525,2	17	17,565	17,38	385,04
17,58	17,40	0,18	139,2	525,4	17	17,565	17,38	385,04
18,38	18,17	0,21	139,0	537,4	18	18,385	18,175	397,28
18,39	18,18	0,21	139,0	537,5	18	18,385	18,175	397,28
19,39	19,13	0,26	138,9	553,7	17	19,39	19,135	413,77
19,39	19,14	0,26	138,8	553,8	17	19,39	19,135	413,77
20,49	20,19	0,29	138,6	572,1	17	20,49	20,205	432,20
20,49	20,22	0,29	138,6	572,1	17	20,49	20,205	432,20
21,17	20,88	0,29	138,4	583,7	17	21,18	20,895	444,03
21,19	20,91	0,29	138,4	583,6	17	21,18	20,895	444,03

Table CXXIX B.

Vapor pressure of a 10.49% solution of iodine in ether at temperatures 17.5°–21.0°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
17,5	384,05	386,85	0,9665	0,9665
18,0	391,55	394,70	0,9669	0,9669
18,5	399,20	402,90	0,9669	0,9674
19,0	407,20	411,45	0,9669	0,9683
19,5	415,45	419,65	0,9669	0,9683
20,0	423,45	428,00	0,9672	0,9683
20,5	431,95	436,80	0,9667	0,9689
21,0	440,70	—	0,9665	—
			0,9668 ± 0,00008	0,9678 ± 0,00007

Table CXXX A.

Boiling temperatures of a 12.49% solution of iodine in ether at pressures of 372.23–439.76 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
\(^\circ C.\)	\(^\circ C.\)	\(^\circ C.\)			\(^\circ C.\)	\(^\circ C.\)	\(^\circ C.\)	mm.
16,88	16,70		138,9	512,2	18	16,89	16,72	372,23
16,90	16,74	0,17	138,9	512,3
18,06	17,86		138,6	529,3	18	18,08	17,87	389,53
18,10	17,88	0,21	138,6	529,3
19,15	18,96		138,5	546,3	18	19,15	18,96	406,70
19,15	18,96	0,19	138,4	546,4
21,13	20,82		138,0	579,0	19	21,13	20,84	439,76
21,13	20,86	0,29	138,0	579,0

Table CXXX B.

Vapor pressure of a 12.49% solution of iodine in ether at temperatures \(17^\circ\)—\(21^\circ\).

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
\(^\circ C.\)	mm.	mm.
17,0	—	376,30		0,9592
17,5	380,90	383,85	0,9587	0,9590
18,0	388,35	391,55	0,9592	0,9590
18,5	396,00	399,30	0,9592	0,9587
19,0	404,00	407,45	0,9594	0,9587
19,5	411,95	415,75	0,9587	0,9594
20,0	420,05	424,45	0,9592	0,9603
20,5	428,45	433,45	0,9587	0,9614
21,0	437,40	—	0,9594
			0,9594 ± 0,0002	0,9594 ± 0,0003

Table CXXXI A.

Boiling temperatures of a solution of iodine in ether, 14.55%, at pressures of 386.45–461.22 mm. ¹)

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Difference	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
18,02	17,81		136,3	523,8	17	18,02	17,81	386,45
18,02	17,81	0,21	136,3	523,7
19,09	18,84		136,2	540,5	17	19,09	18,845	403,19
19,09	18,85	0,25	136,2	540,5
20,26	19,97		136,2	559,1	17	20,26	19,97	421,69
20,26	19,97	0,29	136,2	559,0
21,43	21,06		136,3	578,8	17	21,43	21,06	441,28
21,43	21,06	0,37	136,3	578,8
22,52	22,14		136,1	598,6	17	22,525	22,14	461,22
22,53	22,14	0,38	136,1	598,6

Table CXXXI B.

Vapor pressure of a solution of iodine in ether, 14.55%, at temperatures 18.0°–22.5°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
18,0	386,05	389,30	0,9535	0,9537
18,5	393,50	396,95	0,9530	0,9530
19,0	401,15	405,00	0,9526	0,9532
19,5	409,00	413,35	0,9519	0,9539
20,0	417,25	422,15	0,9528	0,9550
20,5	425,50	430,95	0,9524	0,9559
21,0	433,80	440,20	0,9515	0,9572
21,5	442,40	449,05	0,9497	0,9565
22,0	451,40	458,40	0,9521	0,9581
22,5	460,80	—
			0,9521 ± 0,0004	0,9551 ± 0,0006

¹) Owing to an oversight, this solution was heated for an entire night; on the following day measurements of its vapor pressure were made.

Table CXXXII A.

Boiling temperatures of a solution of iodine in ether, 16.39%, at pressures of 374.20–435.56 mm.

(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(t^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17.41	17.18		140.1	515.3	17
17.41	17.18	0.23	140.1	515.4		17.41	17.18	374.20
18.30	18.08		140.0	528.8	18
18.32	18.10	0.22	140.0	528.9		18.31	18.09	387.73
19.28	19.07		139.9	544.2	18
19.28	19.07	0.21	139.9	544.3		19.28	19.07	403.20
20.46	20.23		139.6	563.5	18
20.46	20.25	0.22	139.6	563.6		20.46	20.24	422.71
21.24	20.96		139.4	576.2	18.5
21.24	20.96	0.28	139.4	576.3		21.24	20.96	435.56

Table CXXXII B.

Vapor pressure of a solution of iodine in ether, 16.39%, at temp. 17.5°–21.0°.

(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
17.5	375.45	378.80	0.9449	0.9465
18.0	382.90	386.30	0.9458	0.9462
18.5	390.55	394.00	0.9458	0.9460
19.0	398.55	402.05	0.9462	0.9460
19.5	406.55	410.00	0.9462	0.9462
20.0	414.45	418.40	0.9465	0.9467
20.5	422.80	427.10	0.9465	0.9473
21.0	431.45	436.30	0.9462	0.9486
			0.9460 ± 0.0001	0.9466 ± 0.0001

Table CXXXIII A.

Boiling temperatures of a solution of iodine in ether, 19.60%, at pressures of 371.40–450.82 mm.
(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Difference	Barom.	Vacuum	\(T^\circ\)	mean \(t^\circ\) liquid	mean \(t^\circ\) vapor	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
17,60	17,29		135,5	507,9	16
17,60	17,30	0,31	135,5	507,9		17,60	17,295	371,40
19,27	18,94		135,3	532,2	16
19,27	18,94	0,33	135,3	532,2		19,27	18,94	395,86
20,36	20,00		135,2	549,5	16
20,38	19,99	0,38	135,2	549,5		20,37	19,995	413,23
21,68	21,26		135,0	572,0	16
21,71	21,29	0,42	135,0	572,0		21,695	21,278	435,85
22,50	22,03		134,8	586,8	16
22,49	22,03	0,46	134,8	586,8		22,495	22,03	450,82

Table CXXXIII B.

Vapor pressure of a solution of iodine in ether, 19.60%, at temperatures 17.5°–22.5°.
(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
17,5	370,00	374,40	0,9313	0,9354
18,0	376,95	381,60	0,9309	0,9348
18,5	384,15	389,10	0,9303	0,9343
19,0	391,55	396,85	0,9296	0,9339
19,5	399,20	405,00	0,9292	0,9348
20,0	407,05	413,40	0,9296	0,9354
20,5	415,30	422,35	0,9296	0,9367
21,0	423,75	431,05	0,9294	0,9371
21,5	432,45	440,25	0,9283	0,9380
22,0	441,50	—	0,9311
22,5	451,15
			0,9299±0,0003	0,9355±0,0005

Discussion of the results. Measurements of the vapor pressure of iodine solutions in ether lead to the same results as measurements of the vapor pressure of mixtures of ether and nitrobenzene. Namely:

1) The temperature of the boiling liquid is always higher than the temperature of the vapor.

2) The vapor-pressure curves of the solutions have the same form as the vapor-pressure curve of the pure liquid; they appear parallel to the vapor-pressure curve of the pure liquid. The vapor-pressure curve corresponding to the temperatures measured in the liquid, and that corresponding to the temperatures measured in the vapors, diverge little by little as the temperature increases.

3) The ratio \(\frac{p_1}{p_0}\) must be regarded, within the limits of the accuracy of the measurements, as independent of the temperature.

Dependence of the vapor pressure of iodine solutions in ether on concentration. In both series of \(\frac{p_1}{p_0}\), namely \(\frac{p_1}{p_0}\) liquid and \(\frac{p_1}{p_0}\) vapor, the arithmetical mean was found, and by the method of least squares the mean error of this mean result was calculated. In Tables B this quantity is given with the mean result.

It turned out that, in the series \(\frac{p_1}{p_0}\) liquid, the mean error of the mean result lies between the limits \(\pm 0.0001\)—\(\pm 0.0004\) (only once was the value \(\pm 0.0009\) obtained); in the series \(\frac{p_1}{p_0}\) vapor, the mean error of the mean result lies between the limits \(\pm 0.0003\)—\(\pm 0.0006\) (only once was the value \(\pm 0.0010\) obtained). The concentration of the solution apparently does not affect the magnitude of the error.

If this error is calculated in millimeters of mercury, then, in the interval of that temperature at which the measurements were made, the extreme limits of the error of the mean result will be as follows: in the series \(\frac{p_1}{p_0}\) liquid, the extreme limits of the error will be \(\pm 0.031\) mm and \(\pm 0.191\) mm, and in the series \(\frac{p_1}{p_0}\) vapor, the extreme limits of the error will be \(\pm 0.11\) mm and \(\pm 0.284\) mm. Thus, in the series \(\frac{p_1}{p_0}\) vapor, here too there is a greater error than in the series \(\frac{p_1}{p_0}\) liquid; this, in all probability, is due to the fact that, when measuring the temperature of the vapor, it was not possible completely to eliminate cooling owing to contact with cold air or by radiation.

The mean values of \(\frac{p_1}{p_0}\) liquid and \(\frac{p_1}{p_0}\) vapor for the concentrations investigated are brought together in Table CXXXIV. The concentration of the solution is expressed by the content of iodine in 100 parts by weight of solution (\(p\%\)) and in 100 parts by weight of solvent (\(c\)).

Table CXXXIV.

Relative vapor pressure of solutions of iodine in ether in the range of concentrations 3.02%—19.60%.

(Experimental data).

\(c\)	\(\pi\%\)	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor	\(\dfrac{p_1}{p_0}\) mean
3.11	3.02	0.9910±0.0009	0.9909±0.0010	0.9910
5.89	5.56	0.9825±0.0004	0.9824±0.0004	0.9825
6.78	6.35	0.9798±0.0002	0.9798±0.0004	0.9798
8.71	8.33	0.9753±0.0003	0.9750±0.0004	0.9752
11.72	10.49	0.9668±0.0008	0.9678±0.0003	0.9671
14.27	12.49	0.9594±0.0002	0.9594±0.0003	0.9594
17.03	14.55	0.9521±0.0004	0.9551±0.0006	0.9531
19.60	16.39	0.9460±0.0001	0.9466±0.0004	0.9462
24.38	19.60	0.9299±0.0003	0.9355±0.0005	0.9314

As is seen from Table CXXXIV, the values of the series \(\dfrac{p_1}{p_0}\) liquid and of the series \(\dfrac{p_1}{p_0}\) vapor are in some cases identical (the differences lie within the limits of experimental error), while in other cases they differ little, and, moreover, the fluctuations proceed irregularly. In view of this I considered it possible to take the mean of each two corresponding values of the one and the other series; in doing so I assigned the values of the series \(\dfrac{p_1}{p_0}\) liquid a weight of 2, and the values of the series \(\dfrac{p_1}{p_0}\) vapor a weight of 1, since in drawing the vapor-pressure curves both here and also for mixtures of ether with nitrobenzene it turned out that the vapor-pressure curve corresponding to temperatures measured in the liquid runs more regularly than the vapor-pressure curve corresponding to temperatures measured in the vapors. These mean values served as the reference numbers for constructing the curve expressing the law of change of the vapor pressure of solutions of iodine in ether with change in concentration.

If the concentration of the solution is expressed in percentages (\(\pi\%\)), the curve proves to be slightly concave; if the concentration of the solution is expressed by the content of iodine in 100 parts by weight of ether (\(c\)), then the curve has the form of a barely noticeable convex curve, very closely approaching a straight line. Table CXXXV gives the values of \(\dfrac{p_1}{p_0}\) mean within the investigated range of concentrations, read from this curve.

Table CXXXV.

Relative vapor pressure of iodine solutions in ether.

(interpolated data).

\(c\)	\(\dfrac{p_1}{p_0}\) mean	\(c\)	\(\dfrac{p_1}{p_0}\) mean
0	1.0000	15	0.9575
1	0.9970	16	0.9547
2	0.9940	17	0.9518
3	0.9910	18	0.9490
4	0.9882	19	0.9462
5	9.9852	20	0.9435
6	0.9823	21	0.9408
7	0.9795	22	0.9382
8	0.9768	23	0.9355
9	0.9742	24	0.9327
10	0.9715
11	0.9687
12	0.9662
13	0.9632
14	0.9604

3. Solutions of iodine in carbon disulfide.

Carbon disulfide was purified as described on p. 146. The iodine was analyzed. Measurements of the vapor pressure were carried out within the temperature range \(22.5^\circ\)—\(27.5^\circ\).

The results of measurements of the vapor pressure of pure carbon disulfide are given in Tables CXXXVI A and B. In Table CXXXVI A the experimental data are collected; in Table CXXXVI B—the results of graphical interpolation of the experimental data of the preceding table.

In Table CXXXVI B, moreover, the numerical values obtained are compared with values calculated for the vapor pressure of carbon disulfide on the basis of measurements by Regnault¹) and Battelli²). The calculations were made according to the formula:

\[ \operatorname{Log} p_0 = a - b \alpha^{\theta} - c \beta^{\theta} \tag{76} \]

For the constants of equation (76), Regnault’s measurements gave: \(a = 5.4011662\), \(b = 3.4405663\), \(c = 0.2857386\), \(\log \alpha = \overline{1}.9977623\), \(\log \beta = \overline{1}.9911997\); \(\theta = (t^\circ + 20^\circ)\) by the air thermometer; Battelli’s measurements, made by the isotherm method, gave for these same constants the numbers: \(a = 5.0720062\), \(b = 2.962430\), \(c = -0.00102909\), \(\log \alpha = \overline{1}.9971662\), \(\log \beta = \overline{1}.9086244\), \(\theta = t^\circ\).

¹) Regnault, Rel. des exp. II. p. 394.
²) Battelli, Mem. della Acc. di Torino (2) 41, 1. 1890; (2) 42, 1. 1891.

Table CXXXVI A.

Boiling temperatures of carbon disulfide \(CS_2\) at pressures of 329.06–392.83 mm.

(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Diff.	Barom.	Vacuum.	\(T^0\)	\(t^0\) liquid, mean	\(t^0\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
22,83	22,53	0,30	154,7	484,7	17	22,83	22,53	329,06
22,83	22,53	0,30	154,7	484,7	17	22,83	22,53	329,06
23,60	23,27	0,33	154,7	494,3	17	23,60	23,27	338,71
23,60	23,27	0,33	154,7	494,3	17	23,60	23,27	338,71
24,31	24,01	0,30	154,4	503,6	17	24,31	24,01	348,25
24,31	24,01	0,30	154,4	503,7	17	24,31	24,01	348,25
25,10	24,80	0,30	154,5	514,7	17	25,10	24,80	359,24
25,10	24,80	0,30	154,3	514,7	17	25,10	24,80	359,24
25,90	25,61	0,29	154,3	525,6	18	25,90	25,615	370,23
25,90	25,62	0,29	154,3	525,6	18	25,90	25,615	370,23
26,62	26,35	0,27	154,1	536,1	18	26,63	26,36	380,93
26,64	26,37	0,27	154,1	536,2	18	26,63	26,36	380,93
27,45	27,20	0,26	154,0	548,0	18	27,465	27,20	392,83
27,48	27,20	0,26	154,0	548,0	18	27,465	27,20	392,83

Table CXXXVI B.

Vapor pressure of carbon disulfide \(CS_2\) at temp. 22.5°–27.5°.

(interpolated data).

| \(t^0\) | \multicolumn{2}{c}{Mikhailenko and Zelter} | Regnault | Battelli | Mean from observations by different authors¹ |
|---:|---:|---:|---:|---:|---:|
| | \(p_1\) liquid | \(p_1\) vapor | | | |
| °C. | mm. | mm. | mm. | mm. | |
| 22,5 | — | 328,70 | 328,45 | 326,66 | |
| 23,0 | 331,20 | 335,00 | 334,81 | 332,98 | 334,7 |
| 23,5 | 337,50 | 341,50 | 341,26 | 339,41 | |
| 24,0 | 344,05 | 348,15 | 347,82 | 345,94 | 347,7 |
| 24,5 | 350,75 | 354,75 | 354,48 | 352,58 | |
| 25,0 | 357,50 | 361,65 | 361,25 | 359,31 | 361,1 |
| 25,5 | 364,45 | 368,60 | 368,12 | 366,16 | |
| 26,0 | 371,60 | 375,70 | 375,08 | 373,12 | 374,95 |
| 26,5 | 378,75 | 382,90 | 382,16 | 380,18 | |
| 27,0 | 386,00 | 390,30 | 389,35 | 387,35 | 389,2 |
| 27,5 | 393,55 | — | 396,64 | 394,63 | |

All three series of observations may be considered, in general, to be in agreement. The values of the vapor pressure corresponding to the temperatures measured in the vapors are very close to Regnault’s numbers, and also to the mean values calculated on the basis of observations by different authors (the difference is expressed in fractions of a millimeter).

Battelli’s numbers, obtained by the isothermal method, are much lower than both the numbers of other authors and the mean values.

The results of the measurements of the vapor pressure of solutions of iodine in carbon disulfide are given in Tables CXXXVII—CXLIII.

Table CXXXVII A.

Boiling temperatures of a solution of iodine in carbon disulfide, 1.65%, at pressures of 337.91—377.73 mm.

(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Difference	Barom.	Vacuum	\(T^0\)	\(t^0\) liquid, mean	\(t^0\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
23,62	23,28	0,33	156,9	495,7	17	23,625	23,29	337,91
23,63	23,30	0,33	156,8	495,7	17	23,625	23,29	337,91
24,32	24,01	0,31	156,7	504,8	18	24,325	24,01	347,20
24,33	24,01	0,31	156,6	504,9	18	24,325	24,01	347,20
25,04	24,70	0,30	156,6	514,7	18	25,05	24,75	357,04
25,06	24,71	0,30	156,6	514,7	18	25,05	24,75	357,04
25,76	25,43	0,28	156,4	524,6	18	25,76	25,48	367,19
25,76	25,43	0,28	156,4	524,7	18	25,76	25,48	367,19
26,47	26,20	0,28	156,4	535,2	18	26,48	26,20	377,73
26,49	26,20	0,28	156,3	535,2	18	26,48	26,20	377,73

Table CXXXVII B.

Vapor pressure of a solution of iodine in carbon disulfide, 1.65%, at temp. 23.5°—26.5°.

(interpolated data).

\(t^0\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
23,5	—	340,55		0,9970
24,0	342,90	347,05	0,9968	0,9968
24,5	349,55	353,60	0,9966	0,9968
25,0	356,35	360,40	0,9966	0,9968
25,5	363,30	367,45	0,9970	0,9966
26,0	370,55	374,65	0,9970	0,9972
26,5	378,05	—	0,9982
			0,9970±0,0002	0,9968±0,00009

TABLE CXXXVIII A.

Boiling temperatures of a solution of iodine in carbon disulfide, 1.76%, at pressures of 310.59–379.10 mm.

(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Difference	Barom.	Vacuum	\(T^0\)	\(t^0\) liquid, mean	\(t^0\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
21.47	21.19	0.28	167.0	478.3	17	21.47	21.19	310.59
21.47	21.19		167.0	478.3
21.99	21.70	0.29	166.9	485.0	18	21.995	21.705	317.22
22.00	21.71		170.0	485.1
23.22	22.93	0.29	166.8	500.9	18	23.225	22.935	333.16
23.23	22.94		166.9	501.0
24.65	24.37	0.30	165.0	517.5	18	24.66	24.36	351.60
24.67	24.35		165.1	517.8
25.55	25.30	0.27	165.0	530.2	17	25.56	25.295	364.15
25.57	25.29		165.1	530.2
26.60	26.33	0.26	165.0	545.0	17	26.60	26.34	379.10
26.60	26.35		164.9	542.2

Table CXXXVIII B.

Vapor pressure of a solution of iodine in carbon disulfide, 1.76%, at temp. 21.5°–26.5°.

(interpolated data).

\(t^0\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
21.5	311.00	314.50
22.0	317.20	320.80
22.5	323.65	327.35		0.9956
23.0	330.25	334.05	0.9970	0.9970
23.5	336.70	340.25	0.9975	0.9961
24.0	343.05	346.65	0.9970	0.9956
24.5	349.55	353.30	0.9966	0.9959
25.0	356.20	360.10	0.9963	0.9959
25.5	363.15	367.05	0.9963	0.9956
26.0	370.25	374.25	0.9961	0.9961
26.5	377.55	—	0.9968
			0.9967 ± 0.0002	0.9959 ± 0.0002

Table CXXXIX A.

Boiling temperatures of a 5.713% iodine solution in carbon disulfide at pressures of 331.8—382.63 mm.

(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Diff.	Barom.	Vacuum	\(T^0\)	\(t^0\) liquid, mean	\(t^0\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
23.45	23.09		164.0	496.8	18	23.465	23.065	331.8
23.48	23.04	0.36	164.0	496.8
24.19	23.83		163.7	506.2	18	24.195	23.835	341.50
24.20	23.84	0.36	163.6	506.1
24.72	24.36		163.5	512.7	18	24.72	24.365	348.15
24.72	24.37	0.36	163.5	512.6
25.56	25.20		157.11	517.6	17	25.58	25.23	359.49
25.60	25.26	0.36	157.10	517.7
26.28	25.92		157.0	527.1	17	26.28	25.92	369.09
26.28	25.92	0.36	156.9	527.1
27.17	26.81		156.5	539.3	17	27.175	26.815	382.63
27.18	26.82	0.36	156.5	539.3

Table CXXXIX B.

Vapor pressure of a 5.713% iodine solution in carbon disulfide at temp. 23.0°—27.0°.

(interpolated data).

\(t^0\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
23.0	—	331.15		0.9886
23.5	332.30	337.25	0.9847	0.9874
24.0	338.60	343.50	0.9842	0.9867
24.5	345.20	349.90	0.9845	0.9863
25.0	351.80	356.45	0.9840	0.9856
25.5	358.35	363.25	0.9831	0.9851
26.0	365.30	370.45	0.9829	0.9861
26.5	372.55	377.75	0.9836	0.9863
27.0	380.00	—	0.9845
			0.9839±0.0002	0.9865±0.0004

Table CXL A.

Boiling temperatures of a solution of iodine in carbon disulfide, 5.91%, at pressures of 335.06–376.35 mm.

(experimental data).

\(t^\circ\) liquid, °C	\(t^\circ\) vapor, °C	Diff., °C	Barom.	Vacuum	\(T^\circ\), °C	Mean \(t^\circ\) liquid, °C	Mean \(t^\circ\) vapor, °C	\(p_1\), mm
23,78	23,35	0,42	152,6	488,6	17	23,785	23,365	335,06
23,79	23,38	0,42	152,6	488,6	17	23,785	23,365	335,06
24,57	24,15	0,42	152,4	498,5	17	24,57	24,155	345,21
24,57	24,15	0,42	152,4	498,6	17	24,57	24,155	345,21
25,38	24,95	0,40	152,2	509,1	17	25,375	24,975	355,85
25,37	25,00	0,40	152,3	509,1	17	25,375	24,975	355,85
26,10	25,68	0,41	152,3	519,2	17	26,10	25,69	365,95
26,10	25,70	0,41	152,2	519,2	17	26,10	25,69	365,95
26,78	26,41	0,37	152,3	529,6	17	26,79	26,425	376,35
26,80	26,44	0,37	152,2	529,7	17	26,79	26,425	376,35

Table CLX B.

Vapor pressure of a solution of iodine in carbon disulfide, 5.91%, at temp. 23.5°–26.5°.

(interpolated data).

\(t^\circ\), °C	\(p_1\) liquid, mm	\(p_1\) vapor, mm	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
23,5	—	336,85		0,9863
24,0	337,80	343,20	0,9820	0,9858
24,5	344,25	349,70	0,9815	0,9858
25,0	350,90	356,20	0,9815	0,9851
25,5	357,65	363,15	0,9813	0,9849
26,0	364,70	370,25	0,9813	0,9854
26,5	371,95	377,50	0,9820	0,9858
			0,9816 ± 0,0001	0,9855 ± 0,0002

Table CXLI A.

Boiling temperatures of a solution of iodine in carbon disulfide, 8.25%, at pressures of 339.56—368.95 mm.

(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Diff.	Barom.	Vacuum	\(T^0\)	mean \(t^0\) liquid	mean \(t^0\) vapor	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
24,21	23,90		156,6	496,1	17
24,27	23,94	0,14	155,5	496,0		24,24	23,92	339,56
24,59	24,29		155,0	500,2	17
24,59	24,29	0,30	155,0	500,2		24,59	24,29	344,26
25,48	25,18		154,5	511,8	17
25,48	25,18	0,30	154,5	511,9		25,48	25,18	356,35
25,83	25,54		154,5	516,2	18
25,84	25,54	0,29	154,5	516,3		25,835	25 54	360,80
26,40	26,10		154,1	524,1	18
26,40	26,10	0,30	154,1	524 0		26,40	26,10	368,95

Table CXLI B.

Vapor pressure of a solution of iodine in carbon disulfide, 8.25%, at temperatures 24.0°—26.0°.

(interpolated data).

\(t^0\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
24,0	340,55	—
24,5	343,0	346.95	0,9781	0,9779
25,0	349,50	353,45	0,9775	0,9775
25,5	356,20	360,40	0,9775	0,9777
26,0	363,20	367,45	0,9772	0,9779
			0,9776±0,0002	0,9777±0,0001

Table CXLII A.

Boiling temperatures of a solution of iodine in carbon disulfide, 10.90%,
at pressures of 336.61–373.63 mm.
(experimental data).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum.	\(T^\circ\)	mean \(t^\circ\) liquid	mean \(t^\circ\) vapor	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
24.23	23.91		150.1	487.6	17	24.23	23.92	336.61
24.23	23.93	0.31	150.1	487.7		24.23	23.92	336.61
24.77	24.44		150.1	494.4	17	24.77	24.44	343.41
24.77	24.44	0.33	150.1	494.4		24.77	24.44	343.41
25.50	25.17		150.0	504.2	17	25.50	25.185	353.2
25.50	25.20	0.32	150.0	504.2		25.50	25.185	353.2
26.25	25.92		150.0	514.77	18	26.275	25.96	363.76
26.30	26.00	0.31	150.0	514.88		26.275	25.96	363.76
26.95	26.64		150.0	524.7	18	26.95	26.64	373.63
26.95	26.64	0.31	150.0	524.8		26.95	26.64	373.63

Table CXLII B.

Vapor pressure of a solution of iodine in carbon disulfide, 10.90%, at
temperatures of 24.0°–27.0°.
(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
24.0	—	337.70		0.9701
24.5	340.00	344.15	0.9696	0.9701
25.0	346.50	350.75	0.9692	0.9698
25.5	353.20	357.45	0.9692	0.9696
26.0	360.00	364.40	0.9687	9.9701
26.5	367.00	371.55	0.9692	0.9703
27.0	374.35	—	0.9696
			0.9693 ± 0.0002	0.9700 ± 0.0001

Table CXLIII. A.

Boiling temperatures of a solution of iodine in carbon disulfide, 12.56%, at pressures of 324.11–363.44 mm.
(experimental data).

\(t^\circ\) liquid	\(t'\) vapor	Difference	Barom.	Vacuum	\(T^\circ\)	mean \(t'\) liquid	mean \(t'\) vapor	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
23,44	23,07		150,4	475,5	18	23,45	23.095	324,11
23,46	23,10	0,36	150,5	475,5		23,45	23.095	324,11
24,26	23,89		150,2	485,7	18	24.265	23,92	334,5
24,27	23,93	0,34	150,2	485,7		24.265	23,92	334,5
24,95	24,62		150,0	494,6	18	24,97	24,63	343,6
24,99	24,64	0,34	150,0	494,6		24,97	24,63	343,6
25,86	25,49		150,0	505,2	18	25,86	25,49	355,25
25,86	25,49	0,37	149,9	505,2		25,86	25,49	355,25
26,44	26,08		149,6	514,2	18	26,435	26,075	363,44
26,43	26,07	0,36	149,8	514,2		26,435	26,075	363,44

Table CXLIII B.

Vapor elasticity of a solution of iodine in carbon disulfide, 12.56%, at temperatures of 23.5°–26.0°
(interpolated data).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
23,5	324,70	329,20	0.9621	0,9641
24,0	330,95	335,50	0,9618	0,9638
24,5	337,35	342,0	0,9618	0,9641
25,0	343,45	348,55	0,9605	0,9638
25,5	350,50	355,40	0,9618	0,9641
26,0	357 15	362,40	0,9609	0,9647
			0,9614±0,0003	0,9641±0,0001

Discussion of the results. All the conclusions that were drawn in measuring the vapor pressure of solutions of iodine in ether apply in full also to solutions of iodine in carbon disulfide. Namely:

1) the temperature of the boiling liquid is higher than the temperature of the vapor;

2) the vapor-pressure curve corresponding to the temperatures of the liquid, and that corresponding to the temperatures of the vapor, diverge little by little. The general form of these curves is the same as that of the vapor-pressure curves of pure carbon disulfide;

3) the ratio $\frac{p_1}{p_0}$ for the liquid and $\frac{p_1}{p_0}$ for the vapor must be regarded as independent of temperature within the limits of the temperatures investigated and within the limits of the experimental errors.

As before, for each series of values of $\frac{p_1}{p_0}$ for the liquid and $\frac{p_1}{p_0}$ for the vapor, the mean value was found, and the mean error of this mean result was calculated by the method of least squares.

In the same form as before, the results of the measurements of the vapor pressure of solutions of iodine in carbon disulfide are presented in Table CXLIV.

The concentration of the solutions is expressed by the content of iodine in 100 parts by weight of solution ($\pi^0/\!_0$) and in 100 parts by weight of solvent ($c$).

Table CXLIV.

Relative vapor pressure of solutions of iodine in carbon disulfide within the concentration range 1,65%—12,56%.

(Summary of experimental data).

$c$	$\pi^0/\!_0$	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor	$\dfrac{p_1}{p_0}$ mean
1,68	1,65	0,9970±0,0002	0,9968±0,00009	0,9969
1,79	1,76	0,9967±0,0002	0,9959±0,0002	0,9964
6,05	5,71	0,9839±0,0002	0,9865±0,0004	0,9847
6,28	5,91	0,9816±0,0001	0,9855±0,0002	0,9829
8,99	8,25	0,9776±0,0002	0,9777±0,0001	0,9776
12,23	10,90	0,9693±0,0002	0,9700±0,0001	0,9695
14,36	12,56	0,9614±0,0003	0,9641±0,0001	0,9623

Since the differences between the corresponding values of the series $\frac{p_1}{p_0}$ liquid and $\frac{p_1}{p_0}$ vapor lie either within the limits of the experimental errors (in half the cases) or are very small, then, in order to characterize the vapor pressure of a given solution, the mean was calculated from each two corresponding values of both series; and, since here too the vapor-pressure curve corresponding to the temperatures of the vapor runs less regularly than the vapor-pressure curve corresponding to the temperature of the liquid, the values of the series $\frac{p_1}{p_0}$ liquid were assigned the weight 2, and the values of the series $\frac{p_1}{p_0}$ vapor—the weight 1.

With the aid of the numbers thus obtained, a curve was finally constructed, expressing the law of variation of the vapor pressure of solutions of iodine in carbon disulfide with change in concentration.

If the concentration of the solution is expressed in percent \((\pi' / \%)\), then the pressure curve is a weakly concave curve. If the concentration of the solution is expressed by the number of grams of iodine in 100 parts by weight of solvent \((c)\), then the curve is a convex curve with barely perceptible convexity (almost a straight line). Table CXLV contains the values of the vapor pressure read from this curve.

Table CXLV.

Relative vapor pressure of solutions of iodine in carbon disulfide.

(interpolated data).

\(c\)	\(\dfrac{p_1}{p_0}\) mean	\(c\)	\(\dfrac{p_1}{p_0}\) mean
0	1.0000	10	0.9742
1	0.9975	11	0.9716
2	0.9950	12	0.9691
3	0.9925	13	0.9665
4	0.9900	14	0.9638
5	0.9872
6	0.9846
7	0.9820
8	0.9795
9	0.9767

4. Solutions of iodine in chloroform.

The chloroform used for the experiments was a preparation from the Merck factory, purified at the plant according to the directions of the German Pharmacopoeia. Before being put into use, this chloroform was shaken three times with an equal volume of water, then dried with calcium chloride and, finally, distilled.

It distilled almost entirely within the limits \(55.9^\circ\)—\(60.1^\circ\) at a pressure of 743 mm. The fraction distilling within \(0.1^\circ\) was taken for use.

Tables CXLVI A and CXLVI B contain the results of measurements of the vapor pressure of pure chloroform. In Table CXLVI B, moreover, the results obtained are compared with the results of measurements of the vapor pressure of chloroform carried out by Regnault\(^1\) by the barometric method. The numbers given in the table were calculated by the interpolation formula:

\[ Log\, p_0 = a - b\alpha^\theta - c\beta^\theta, \tag{76} \]

for the constants of which Regnault gives the following values: \(a = 5.2253893\), \(b = 2.9531281\), \(c = 0.0668673\), \(\log \alpha = 1.9974144\), \(\log \beta = 1.9868176\); \(\theta = (t - 20)\) by the air thermometer.

\(^1\) Regnault, Rél. des exp. II, p. 403.

Table CXLVI A.

Boiling temperatures of chloroform CHCl₃ at pressures 185.35 mm—231.18 mm.
(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Difference	Barom.	Vacuum.	\(T^0\)	\(t^0\) liquid, mean	\(t^0\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
23,81	23,52		144,1	330,0	18	23,815	23,53	185,35
23,82	23,54	0,28	144,1	330,0
25,24	25,00		143,8	342,2	18	25,24	25,00	197,71
25,24	25,00	0,24	143,9	342,1
26,50	26,30		143,7	353,2	18	26,50	26,30	208,9
26,50	26,30	0,20	143,7	353,2
27,82	27,62		143,6	365,4	18	27 845	27,645	221,26
27,87	27,67	0,20	143,5	365,5
28,88	28,71		143,5	375,3	18	28.885	28,71	231,18
28,89	28,71	0,17	143,4	375,3

Table CXLVI B.

Elasticity of chloroform vapor CHCl₃ at temp. 23.5°—28.5°.
(interpolated data).

\(t^\circ\)	Mikhailenko and Czeltnner, \(p_1\) liquid	Mikhailenko and Czeltnner, \(p_1\) vapor	Regnault, \(p^\circ\)
°C.	mm.	mm.	mm.
23,5		185,15	187,51
24,0	186,95	189,20	191,66
24,5	191,15	193,40	195,88
25,0	195,50	197,60	200,18
25,5	199,90	201,90	204,35
26,0	204,35	206,30	209,00
26,5	208,90	210,70	213,53
27,0	213,40	215,20	218,14
27,5	218,05	219,80	222,82
28,0	222,75	224,45	227,60
28,5	227,55	229,20	232,45

The results of comparing the numbers obtained with Regnault’s numbers may be considered satisfactory only in the sense that the differences do not exceed the limits of differences usual for measurements of this kind. The difference, however, is considerably greater than the errors of the method employed. The reason for this is the nonuniformity of the material used for the measurements in the two cases. According to Regnault, the chloroform preparation in his hands was not entirely free of impurities, and all efforts to purify it did not lead to the desired end. Since then the technique of factory preparation of chemical reagents has made great progress, and one may hope that the preparation found-

which we had at our disposal and, moreover, had been carefully fractionated, was a preparation of considerably greater purity than Regnault’s preparation.

Because the solubility of iodine in chloroform is small, the vapor pressures of only four solutions were measured, the last two of these solutions being saturated.

The measurement results were treated in the same way as before and are given in Tables CXLVII–CL.

Table CXLVII A.

Boiling temperatures of a 1.56% solution of iodine in chloroform at pressures of 180.21 mm–219.9 mm.
(experimental data).

\(t^\circ\) liquid, °C	\(t^\circ\) vapor, °C	Difference, °C	Barom.	Vacuum	\(T^\circ\), °C	mean \(t^\circ\) liquid, °C	mean \(t^\circ\) vapor, °C	\(p_1\), mm
23.26	22.97		144.9	325.5	16	23.27	22.98	180.21
23.28	22.99	0.29	144.9	325.6
24.36	24.07		144.9	334.6	17	24.37	24.08	189.22
24.38	24.09	0.29	144.9	334.5
25.50	25.22		145.0	344.3	17	25.505	25.22	198.80
25.51	25.22	0.28	145.0	344.3
26.66	26.38		145.0	354.3	17	26.655	26.38	208.85
26.65	26.38	0.27	144.9	354.4
27.86	27.60		144.9	365.4	17	27.86	27.605	219.90
27.86	27.61	0.26	144.9	365.4

Table CXLVII B.

Vapor pressure of a 1.56% solution of iodine in chloroform at temperatures 23.0°–28.0°.
(interpolated data).

\(t^\circ\), °C	\(p_1\) liquid, mm	\(p_1\) vapor, mm	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
23.0	—	180.35
23.5	182.05	184.40		0.9963
24.0	186.15	188.50	0.9956	0.9963
24.5	190.30	192.70	0.9963	0.9963
25.0	194.55	196.90	0.9949	0.9963
25.5	198.80	201.20	0.9945	0.9966
26.0	203.15	205.55	0.9940	0.9961
26.5	207.55	210.00	0.9933	0.9966
27.0	211.95	214.45	0.9929	0.9963
27.5	216.50	—	0.9931
28.0	—	—
			0.9943 ± 0.0004	0.9963 ± 0.00006

Table CXLVIII A.

Boiling temperatures of a 3.08% solution of iodine in chloroform at pressures of 181.68 mm—221.88 mm.

(experimental data).

\(t^0\) liquid	\(t^0\) vapor	Diff.	Barom.	Vacuum.	T°	\(t^0\) liquid mean	\(t^0\) vapor mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
23,52	23,24		153,0	335,2	17	23,52	23,24	181,68
23,52	23,24	0,28	153,0	335,2
24,77	24,50		153,1	345,4	17	24,785	24,505	191,83
24,80	24,51	0,28	153,1	345,4
26,00	25,73		152,9	356,0	17	26,005	25 74	202,43
26,01	25,75	0,26	153,0	356,0
27,05	26,80		153,0	365,0	18	27,055	26,80	211,38
27,06	26,80	0,25	153,0	365,0
28,21	27,96		153,0	375,5	18	28,215	27,97	221,88
28,22	27,98	0,24	153,0	375,6

Table CXLVIII B.

Vapor pressure of a 3.08% solution of iodine in chloroform at temp. 23.5°—28.0°.

(interpolated data).

\(t^0\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C.	mm.	mm.
23,5	181,50	183,70		0,9924
24,0	185,55	187,80	0,9924	0,9927
24,5	189,70	191,90	0,9927	0,9922
25,0	193,90	196,00	0,9920	0,9920
25,5	198,15	200,20	0,9911	0,9917
26,0	202,40	204,50	0,9906	0,9913
26,5	206,70	208,80	0,9895	0,9908
27,0	211,05	213,20	0,9888	0,9908
27,5	215,45	217,65	0,9879	0,9901
28,0	219,95	222,20	0,9874	0,9901
			0,9902 ± 0,0006	0,9917 ± 0,0003

Table CXLIX A.

Boiling temperatures of the saturated solution of iodine in chloroform at pressures of 181.77–221.28 mm.

(experimental data; first solution).

\(t^\circ\) liquid	\(t^\circ\) vapor	Difference	Barom.	Vacuum	\(T^\circ\)	\(t^\circ\) liquid, mean	\(t^\circ\) vapor, mean	\(p_1\)
°C.	°C.	°C.			°C.	°C.	°C.	mm.
23.70	23.33		153.2	335.5	18	23.71	23.33	181.77
23.72	23.33	0.38	153.1	335.4	18	23.71	23.33	181.77
25.11	24.72		152.9	346.5	19	25.11	24.725	193.06
25.11	24.73	0.39	152.8	346.5	19	25.11	24.725	193.06
26.30	25.94		152.5	356.6	19	26.30	25.94	203.45
26.30	25.94	0.36	152.5	356.6	19	26.30	25.94	203.45
27.50	27.14		152.3	367.0	19	27.51	27.14	214.05
27.52	27.14	0.37	152.3	367.0	19	27.51	27.14	214.05
28.28	27.95		152.1	374.1	19	28.28	27.945	221.28
28.28	27.94	0.34	152.1	374.0	19	28.28	27.945	221.28

Table CXLIX B.

Vapor pressure of the saturated solution of iodine in chloroform at temp. 23.5°–28.0°.

(interpolated data; first solution).

\(t^\circ\)	\(p_1\), liquid	\(p_1\), vapor	\(\dfrac{p_1}{p_0}\), liquid	\(\dfrac{p_1}{p_0}\), vapor
°C.	mm.	mm.
23.5	—	—	—	—
24.0	184.05	187.20	0.9845	0.9895
24.5	188.90	191.30	0.9883	0.9890
25.0	192.15	195.45	0.9827	0.9888
25.5	196.40	199.70	0.9824	0.9892
26.0	200.75	203.90	0.9822	0.9883
26.5	206.00	208.35	0.9863	0.9886
27.0	209.55	212.25	0.9817	0.9861
27.5	214.00	217.25	0.9815	0.9883
28.0	218.50	221.80	0.9813	0.9886
			0.9834 ± 0.0008	0.9884 ± 0.0003

Table CL A.

Boiling temperatures of a saturated solution of iodine in chloroform at pressures of 181.88–224.25 mm.

(experimental data; second solution).

\(t^\circ\) liquid	\(t^\circ\) vapor	Diff.	Barom.	Vacuum	\(T^\circ\)	mean \(t^\circ\) liquid	mean \(t^\circ\) vapor	\(p_1\)
°C	°C	°C			°C	°C	°C	mm
23.70	23.33		150.5	332.8	18	23.71	23.325	181.88
23.72	23.32	0.39	150.4	332.7
24.98	24.61		150.3	343.0	18.5	24.98	24.615	192.15
24.98	24.62	0.37	150.3	343.0
26.31	26.00		150.0	354.5	18	26.31	26.00	203.93
26.31	26.00	0.31	150.0	354.5
27.50	27.21		150.0	365.2	18	27.505	27.215	214.63
27.51	27.22	0.29	150.0	365.3
28.50	28.26		149.9	375.8	18	28.51	28.26	224.25
28.52	28.26	0.25	149.9	375.8

Table CL B.

Vapor pressure of a saturated solution of iodine in chloroform at temperatures of 23.5°–28.5°.

(interpolated data; second solution).

\(t^\circ\)	\(p_1\) liquid	\(p_1\) vapor	\(\dfrac{p_1}{p_0}\) liquid	\(\dfrac{p_1}{p_0}\) vapor
°C	mm	mm
23.5	—	182.50	—	0.9861
24.0	184.25	187.25	0.9856	0.9895
24.5	188.30	191.35	0.9854	0.9890
25.0	192.40	195.45	0.9842	0.9888
25.5	196.70	199.65	0.9840	0.9888
26.0	201.10	203.90	0.9842	0.9883
26.5	205.55	208.35	0.9838	0.9886
27.0	210.00	212.25	0.9840	0.9861
27.5	214.60	217.25	0.9842	0.9883
28.0	219.45	221.80	0.9851	0.9886
28.5	224.15	—	0.9849	—
			0.9845 ± 0.0002	0.9882 ± 0.0003

Discussion of the results. Solutions of iodine in chloroform, when the elasticity of their vapor is investigated, behave in exactly the same way as solutions of iodine in ether and in carbon disulfide, with the sole exception that the series $\dfrac{p_1}{p_0}$ liquid mean and $\dfrac{p_1}{p_0}$ vapor mean differ so much from one another that it is possible to construct for each series a separate curve expressing the law of change of the vapor elasticity of the solution with change in concentration. Another peculiarity of these solutions consists in the fact that saturated solutions, when the elasticity of their vapor is changed, behave in exactly the same way as unsaturated ones—at least, no difference could be detected. Namely: the curve of vapor elasticity of saturated solutions has the same form as the curve of vapor elasticity of unsaturated solutions; it, just like the curve of vapor elasticities of unsaturated solutions, seems to be parallel to the curve of vapor elasticity of the pure solvent; finally, the ratio $\dfrac{p_1}{p_0}$ in both series, as also for unsaturated solutions, does not depend on temperature—more precisely, this dependence cannot be established.

Table CLI gives the results of the measurements; moreover, next to the mean value of $\dfrac{p_1}{p_0}$ is placed the mean error of this mean value, calculated by the method of least squares. The concentration of the solution is expressed in the same ways as before.

Table CLI.

Relative vapor elasticity of solutions of iodine in chloroform.
(experimental data).

$c$	$x^0/\!_0$	$\dfrac{p_1}{p_0}$ liquid	$\dfrac{p_1}{p_0}$ vapor
1,58	1,56	0,9943±0,0004	0,9963±0,00006
3,18	3,08	0,9902±0,0006	0,9917±0,0003
1st saturated solution.		0,9834±0,0008	0,9884±0,0003
2nd saturated solution.		0,9845±0,0002	0,9882±0,0003

As is seen from Table CLI, the mean error of the mean value of the quantities $\dfrac{p_1}{p_0}$ lies between the limits ±0,0008 and ±0,00006.

Since, at those temperatures at which the measurements were carried out, $p_0$, i.e. the vapor elasticity of chloroform itself, has a value between 186,95 mm.—229,20 mm., the greatest error of the mean value, calculated in millimeters of mercury column, is expressed as 0,18 mm., and the smallest as 0,0011 mm.

The mean values of $\dfrac{p_1}{p_0}$ liquid and $\dfrac{p_1}{p_0}$ vapor for both saturated solutions proved to be identical; more precisely, the differences between these quanti-

we have found ourselves lying within the limits of error. What attracts attention is that the difference between the values \(\frac{p_1}{p_0}\) vapor for two saturated solutions (namely 0.0002) is considerably smaller than the difference between the corresponding values of \(\frac{p_1}{p_0}\) liq.; accordingly, the mean error of each average result is also smaller. Expressed in millimeters of mercury, this difference within the investigated temperature range will have the values 0.0372–0.0458. Such a perfect agreement of the numerical values of vapor pressure obtained for saturated solutions may once again be pointed to as evidence of the perfection of the method being developed. In the future, the development of this method promises to lead to still more accurate results.

Although the vapor pressure of only two unsaturated solutions of iodine in chloroform was measured, nevertheless the results were plotted on coordinate paper. It turned out that the two plotted points and the zero point, i.e. the point corresponding to zero concentration, lie exactly on one straight line, if the concentration of the solution is expressed as the number of grams of iodine per 100 grams of solvent. Considering it probable that here too, as before, the relation between the change in vapor pressure and the concentration of the solution \((c)\) is expressed by a curve very close to a straight line, I decided to use the straight line obtained for interpolation.

Table CLII gives the values of the vapor pressure of solutions of iodine in chloroform, read from this curve. In assessing the reliability of the numerical values in this table, it goes without saying, one must bear in mind what has been said above.

Table CLII.

Relative vapor pressure of solutions of iodine in chloroform.
(interpolated data).

\(c\)	\(\dfrac{p_1}{p_0}\) liq.	\(\dfrac{p_1}{p_0}\) vapor
0	1.0000	1.0000
1	0.9968	0.9975
2	0.9937	0.9950
3	0.9907	0.9925
4	0.9877	0.9902
4.75¹)	—	0.9880
5	0.9845	—
5.20¹)	0.9840	—

¹) The relative vapor pressure of a solution at a given temperature decreases continuously with increasing concentration. When the solution becomes saturated, the relative vapor pressure becomes constant and the pressure curve passes into a straight line. The abscissa of the point of intersection of the curve with the straight line corresponds to the saturation concentration, i.e. the solubility. It follows from this that the method of measuring the vapor pressure of solutions can also be applied to determine the solubility value.

Quite unexpectedly, the experiment showed that for saturated solutions of iodine in chloroform, just as for unsaturated ones, the ratio \(\frac{p_1}{p_0}\) is independent of temperature. This conclusion, of course, is hardly harmed by the fact that the adopted method of measuring the vapor pressure of a solution is not sensitive enough to reveal this dependence, and therefore cannot be used to measure solubility with sufficient accuracy.

From the data of Table CLII, the solubility of iodine in chloroform within the temperature limits \(24^\circ\)—\(28^\circ\) is determined in two ways: from the point of transition of the curve \(\dfrac{p_1}{p_0}\) of the vapors into a straight line, the solubility is expressed by the number 4.75 parts by weight of iodine in 100 parts by weight of chloroform; from the point of transition of the curve \(\dfrac{p_1}{p_0}\) of the liquid, the solubility is determined by the number 5.20 parts by weight of iodine in 100 parts by weight of chloroform.

On the Temperature of the Vapor of a Boiling Liquid.

The chief task of the work of measuring the vapor pressure of solutions was to obtain new experimental data for investigating the relation between the vapor pressure of a solution and its partial density. But alongside this chief task, other aims also incidentally came into view, namely:

1) to develop the boiling method in certain details of its practical application;

2) to collect experimental material on the question of the temperatures of a boiling liquid and of its vapor in the case when the vapor phase has a different composition from the boiling liquid;

3) to elucidate the theory of the boiling method for this latter case and to determine those conditions under which the method gives satisfactory results also for solutions.

Everything new that was introduced into Kahlbaum’s apparatus for measuring the vapor pressure of liquids has already been described above. Above, too, in the tables, together with the data of measurement of vapor pressure, numerical results of observations on the temperatures of the vapor of the liquid were also given. Here it remains to bring this experimental material into a system, to compare it with the observations of other authors, and to draw from it the conclusions that can clarify the theory of the dynamic method of determining the vapor pressure of liquids as applied to solutions.

The investigation of the question of the temperatures of a boiling liquid and of its vapor is closely connected with elucidating the very theory of boiling and, consequently, also with elucidating the theory of the dynamic method of measuring vapor pressure; among other things, also with resolving a question which not long ago was still disputed—whether, by the dynamic method, results are obtained for the vapor pressure that are identical with those obtained by the barometric method, or different.

The boiling method, as is known, consists in the fact that a liquid is boiled in a closed apparatus in which one or another pressure has been reproduced. It is assumed that the pressure in the apparatus is equal to the vapor pressure of the liquid at the temperature of its boiling. But it is known that the temperature of the boiling liquid is not the same as the temperature of the vapor evolved from it.

What, then, should be regarded as the boiling temperature—the temperature of the boiling liquid itself or the temperature of its vapor?

Experience shows that, in the case of pure liquids, the temperature of boiling must be taken to be the temperature of the vapor, and not the temperature of the boiling liquid; more precisely, experience shows that for vapor pressure the dynamic method gives numbers which, if not identical, are close to the numbers obtained—

… measured in a barometric vacuum, only in the case when these numbers are referred to the temperature not of the boiling liquid, but to the temperature of the vapor.

The reasons why this is so were not always sufficiently clearly recognized even by those authors who themselves made measurements of vapor pressure by the dynamic method: as an example, one may point to the comparatively recent dispute of Kahlbaum with Ramsay and Young¹ concerning the identity of the results of the dynamic and static methods—a dispute which was finally resolved by a complete elucidation of those conditions (though only for pure liquids) under which, by either method, results are obtained that are, if not identical, then at least close within the limits of experimental error.

What should be regarded as the boiling temperature in the case when the liquid is a solution, and under what conditions the boiling method is applicable for measuring the vapor pressure of solutions—this question remained completely unexplained.

Theory of boiling. The phenomenon of boiling is the formation of vapor inside a liquid in the form of bubbles; these bubbles rise upward, penetrating the layer of boiling liquid, and at the surface of the liquid disappear—the vapor passes into the gaseous phase.

By the efforts of a number of investigators, such as: de Luc (1772), Gay-Lussac (1812), Munke, Rudberg (1837), Marcet (1842), Donny (1846), Dufour (1861–1865), Grove (1863), Gernez (1866–1867), Tomlinson (1867), Krebs (1874), and others,² the conditions of boiling of liquids have been clarified as follows.

1) For a liquid to boil, the presence within the liquid of bubbles of air or of some other gas is necessary, i.e., of a free surface. Liquids deprived of the latter, as a result of the absence of free gases, can be superheated considerably above their boiling temperatures corresponding to the pressure at which the experiment is performed; in doing so they do not boil, but evaporate vigorously. For example, Donny³ succeeded, in ordinary glass vessels, in heating water to a temperature of \(137^\circ\) without causing boiling; Dufour⁴, in a mixture of linseed and clove oils, superheated drops of water to \(178^\circ\), etc. The long-noted influence of solid bodies on the onset of boiling is explained only by air bubbles adhering to the solid bodies, and not otherwise, as Tomlinson⁵ defended this.

2) The temperature of a boiling liquid depends not only on the pressure at that level at which vapor bubbles are formed, but also on the material of the vessel in which boiling is carried out, and on the magnitude of the adhesion between the particles of the boiling liquid itself.

3) The temperature of the vapor of a boiling liquid, observed by a thermometer at a sufficient distance from the surface of the boiling liquid, depends only on the external pressure.

Thus, in experiments measuring vapor pressure by the boiling method, the pressure of vapor bubbles inside the liquid is greater than the pressure on the surface not only because vapor formation occurs only at certain definite places, as a result of which superheating of liquids is possible elsewhere; not only because vapor formation occurs at different levels of the boiling liquid; but also because the vapor being formed must also overcome the cohesive forces of the liquid¹. And from this it follows that the temperature of the boiling liquid will always be higher than the temperature of the maximum vapor pressure at a pressure equal to the external pressure, even if it were possible to avoid perfectly the superheating of the liquid by the external source of heating. Consequently, the temperature measured in the boiling liquid does not correspond to the pressure of the saturated vapor equal to the external pressure measured by the manometer.

The vapor that has emerged from the liquid—let us represent it in this way—raises the layer of air above the surface of the liquid, as though it were an elastic movable piston with a load equal to the external pressure. The vapor pressure at this moment is, obviously, equal to the external pressure. At some level the vapor condenses into liquid, which returns back to the boiling vessel, partly falling in the form of rain toward the rising vapor, and partly flowing down the walls of the vessel. Along its path the liquid formed by condensation of the vapor is heated to the temperature of the vapor, and here, and precisely only here, together with the vapor it forms that equilibrium system which is identical to the system of vapor and liquid reproduced in a barometric vacuum in an experiment measuring vapor pressure by the static method. With the boiling liquid, the vapor, even if it forms an equilibrium system, forms one in which the two phases have different temperatures. Since, in place of the condensed liquid, the boiling liquid sends up new quantities of vapor, one may expect that the vapor pressure will not be exactly equal to the external pressure, but will fluctuate within certain limits—which only experiment can determine—around the external pressure. Analogously, the temperature of the vapor, owing to the fact that the vapor is cooled by the cold liquid passing through it, may likewise undergo fluctuations.

Consequently, in the boiling method a certain average pressure and a certain average temperature of the vapor are measured; it has quite deservedly received the name of the dynamic method, since both temperature and pressure are in evident motion, in contrast to the static method, when pressure and temperature change by an infinitely small amount.

Do the static and dynamic methods give identical, or at least concordant, results, or not?

Before answering this question, it is necessary to distinguish two cases:

1) the first case—when the composition of the vapor is the same as the composition of the liquid;

2) the second case—when the composition of the gaseous phase is different from that of the liquid.

The composition of the vapor is the same as the composition of the liquid. Since, when a liquid boils under a definite pressure, the equilibrium system, as has just been clarified, is constituted by the vapor and the liquid condensed from the vapor, having one and the same temperature, and since this liq-

has the same composition as the vapor, then, obviously, in this case the static and dynamic methods of measuring the elasticity of the vapor must give either identical or close results, depending on the magnitude of the interval within which, in the experiment, it is possible to maintain fluctuations of pressure and temperature.

Only experiment can give the answer to this, i.e., a comparison of the numerical values of the elasticity of vapor obtained by the one and by the other methods. Such comparisons, however, are very difficult to make, since it is necessary to isolate the individual errors of the authors, as well as the errors due to the nonidentity of the preparations investigated. In addition, one must also bear in mind that observations by the barometric method are extremely difficult and give satisfactory results, as Regnault already indicated¹, only in the case when the liquids investigated contain absolutely no impurities. Trifling quantities of foreign substances affect the value found for the elasticity of the vapor to such an extent that this even led Tammann² to state that, by the barometric method, entirely exact results can be obtained only for water alone.

Nevertheless, in the literature one can find several cases where the elasticity of vapor of the same preparations was measured by the same investigators simultaneously by both the static and the dynamic method. We shall point to the measurements of the elasticity of vapor of water and ether, carried out by Regnault³, the measurements of the elasticity of vapor of fatty acids made by Kahlbaum⁴, and to the measurement of the elasticity of vapor of butyric acid, carried out by Ramsay and Young in an apparatus that made it possible to measure the elasticity of vapor simultaneously by both the static and the dynamic methods. The latter measurements were made with the special purpose of comparing the results given by both methods. The numbers obtained by them are given in Table CLIII.

Table CLIII.

Comparison of the results of measurement of the elasticity of vapor of butyric acid by the dynamic and static methods by Ramsay and Young⁵.

Temperature	Pressure in barometric vacuum	Boiling pressure
°C.	mm.	mm.
66,50	12,75	12,85
76,15	21,90	22,75
85,85	36,85	36,9
93,00	51,90	51,95
99,30	70,25	69,80
105,10	90,65	90,00
111,50	119,55	118,30
117,80	152,75	151,55
123,10	187,70	186,50
127,4	222,90	221,90
133,7	281,10	281,45

Tables LXXXI, LXXXII, LXXXVI, CVI and CXXVI B, in which the results obtained by me by the dynamic method for the elasticity of the vapor of water, ether, and carbon disulfide are compared with the results of other authors obtained by other methods, may also serve as material for the conclusion sought.

The conclusion, evidently, is this: experiment shows that only in cases where the liquid and gaseous phases have one and the same composition do the static and dynamic methods of measuring vapor elasticity give, if not identical, then in any case identical results (differences within the limits of experimental error).^1

The composition of the vapor is different from the composition of the liquid. The case in which the vapor evolved by the liquid has a different composition than the liquid (the case of a solution) is more complex.

For simplicity let us assume that the dissolved substance is not volatile. In this case, from a superheated liquid there is evolved a vapor whose elasticity, when it leaves the liquid, is exactly equal to the external pressure, while its density is less than the maximum corresponding to the temperature which it has; at the existing external pressure this vapor, obviously, cannot be in equilibrium with the pure liquid, since the latter at the existing pressure cannot be heated to the temperature of the vapor; for this to occur it must cool to the temperature at which, at the given external pressure, it can form an equilibrium system with the liquid. Such cooling of the vapor in parts remote from the boiling liquid may be produced by the condensing solvent, which penetrates the layer of vapor on its return path into the solution. In these places there is then formed an equilibrium system of vapor and solvent, analogous to the system of vapor and solvent in a barometric vacuum. In these places the temperature is equal to the temperature of the saturated vapor of the solvent at a pressure equal to the external pressure.

The nearer to the surface of the boiling liquid, the higher will be the temperature of the vapor, and at the very surface of the liquid it reaches its maximum. If one admits (and such an admission is apparently very close to reality) that the surface layer of the boiling liquid has the same temperature as the vapor in contact with this layer, then in this place we shall have a second equilibrium system of vapor and solution, identical with the analogous system in a barometric vacuum. Here the external pressure is equal to the elasticity of the saturated vapor of the solution at the temperature of the vapor.^2

Observations on the boiling of solutions confirm this picture of the mechanism of boiling.

If a thermometer is immersed in a boiling solution, then the temperature of its boiling is higher than the boiling temperature of the solvent at the same pressure. But if the bulb of the thermometer is placed in the vapors far from the surface of the boiling liquid, then the temperature indicated by it is equal to the temperature

^1 A comparison of the numerical values of the vapor elasticity of liquids obtained by different observers by no means always gives results agreeing within the limits that occur in the tables to which reference has been made. Usually the differences are considerably greater. This, however, is explained by the difficulty of experiments for measuring vapor elasticity and by the nonuniformity of the apparatuses used for the work.

^2 An experiment for measuring the vapor elasticity of a solution by the boiling method would be theoretically unobjectionable if it were arranged so that toward the vapor issuing from the solution there would fall a liquid solution of the same composition as the boiling solution, and the readings were taken with a thermometer placed in the vapors, not far from the surface of the boiling liquid.

the boiling point of the solvent at a pressure equal to the external pressure of the experiment. This fact was first noticed by Rudberg¹. Subsequently, Regnault’s observations confirmed Rudberg’s observations and showed their generality. The following data, illustrating this observation, are taken from Regnault’s work².

Table CLIV.

Boiling temperatures of an aqueous solution of calcium chloride according to Regnault’s observations.

Pressure	Temp., measured in the boiling liquid.	Temp., measured in the vapors.	Temp. that the vapor would have if water were boiled under the same pressure.
mm.	°C.	°C.	°C.
82,52	52,0	47,88	47,84
136,61	61,58	58,20	58,16
219,44	71,80	68,73	68,61
286,43	—	74,94	74,84
434,19	87,54	85,09	85,07
757,22	—	99,88	99,90
1807,15	129,86	126,63	126,16
2182,35	136,30	132,92	132,42
2702,13	142,79	140,35	139,81
3123,69	147,91	145,57	145,00

These experiments were at first interpreted in the sense that the vapor, while it is in the midst of the boiling liquid, possesses, owing to the attraction of the salt particles, a greater density than that which corresponds, at the same temperature, to the hydrostatic pressure on the surface of the liquid, and that it assumes its normal density at the moment when, having separated from the liquid, it encounters this pressure. The vapor then undergoes a sudden expansion, which converts into the latent state an excess of heat and brings it exactly to the temperature at which its elasticity balances the atmospheric pressure (Regnault, loco cit.). Against this view, however, objections were soon raised.

Wüllner³ pointed out that the vapor released in the form of bubbles in a boiling solution and undoubtedly having the temperature of the boiling liquid must have a density smaller than the density of the saturated vapor of the solvent at the same temperature; its elasticity should exceed the external pressure only by an insignificant amount, and therefore theoretically one should expect that the temperature of the vapor will be the same as the temperature of the boiling liquid, and that the observed cooling is due to certain secondary causes.

Regnault¹, having confirmed by his experiments the results obtained by Rudberg, at the same time made the observation that, when solutions were boiled on the bulb of a thermometer, no matter what measures he took against it, water always condensed; from this he concluded that the temperature observed by the thermometer is nothing other than the boiling temperature, at the given pressure, of the solvent, or, more precisely, the temperature at which, at the given pressure, the solvent and its vapor constitute an equilibrium system.

Thus Regnault at once found an explanation for the fact, which had seemed incomprehensible, that in the boiling experiment the temperature of the vapor of the solution is observed to be equal to the temperature of the vapor of the pure solvent.

It remained to prove experimentally that the temperature of the vapor of a boiling solution is in reality higher than the temperature of the vapor of the solvent boiling at the same external pressure.

The first such attempt was made by Magnus, who showed that the vapor escaping from a solution does indeed have a higher temperature than that at which the pure solvent boils at the same pressure. The experiments were carried out with aqueous solutions of calcium chloride in a special apparatus arranged so that the thermometer by which the temperature was measured was preheated and the condensed water could not fall onto the thermometer.

The results of Magnus’s experiments are collected in Table CLV.

Table CLV.

Boiling temperatures of a calcium chloride solution at atmospheric pressure, measured in the liquid and in the vapor.

(according to Magnus’s experiments.)²

Temperature of the liquid	Temperature of the vapor	Difference
°C	°C	°C
107.0	105.25	1.75
107.5	105.5	2.0
108.0	105.8	2.2
109.2	106.5	2.7
110.0	107.0	3.0
111.0	107.6	3.4
112.0	108.1	3.9
113.0	108.8	4.2
114.0	110.0	4.0
115.0	110.9	4.1
116.0	111.2	4.8

After Magnus, experiments measuring the temperature of the vapor of boiling solutions were carried out by Kahlbaum.¹ The occasion for this work was the desire to determine whether the static and dynamic methods give identical or different results. In Kahlbaum’s experiments the thermometer was surrounded by double walls, between which there circulated the vapor evolved from the boiling solution, analogous to the way this is arranged in instruments for checking the 100-degree point of the thermometric scale. In addition, to avoid heat radiation the bulb of the thermometer was covered by a metal cylinder polished inside and out, and protected by a special device from droplets of the solution falling on the thermometer. It turned out that, whereas the temperature of the boiling solution was 135°, the temperature of the vapor at a distance of 50 cm from the surface of the boiling solution varied within the limits 111.8°—110.2°—109.5°. When the concentration of the solution was changed, in all cases it was found that the temperature of the vapor followed the changes in concentration. Kahlbaum was able to demonstrate the higher temperature of the vapor even in the case when the temperature of the solution was only 0.6° higher than the boiling temperature of pure water, and notwithstanding the fact that the distance of the thermometer bulb from the surface of the boiling liquid was 30 cm.

Finally, measurements of a similar kind were carried out by Sacurai.² To protect the vapor from cooling as a result of contact with the cold walls of the vessel, in Sacurai’s experiments that part of the vessel which was filled with vapor was surrounded by double walls, through the spaces between which he passed the vapor of another liquid, having a temperature somewhat lower than the temperature of the boiling solution.

The boiling liquid was heated by passing steam into the solution.

The results obtained by him are given in Table CLVI.

Table CLVI.

Boiling temperature of an aqueous solution of calcium chloride, measured in the vapor and in the liquid.

In the liquid	In the vapor	Temperature of the vapor between the double walls3
°C.	°C.	°C.
128,3	127,5	126,5
128,5	128,1	126,8
128,9	128,6	127,2
129,2	129,1	127,8
129,5	129,4	128,1
129,8	129,7	128,3
129,8	129,8	128,5

Consequently, Saccura found the temperature of the vapor to be only slightly below the temperature of the boiling solution and much higher than the boiling temperature of pure water.

From all these investigations it may be considered established that the temperature of the vapor evolved from a boiling solution (the dissolved substance being nonvolatile) is lower than the temperature of the boiling liquid, but, in any case, higher than the boiling temperature of the pure solvent.

It remained completely unclear whether it should be assumed that the vapor evolved from a solution and having a pressure equal to the external pressure will form, together with the solution, an equilibrium system analogous to the same one in a barometric vacuum, at the temperature of the vapor or at the temperature of the boiling solution; in other words, the elasticity of the vapor evolved from a solution is the maximum elasticity of the vapor of the solution at the temperature possessed by the liquid solution, or at the temperature possessed by the vapor.

The measurements of the vapor elasticity of solutions that I have given above decide this question, at least for the conditions under which the measurements were made.

In my experiments the boiling temperature was measured by two thermometers: the bulb of one thermometer was immersed in the boiling liquid, while the bulb of the other thermometer was in the vapor a few millimeters above the level of the liquid. The vapor was protected from cooling by a cardboard box lined on the inside with sheets of tin,¹ and then padded with moss.² The temperature of the surrounding air was 1°–5° higher than the temperature of the vapor.

To avoid superheating, the lower part of the boiler was filled with garnets saturated with air; in addition, through a capillary reaching to the bottom of the vessel, air was continuously introduced into the solution throughout the experiment. It may be thought that these measures, if they did not completely exclude the possibility of superheating of the liquid, then in any case reduced this superheating to a minimum.

Of the observations made, those on mixtures of nitrobenzene and ether give the most complete picture of the regularities observed, since the concentration of the solutions varied over wide limits. Observations on other solutions merely confirm the conclusions drawn from the solutions of nitrobenzene.

The results of measuring the boiling temperatures of solutions of nitrobenzene in ether at different pressures are summarized in Table CLVII.

¹ In this way, the mediator implemented the principle of partitions impermeable to heat, adopted in the Chamber of Weights and Measures.

² However, the first measurements, namely the measurements of the boiling temperature of solutions of iodine in carbon disulfide and some solutions of nitrobenzene in ether, were carried out with the vessel unprotected.

Table CLVII.

Boiling temperatures of mixtures of nitrobenzene and ether at various pressures, measured in vapor and liquid.

Pressure	Pure ether.	Pure ether.	Pure ether.	Mixture, containing 7.63% nitrobenzene.	Mixture, containing 7.63% nitrobenzene.	Mixture, containing 7.63% nitrobenzene.	Mixture, containing 9.95% nitrobenzene.	Mixture, containing 9.95% nitrobenzene.	Mixture, containing 9.95% nitrobenzene.
mm.	\(t^\circ\) liquid, °C.	\(t^\circ\) vapor, °C.	Diff., °C.	\(t^\circ\) liquid, °C.	\(t^\circ\) vapor, °C.	Diff., °C.	\(t^\circ\) liquid, °C.	\(t^\circ\) vapor, °C.	Diff., °C.
390	—	—	—	—	—	—	18,58	18,18	0,40
400	—	—	—	—	—	—	19,24	18,82	0,42
410	18,30	18,10	0,20	19,56	19,14	0,42	19,86	19,46	0,40
420	18,85	18,60	0,25	20,17	19,70	0,47	20,46	20,06	0,40
430	19,54	19,32	0,22	20,76	20,28	0,48	21,06	20,64	0,42
440	20,10	19,89	0,21	21,34	20,82	0,52	21,66	21,22	0,44
450	20,67	20,45	0,22	—	—	—	—	—	—
460	21,20	20,99	0,21	—	—	—	—	—	—

Table CLVII.

(Continued).

Pressure	Mixture, containing 15.96% nitrobenzene.	Mixture, containing 15.96% nitrobenzene.	Mixture, containing 15.96% nitrobenzene.	Mixture, containing 20.81% nitrobenzene.	Mixture, containing 20.81% nitrobenzene.	Mixture, containing 20.81% nitrobenzene.	Mixture, containing 25.39% nitrobenzene.	Mixture, containing 25.39% nitrobenzene.	Mixture, containing 25.39% nitrobenzene.
mm.	\(t^\circ\) liquid, °C.	\(t^\circ\) vapor, °C.	Diff., °C.	\(t^\circ\) liquid, °C.	\(t^\circ\) vapor, °C.	Diff., °C.	\(t^\circ\) liquid, °C.	\(t^\circ\) vapor, °C.	Diff., °C.
360	—	—	—	—	—	—	18,92	18,40	0,52
370	—	—	—	18,89	18,37	0,52	19,62	19,11	0,51
380	18,87	18,54	0,33	19,57	19,00	0,57	20,32	19,78	0,54
390	19,53	19,15	0,38	20,24	19,63	0,61	20,98	20,43	0,55
400	20,16	19,78	0,38	20,88	20,24	0,64	21,61	21,05	0,56
410	20,77	20,37	0,40	21,50	20,80	0,70	22,25	21,63	0,62
420	21,37	20,94	0,43	22,10	21,36	0,74	—	—	—
430	22,00	21,54	0,46	—	—	—	—	—	—

Table CLVII.

(Continuation).

Pressure	Mixture containing 30.56% nitrobenzene: \(t^\circ\) liquid	Mixture containing 30.56% nitrobenzene: \(t^\circ\) vapor	Mixture containing 30.56% nitrobenzene: Difference	Mixture containing 35.26% nitrobenzene: \(t^\circ\) liquid	Mixture containing 35.26% nitrobenzene: \(t^\circ\) vapor	Mixture containing 35.26% nitrobenzene: Difference	Mixture containing 40.01% nitrobenzene: \(t^\circ\) liquid	Mixture containing 40.01% nitrobenzene: \(t^\circ\) vapor	Mixture containing 40.01% nitrobenzene: Difference
mm.	°C.	°C.	°C.	°C.	°C.	°C.	°C.	°C.	°C.
330	—	—	—	18,40	17,80	0,60	19,26	18,54	0,72
340	—	—	—	19,15	18,49	0,66	20,02	19,28	0,74
350	19,04	18,50	0,54	19,88	19,20	0,68	20,74	19,98	0,76
360	19,75	19,22	0,53	20,60	19,91	0,69	21,46	20,68	0,78
370	20,44	19,94	0,50	21,30	20,60	0,70	22,20	21,42	0,78
380	21,13	20,59	0,54	21,98	21,25	0,73	22,89	22,12	0,77
390	21,80	21,20	0,60	22,66	21,90	0,76	22,56	22,78	0,78
400	21,45	21,81	0,64

Table CLVII.

(Continuation).

Pressure	Mixture containing 44.85% nitrobenzene: \(t^\circ\) liquid	Mixture containing 44.85% nitrobenzene: \(t^\circ\) vapor	Mixture containing 44.85% nitrobenzene: Difference	Mixture containing 49.99% nitrobenzene: \(t^\circ\) liquid	Mixture containing 49.99% nitrobenzene: \(t^\circ\) vapor	Mixture containing 49.99% nitrobenzene: Difference	Mixture containing 60.04% nitrobenzene: \(t^\circ\) liquid	Mixture containing 60.04% nitrobenzene: \(t^\circ\) vapor	Mixture containing 60.04% nitrobenzene: Difference
mm.	°C.	°C.	°C.	°C.	°C.	°C.	°C.	°C.	°C.
270							18,44	17,97	0,47
280							19,38	18,85	0,53
290							20,28	19,70	0,58
300							21,15	20,50	0,65
310				19,78	19,02	0,76	22,01	21,37	0,64
320	19,34	18,72	0,62	20,62	19,82	0,80	22,82	22,02	0,80
330	20,12	19,50	0,62	21,42	20,61	0,81
340	20,88	20,24	0,64	22,20	21,36	0,84
350	21,61	20,96	0,65	22,96	22,08	0,88
360	22,34	21,69	0,65	23,70	22,77	0,93
370	23,03	22,38	0,65

Table CLVII.

(Continuation).

Pressure	Mixture containing 70.24% nitrobenzene	Mixture containing 70.24% nitrobenzene	Mixture containing 70.24% nitrobenzene	Mixture containing 78.86% nitrobenzene	Mixture containing 78.86% nitrobenzene	Mixture containing 78.86% nitrobenzene
	liquid temp.	vapor temp.	Diff.	liquid temp.	vapor temp.	Diff.
mm.	°C.	°C.	°C.	°C.	°C.	°C.
200				20.02	18.94	1.08
210				21.23	20.11	1.22
220				22.58	21.34	1.24
230				23.78	22.50	1.28
240	19.46	18.76	0.70	24.86	23.52	1.34
250	20.51	19.78	0.73	25.91	24.48	1.43
260	21.53	20.75	0.78
270	22.52	21.68	0.84
280	23.47	22.56	0.91
290	24.38	23.36	1.02

Table CLXII illustrates the following conclusions.

1) The boiling temperature of a solution, measured in the vapors, is never equal to the boiling temperature of the pure solvent.

2) The boiling temperature measured in the liquid is always higher than the boiling temperature measured in the vapors. This proposition is equally applicable both to a pure liquid and to a solution.

The difference between the temperatures of the boiling liquid and of the vapor given off by it is the greater, the higher the boiling temperature; this is noticeable even for the relatively small temperature interval (about 5°) within which the measurements were made.

The difference between the temperatures of the boiling liquid and of its vapor is the greater, the more concentrated the solution. If superheating proper is excluded, then the temperature of the boiling liquid depends on the hydrostatic pressure of the overlying layer of boiling liquid and on the capillary properties of the liquid. In the present case, the specific gravity of the liquid increases with increasing concentration. It is very probable that the capillary properties, with increasing concentration, also change in the direction of “impeding” vapor formation.

3) The temperature of the vapor follows the change in the concentration of the solution. The curve expressing the law of change of the vapor temperature of a boiling solution with change in the concentration of the solution has the same form as the corresponding curve of boiling temperatures measured in the liquid. It proceeds, however, less smoothly than this second curve.

Under what conditions does measurement of the elasticity of the vapor of solutions by the boiling method give the same results as the barometric method?

Since the temperature of the vapor is different from the temperature of the boiling liquid, it is obvious that there can be no question of such an equilibrium between the solution and the vapor above the solution as exists in a barometric vacuum, when both the solution and the vapor have one and the same temperature.

But one may imagine, at one and the same temperature, two equilibrium systems: the first equilibrium system, at the temperature of the boiling liquid, consists of the liquid and the vapor in contact with it, enclosed in bubbles inside the liquid; the second equilibrium system, at a temperature equal to the temperature of the vapor, consists of the vapor above the liquid and of the very upper layer of the boiling liquid, or of droplets of liquid (solution) thrown off during boiling, whose temperature, owing to cooling, has time to fall to the temperature of the vapor.

The pressure under which the first equilibrium system is found is, evidently, greater than the atmospheric pressure in the apparatus; namely, it is equal to the atmospheric pressure in the apparatus + the hydrostatic pressure of the layers of liquid lying above the mean level of vapor formation, + the capillary pressure. Consequently, the pressure observed by the manometer in an experiment on the boiling of a solution is not equal (is less than) the elasticity of the vapor of the solution in the barometric vacuum at the temperature of the boiling liquid.

The pressure under which the second equilibrium system is found is equal to the external atmospheric pressure. This pressure must be equal to the elasticity of the vapor of the solution at the same temperature in the barometric vacuum.

Thus, theoretical considerations allow one to foresee that the pressure at which a solution boils is equal to the elasticity of the vapor of the solution at the temperature measured in the vapor by a thermometer placed as close as possible to the boiling liquid.

The materials collected by this investigation confirm this. In Table CLVIII the values of the vapor elasticity of mixtures of nitrobenzene and ether, obtained by Raoult and by D. P. Konovalov, are compared with the values of elasticity found by me by the boiling method and referred to the temperature of the boiling liquid and to the temperature of the vapor. Raoult’s measurements ¹) were made by the barometric method at temp. 16°, Konovalov’s measurements ²) were made by the density method (isothermal distillation in a stream of gas) at temp. 18.1°. The comparisons were made at a temperature of 17°, since Raoult’s measurements, as well as my own, showed that the relative lowering of the vapor elasticity of mixtures of ether and nitrobenzene may be considered independent of temperature.

Table CLVIII.

Comparison of the values of the vapor elasticity of mixtures of nitrobenzene and ether, obtained by various authors.

$\pi^0/\%$	Raoult $p_1$	Mikhailenko and Zelter $p_1$ vapor	Mikhailenko and Zelter $p_1$ liquid	$\pi^0/\%$	Konovalov $p_1$	Mikhailenko and Zelter $p_1$ vapor	Mikhailenko and Zelter $p_1$ liquid
0	392,4	392,4	388,4	0	392,4	392,4	388,4
9,6	370,7	373,2	366,3	24,0	340,9	344,1	335,9
26,7	336,6	338,6	330,1	52,9	279,8	280,3	271,9
47,2	291,9	293,9	285,5	63,3	248,4	250,7	243,2
65,4	243,2	243,3	235,8	70,6	220,5	223,2	215,6
				74,6	204,8	206,0	198,5
				76,8	193,4	195,4	187,6

¹) Raoult, Zeitschr. phys. Ch. 2, 362. 1888; Ann. de chim. et de phys. (6) 15, 375. 1888.
²) Konovalov, Zh. R. F. Kh. O. 34 (1) 738. 1902.

In Table CLVIII the concentration (wt. %) of the solution is expressed as the content, in grams, of nitrobenzene in 100 grams of the mixture. In the column \(p_1\) vapor are placed the vapor pressures of the solution corresponding to a temperature of 17°, measured in the vapor; in the column \(p_1\) liquid are placed the vapor pressures of the solution corresponding to a temperature of 17°, measured in the liquid.

Table CLVIII shows that for solutions as well the boiling method gives the same results as the barometric method and the density method, provided that the pressure is referred to the observed temperature not of the liquid, but of the vapor. The differences do not exceed the limits of the usual discrepancies between numerical values of vapor pressure obtained by different observers even by one and the same method, and arising from nonuniformity of materials and from the difficulty of the experiment.

Moreover, it is easy to note that, while the difference between the values \(p_1\) vapor and the values obtained by the other method remains approximately the same at different concentrations of the solutions, the difference between the values \(p_1\) liquid and the analogous values obtained by the other method increases with increasing concentration.

This same conclusion—namely, that the boiling method, when applied to solutions, gives the same results as the other methods—is also confirmed by Table XCIX, which for aqueous sugar solutions gives a comparison of the vapor-pressure values obtained by me by the boiling method with the vapor-pressure values obtained by other authors by other methods.

The same conclusion is supported by the results of measurements of the vapor pressure of two saturated solutions of iodine in chloroform, placed in Tables CXLIX B and CL B. The vapor-pressure values corresponding to the temperatures measured in the vapor proved to be identical for both solutions.

The experiments just described on the measurement of vapor pressure, of course, by no means exhaust the question of the application of the boiling method to the measurement of the vapor pressure of solutions. Having provided known experimental material, they have established with complete definiteness only the proposition that, when measuring the vapor pressure of solutions by the boiling method, the observed vapor pressure must be referred not to the temperature of the boiling liquid, but to the temperature of its vapor. For lack of experimental material, however, it cannot be asserted with complete certainty that in the experiments cited it was possible to measure the temperature of the vapor (which was in equilibrium with the solution of the same temperature, at a pressure equal to the pressure in the apparatus) with the accuracy permitted by the thermometers. There are no data that would fully eliminate the supposition that the temperature indicated by the thermometer in the vapor was somewhat below the actual temperature of the saturated vapor of the solution.

Further experiments must be directed toward finding the best way to protect the vapor from cooling, and also toward finding such an arrangement of the experiment that the vapor already evolved by the solution would be in closer contact with the boiling liquid. Observations of the boiling of solutions, as well as theoretical considerations, expressed

set forth above led me to the following scheme of experiment, which gave good results in preliminary trials. A thermometer, the bulb of which is wrapped in cotton wool, is placed in the vapors of the boiling solution; then a solution of the same substance in the same solvent, but of a concentration weaker than that of the boiling solution, is made to flow slowly onto the cotton wool of the thermometer. The solution, entering a medium whose temperature is above its boiling point, begins to evaporate and, since the evaporation takes place amid the vapor of the solvent, whose vapor pressure is relatively only slightly lower than the vapor pressure of the solution, and since, moreover, the solution continuously flows onto the cotton wool wrapping the bulb of the thermometer, the concentration of the solution soaking the cotton wool should change only to the most negligible degree; the temperature indicated by the thermometer should differ only negligibly from the actual temperature of the saturated vapor of the inflowing solution.

The development, now under way, of experiments for measuring the vapor pressure of solutions according to this scheme will show to what extent these expectations are justified.

Contents

	Page
CHAPTER ONE. Derivation of the relation between the partial density of the solvent in a solution and the elasticity of its vapor, with application of the law of acting masses to the equilibrium between the solution and its vapor	1
Aqueous solutions	12
Solutions in organic solvents	28
CHAPTER TWO. Relations between the partial density of the solvent in a solution and other quantities	42
Partial density and temperature	42
Partial density and osmotic pressure	51
Partial density and concentration	77
Calculation of the molecular weight of dissolved substances from the density of the solution	98
Molecular weight of iodine in solutions of iodine in organic solvents	108
CHAPTER THREE. Experiments on determining the specific gravity of solutions	113
Liquids mixing with one another in all proportions	132
Solutions of iodine in organic solvents	141
Separate determinations	147
CHAPTER FOUR. Experiments on measuring the elasticity of the vapor of solutions	149
Measurement of the vapor elasticity of aqueous solutions of cane sugar	150
Measurement of the vapor elasticity of solutions in organic solvents	178
On the vapor temperature of a boiling liquid	238

1. Kahlbaum, “Über die Temperatur des aus kochenden Salzlösungen aufsteigenden Dämpfe”; Verhandl. d. Naturforsch. Gesellsch. in Basel. T. 8; Zeitschr. phys. Ch. 2, 251. 1883. ↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩

2. Sacurai, Journ. of chem. Soc. 61, 495. ↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩

3. Vapor of boiling amyl alcohol. ↩↩↩↩↩↩↩↩↩

4. Kahlbaum, Studien über Dampfspannkraftsmessungen. 1093. ↩↩↩↩

5. Ramsay and Young, Ber. deutsch. chem. Gesellsch. 19, 2107. 1886. ↩↩↩↩

6. Beckmann, Zeitschr. phys. Chem. 2, 729. 1888. ↩↩

7. Beckmann, Zeitschr. phys. Chem. 2, 734. 1888. ↩

8. Zawidzki, Zeitschr. phys. Chem. 35, 129. 1900. ↩

9. Linebarger, loco cit. ↩