STRUCTURE OF ELECTROLYTE SOLUTIONS1

M. Wien, G. Joos, E. Lange.

I. M. Wien (Jena). On the Deviation of Electrolytes from Ohm’s Law.

Until quite recently it seemed that the nature of solutions and of the phenomena observed in electrolytic conductivity had been fully clarified by the classical works of Van’t Hoff, Arrhenius, and Kohlrausch. According to these works, electrical conductivity was determined by the mobility of the ions and by the degree of dissociation. The agreement between the results of electrical and osmotic measurements of the degree of dissociation seemed to provide the best confirmation of the theory of dissociation; it thus became the foundation of the doctrine of electrolyte solutions. For decades all of us readily and proudly expounded it in our lectures.

However, certain doubts had already appeared long ago. It turned out that the course of the decrease in the equivalent conductivity of strong electrolytes was incompatible with the law of mass action. A number of theories were developed on the assumption that, for strong electrolytes, dissociation is complete, and that the decrease of equivalent conductivity with concentration depends on the electrostatic forces with which the ions act upon one another, forces that increase at more appreciable concentrations owing to the small distances between the ions. In recent years, after a number of not

quite successful experiments, Debye and his collaborators developed a theory which agrees with observation qualitatively and, within broad limits, also quantitatively. This theory will be presented in greater detail by Joos1.

Debye’s theory did not prove suitable for universal assimilation, especially by chemists. The clear and flexible theory of dissociation, particularly when in some cases it is supplemented by equally flexible notions of hydrolysis, complex formation, etc., fully satisfies the theoretical needs of most chemists. But however convenient the theory of dissociation may be, we must abandon it both in research work and in teaching if it turns out to be fundamentally incorrect.

The leaders of modern physical chemistry—for example, Nernst, in the latest edition of his classic textbook of theoretical chemistry—take at best a cool attitude toward the new theory. True, in his most recent works Nernst already carries out calculations with its aid and merely tries to determine the limits beyond which, along with the Debye effect, association also begins to manifest itself. Such an expert on electrolytic phenomena as Walden is also, in essence, opposed to Debye’s theory, as is expressed in his article dedicated to the memory of Arrhenius. There he states the opinion that the modern theory, with its more or less complicated and purely physical auxiliary conceptions, is moving farther and farther away from Mendeleev’s ideal, according to which every general solution must ultimately take chemical relations into account on an equal footing with physical ones. In conclusion Walden compares Arrhenius with Berzelius, to whose ideas about electropositive and electronegative elements, in the end, they returned again, and he asks with reason: will there likewise someday be, in the doctrine of electrolytic solutions, a return to Arrhenius’s ideas?

The reason why a definite and clear solution to the question of dissociation is difficult lies in the impossibility of sufficiently reliable measurements of the dependence of equivalent electrical conductivity on concentration, to which I shall now turn. To choose between the two conceptions, new observations are needed, new phenomena that could truly serve as a touchstone for the theories. If one theory can fully explain such new phenomena and is even capable of predicting them, while the other stands helpless before them, then the choice is made. Such experiments are possible in various directions. First, experiments concerning electrical conductivity will be reported; then G. Joos will show how far the theory is able to explain new phenomena; and, in conclusion, E. Lange will speak about calorimetric and optical experiments that make it possible to draw certain conclusions about dissociation.

Change of Electrical Conductivity with Concentration.

The change of electrical conductivity with concentration was accurately investigated already by Kohlrausch for \( \frac{1}{128}\% \) and by many others; however, the results have been established to a certain degree reliably only for the simplest electrolytes with 1–1- and 1–2-valent ions1. For electrolytes with multivalent ions they are very inaccurate, although precisely

Fig. 1.

here, where the changes with concentration are especially large, the theory could be tested best of all. Fig. 1 shows the percentage deviation of solutions of various concentrations in comparison with the electrical conductivity at infinite dilution for electrolytes with ions of different valence. The ordinates give the electrical conductivity as percentages of \(\lambda_{\infty}\), the abscissae—the square root of the equivalent concentration. Only for electrolytes with 1—1- and 1—2-valent ions is the curve rectilinear over a large region of concentrations.

Fig. 2.

For ions of higher valence, for example magnesium sulfate, potassium ferricyanide, the observations are, on the one hand, very inaccurate, and moreover the straight line is curved, the curvature beginning at the larger dilutions the greater the valence of the ion. In addition, it is clearly seen that extrapolation of observations for very dilute solutions often leads not to the value 100, but to higher values; this is probably a consequence of changes in the ions (for example, hydrolysis). Fig. 2 shows that this uncertainty appears even with such a salt as magnesium sulfate. From all this it follows that a reliable and clear test of the theory on the basis of these measurements is impossible.

Dependence of the electrical conductivity of electrolytes on frequency and on field strength

In studying the electrical conductivity of electrolytes, one may expect new phenomena in two directions: first of all, if, for measuring electrical conductivity, an alternating current of very high frequency is used and it is investigated whether the electrical conductivity and dielectric constant depend on the frequencies employed for the measurements. The theory for this case was developed recently by Debye and Falkenhagen. The measurements are still at the very initial stage, since for very high frequencies there as yet exist no methods that would make it possible simultaneously to measure, with sufficient accuracy, the electrical conductivity and dielectric constant of conducting liquids. Preliminary measurements at the Leipzig Physical Institute have confirmed the theory.

The second direction of research consists in measuring the electrical conductivity of electrolytes in fields of very high strength, where the ions acquire very great velocities, and in seeing whether changes of electrical conductivity with voltage will occur. This latter question has recently been developed by me and my collaborators, and I wish to report on it briefly.

We are accustomed to ions moving in electrolytes at a snail’s pace. For example, in a field of \(1\ \mathrm{V/cm}\), the sodium ion moves at a speed of \(1.6\ \mathrm{cm}\) per hour. The question arises: will the velocity of the ions increase proportionally to the field up to voltages greater than \(100\,000\ \mathrm{V/cm}\), so that the ions attain velocities of several meters per second, and will Ohm’s law retain its validity for such velocities? The difficulty of the investigation lies in the fact that, with any somewhat longer duration of the current, powerful thermal effects and electrolytic decomposition would make any measurements impossible. Thus it remains only to use, for these measurements, extremely short currents, for

lasting approximately one millionth of a second. Naturally, it would be good if the high voltage remained constant during this short time and had the form of the solid line in Fig. 3. However, this is unfortunately impossible, and one can only employ brief, strongly damped discharges of a capacitor, the voltage changing with time approximately according to the dotted curve in Fig. 3. In this case one can approximately compute the time average of the voltage and of the field. The pulsed current that produced the voltage was used simultaneously for measuring the electrical conductivity, the effect of the current being measured by means of a thermoelement or detector (Fig. 4).

Fig. 3.

In the simplest manner this was carried out if the resistance under investigation was connected in turn with some other resistance independent of the voltage, and was varied until the same current effect was obtained. When the voltage was raised by increasing the spark gap, a change of the resistance under investigation with voltage was obtained. This method was improved by I. Malysh and myself to the degree of a precision method, with a null method introduced instead of observing a deflection (Fig. 5). The current circuit was branched: into one branch was inserted the resistance under investigation, into the other one serving for comparison. Both branches were connected with one branch of the barretter; if they had equal resistances, then in the barretter

Fig. 4.

no deflection of the galvanometer was observed. This method is very accurate; with it one can confidently determine changes in electrical conductivity equal to \(0.01\%\)—an accuracy which, as a rule, can hardly be hoped to be attained by the Kohlrausch bridge method.

Fig. 5.

From these measurements it follows that in electrolytes there is always an increase in electrical conductivity when the voltage is raised. Changes of up to \(50\%\) were observed. The course of the changes with increasing field is given schematically for three solutions with ions of different valency in Fig. 6, the field voltages being plotted as abscissae.

Fig. 6.

The electrical conductivity at first increases slowly together with the field (the first dotted part of the curve), then there follows an approximately straight-line part (shown in the figure by a solid line), and finally there is again a downward bend (the second dotted part of the curve). Both dotted parts are of special interest. The first dotted part, i.e. the action of relatively weak fields, can be represented empirically by a formula of the form:

\[ \Delta\lambda = AX^{2}(1 - LX^{2}), \]

where \(X\) denotes the field voltage. The constant \(A\) increases rapidly with the valency of the ions and is the greater, the stronger the dilution, increasing also with a decrease in the dielectric constant of the solvent. Accordingly

For this reason we see in Fig. 6 a steeper rise of the curve for a solution with 2–4- and 2–3-valent ions than for a solution with 1–3-valent ions.

In Table 1 some observations are given and compared with the empirical formula:

\[ A=z_1^2 z_2^2 \sqrt{\frac{z_0}{z}}\,1{,}1\cdot 10^{-12}\ \mathrm{V/cm}. \]

It is evident that this formula represents the observations correctly to a certain degree.

Table 1.

In this table \(z_1\) and \(z_2\) denote the valencies of the ions composing the given electrolyte, and the specific electrical conductivity of the solution; the figures written on the same line as the chemical formula give the empirical value of the constant \(A\), while those below give the values calculated according to the formula just presented.

This first part is especially interesting, since it can quite well be compared with theoretical data.

I now turn to stronger fields, i.e. to the upper dotted part of the curve. The field at which the downward bend of the curve becomes noticeable depends to a high degree on the concentration. This bend occurs the earlier,

the more dilute the solution, so that in very dilute solutions the rise of the curve is at first very steep, but soon becomes gentle, whereas in more concentrated solutions the initial rise is small, but continues up to very strong fields. Thus the pattern of Fig. 7 is obtained; the curves intersect.

The increase of conductivity with field strength becomes ever weaker at strong fields, and it appears that it tends toward some limiting value. For very dilute solutions this limiting value is reached much earlier and lies lower than for more concentrated solutions.

Fig. 7.            Fig. 8.

Because of sparking I was able to observe the limiting effect only for very dilute solutions. At the same time, these latter experiments confirmed the assumption, expressed in an earlier work, that within the limits of experimental error the limiting value of the conductivity in very strong fields agrees with the value of the conductivity at infinite dilution \((\lambda_\infty)\). This means that at very high velocities the causes responsible for the decrease of the equivalent electrical conductivity with concentration disappear. In Fig. 8 I give the course of the electrical conductivity at very large fields for four different solutions. It is seen that the limiting values have approximately been reached, and that for electrolytes of higher valence they lie higher than for electrolytes of lower valence. In Tab-

In Table II some figures are given for the limiting effect, and the observed values \(\Delta\lambda_0\) are compared with \(\Delta\lambda_c\), obtained from measurements of electrical conductivity at two different concentrations. If the unreliability of both methods of measurement is taken into account, the agreement is satisfactory.

Geymant1 has recently also observed, in very poorly conducting liquids, an increase of electrical conductivity with increasing field. With negligible conductivity he could, without fear of too great an evolution of Joule heat or of electrolysis, apply strong fields for a long time. In this way he was able to separate the measurement of electrical conductivity and the production of a strong field from one another. It was thereby established, as an important fact for the theory, that the increase of electrical conductivity occurs only when the strong field is directed in the same way as the voltage used for the measurement, and does not occur if the field and the voltage are directed perpendicular to one another.

Table II.

\[ \chi = 2{,}3\cdot 10^{-5} \]

\[ \chi = 9{,}2\cdot 10^{-5} \]

In conclusion, let us compare the new phenomena once more:

In electrolytic conduction there is always an increase of electrical conductivity with the field. In weaker fields this increase is at first proportional to the square of the field. The coefficient of proportionality grows approximately in parallel with the square of the product of the valences and is large for small dielectric constants and lower concentrations. In very strong fields the electrical conductivity tends toward a certain limiting value, which is reached the sooner the greater the dilution. Within the limits of experimental error, this limiting value coincides with the electrical conductivity at infinite dilution. If the field is perpendicular to the voltage applied for measuring the electrical conductivity, then no increase in electrical conductivity occurs.

All these diverse phenomena must be explained by a true theory of electrolyte solutions qualitatively, and as far as possible quantitatively. How far this is actually the case will be shown in his report by G. Joos.

II. G. Joos (Jena). Theoretical explanation of the dependence of electrolytic conductivity on voltage and current frequency.

As has already been mentioned, the theory of electrolytic dissociation provides no means even for a qualitative explanation of the dependence of electrolytic conductivity on the field strength and of the dependence of this effect on the valence of the ions, the dielectric constant of the solvent, and the concentration. On the contrary, on the basis of the new ideas about electrical conductivity—which, in contrast to the classical theory of dissociation, take as the principal cause of the dependence of electrical conductivity on concentration in strong electrolytes the mutual connection of the ions due to their electrostatic interactions—a detailed theoretical explanation is obtained for the dependence of electrical conductivity on voltage and frequency. I must now dwell somewhat more closely on the principal ideas of the new theory of electrolytes, in order to obtain some measure of the extent to which the numerical calculation of the effect under consideration may be regarded as a confirmation of the theory,

since the agreement between theory and experiment is judged differently, depending on the number of arbitrary constants introduced. These foundations of the theory are quite clear and beyond any doubt: we regard ions as spheres which move under the influence of an applied field in a solvent possessing internal friction, and we pay attention exclusively to what had previously been neglected: namely, to the fact that ions are carriers of electric charges, as a result of which they must act upon one another with certain forces. That these electrostatic forces are not very small may be judged from the following little joke of a problem: let us divide a mole of common salt into ions and remove the opposite ions to the distance of the earth’s poles; then, as is easy to calculate, there will nevertheless exist a force of attraction, in round numbers equal to \(50\,000\) tons. But however clear the physical essence is, the mathematical treatment of the question of these interionic forces is correspondingly difficult. In 1923 Debye and Hückel for the first time found a way which, on the one hand, could be overcome mathematically and which, on the other hand, despite the inevitable simplifications, did not distort the natural picture of the phenomenon.

When we form a visual representation of the arrangement of ions in a salt solution, we think that this distribution at room temperature still does not differ too greatly from the arrangement occurring at absolute zero, corresponding to the least electrostatic energy. We can most clearly imagine this arrangement on a crystal lattice of the rock-salt type. It is characteristic that in the immediate neighborhood of some given ion there are ions of the opposite sign. Imagining this arrangement as somewhat distorted, we arrive at the picture of the arrangement of ions in electrolytes. The great merit of Debye and Hückel, who for the first time made the force actions in such a complex system accessible to calculation, consists in the following: imagining, in the presence of many positive ions, the arrangement of the surrounding positive and negative ions to be fixed, we may form a certain average

charge distribution, which corresponds to a certain continuous negative spatial charge decreasing with distance. In what follows we shall carry out calculations only with this mean continuous charge. Thus it becomes possible to apply to the region surrounding a certain ion chosen by us the concepts “potential” and “density of spatial charge,” borrowed from continuum physics. When the ion moves, the spatial charge surrounding the ion acts upon it with forces of two kinds: the first is the Stokes frictional force of the solvent, connected with its increase, which decreases with distance but extends far beyond the ion’s own radius. If, on average, there were the same number of positive and negative ions around a positive ion, then the current arising near the very ion under consideration would be completely annihilated. But, owing to the excess of opposite charges, the component opposite to the motion of the positive ions predominates, and thus acts as though the resistance to friction had increased. We shall call this first additional force the electrophoretic force. Still more important is the second force, the cause of whose appearance lies in the finite time of formation of the ionic atmosphere. If at first we imagine this atmosphere to be very inert, so that it possesses the spherical symmetry that still existed at the time \(t\), when over the interval \(\Delta t\) the ion had advanced a certain distance forward, then we shall see that behind it there will be some excess negative charge, causing the appearance of a certain retarding force. The force caused by this lag of the spatial charge we shall call the relaxation force. Debye and Hückel formulate differential equations for the formation of the spatial charge, but for the moment confine themselves only to the stationary state of interest to them, in which the spatial charge, considered from the moving ion, retains its position. An approximate integration of these very complicated equations gives, for both the electrophoretic and the relaxation force, a value,

M. WIEN, H. JOOS, E. LANGE

proportional to the velocity of the ion and, consequently, to the applied field strength; in other words, Ohm’s law, the proportionality between field strength and current, determined by the velocity of the ions, is not violated in the first approximation by the ionic forces. But it is clear that, with an increase in the accuracy of the calculations, deviations from this proportionality may be expected. The principal result of Debye and Hückel’s calculations is the derivation of Kohlrausch’s empirical limiting law, according to which, for very dilute solutions, the decrease in electrical conductivity, i.e. the relative deviation of the equivalent conductivity from the value of the conductivity at infinite dilution, is proportional to the square root of the concentration, whereas the theory of dissociation requires, by virtue of the law of mass action, proportionality to the first power of the concentration. As for a numerical verification of Debye’s calculations, we note that his formulas still contain a certain arbitrary constant, namely the ionic radius introduced for calculating the electrophoretic force, which is not identical with the radius calculated from the mobility of the ion according to Stokes’ law. The numerical verification therefore consists in the fact that acceptable values are obtained for these radii, i.e. numbers of the order of \(10^{-8}\), which is indeed observed.

Now it remains to consider, from the standpoint of the Debye–Hückel theory, the increase in electrical conductivity observed by Wien at high voltages. Qualitatively, such an effect may be expected on the following grounds: if one imagines that the ionic atmosphere is very inert and that the ion is suddenly displaced to a large distance farther on, then its influence in this direction is very slight and disappears at sufficiently large distances. These considerations, which in this form bear some resemblance to the story of Achilles and the tortoise, would become legitimate if we knew something quantitative about the time of formation of the ionic atmosphere, which has now been attained by the calculations of Debye and Falkenhagen, discussed below. One may, however, expect that the retard-

the moving force does not increase to the same degree as the velocity of the ion, and this follows rigorously if one calculates the nearest approximate solution of the differential equations of Debye and Hückel: one obtains, at least qualitatively, all the essential features of the observed phenomenon, such as the dependence of the effect of voltage on the concentration, the valence of the ions, and the dielectric constant of the solvent. As for the dependence on the field strength, the theory does not give the observed linear dependence. But it can be shown that the observed curve is tangent to a certain integral curve, and further measurements at relatively small voltages do in fact give the course required by the theory.

These calculations were meanwhile considerably simplified by Mr. Blumentritt on the basis of improvements, made by L. Onsager,¹) to the calculations of Debye–Hückel. The Debye–Hückel theory contains in one place a small inconsistency: the formation and change of the ionic atmosphere is, in essence, conditioned by thermal motion. But for the ion under consideration this is not taken into account, since it is assumed that it moves straight in the direction of the field. In Debye’s comparison, such an ion is like a very heavy, thick man who forces his way through a disorderly jostling crowd. Such singling out of the ion under consideration from the others is incorrect. This man, because he has a mass no greater than that of the people jostling him, is himself knocked now here, now there, and this zigzag motion substantially changes the calculations. The theory, improved in this way, makes it unnecessary to introduce the actual electrophoretic radius; very good agreement is obtained if the calculation is carried out only with the radius estimated by Stokes’ law from the frictional resistance of the medium. Thanks to this, Onsager’s final formulas, which no longer change the already mentioned result of Debye’s theory—the law of square roots—contain no individual

¹) L. Onsager, Phys. ZS. 27, 388, 1926; 28, 277, 1927.

dual constants, apart from the mobility at infinite dilution, from which the radius is obtained by means of Stokes’ law. If one takes Onsager’s differential equations as the basis, then the following final formula is obtained for the dependence of the electrical conductivity on the voltage; expressing this dependence on the voltage by a formula with two constants:

\[ \Delta\lambda=\frac{\lambda-\lambda_0}{\lambda_0}=AX^2(1-\mathfrak{B}X^2) \]

for the coefficients we shall have

\[ A=6.61\cdot10^{-5}\, \frac{z_1z_2\,(z_1+z_2)^{1.5}}{T^{2.5}\sqrt{D}\sqrt{\eta}\,f_\lambda}\, \frac{q^{2.5}}{(1-q)^3}\,K_1+ \]

\[ +\,6.3\cdot10^{-11}\, \frac{z_1z_2\sqrt{z_1+z_2}\,q^{1.5}\sqrt{D}} {T^{1.5}\sqrt{\eta}\,(1+\sqrt{q})^2\Lambda\xi} \]

\[ K_1=-0.2\sqrt{q}+0.075+0.15q-0.025q^2. \]

\[ q=\frac{z_2\rho_1+z_1\rho_2}{(z_1+z_2)(\rho_1+\rho_2)};\quad \mathfrak{B}=1.09\cdot10^{-11}\, \frac{D(z_1+z_2)qK_2}{T\eta(1-q)^2K_1} \]

\[ K_2=-0.00558+0.06696q+0.10045q^2-0.02232q^3+ \]
\[ +0.00335q^4-0.14286q^{1.5}. \]

Here the symbols denote: \(T\)—the absolute temperature, \(D\)—the dielectric constant, \(\eta\)—the equivalent concentration per liter, \(z_i\)—the valence of the ions, \(\rho_i\)—their constant of friction at infinite dilution (i.e. the reciprocal values of the mobilities), \(f_\lambda=\dfrac{\Lambda}{\Lambda\infty}\); \(\Lambda\infty\)—the equivalent electrical conductivity at infinitely great dilution, \(\xi\)—the viscosity of the solvent.

As is seen, no further individual constants enter here, apart from the mobility of the ions, which can be measured. The numerical agreement with Wien’s results, which can be shown on any arbitrarily chosen example, is as good as can be expected for a theory with such great simplifications.

Numerical values of the coefficients \(A\) and \(B\) for the voltage effect

What does this agreement between theory and experiment prove to us? It shows that the calculation of ionic forces was carried out correctly; because an almost quantitative calculation in phenomena as complex as those measured in the Wien experiments is worth something. As to the next question—how far, in fact, solutions of strong electrolytes are dissociated, if one takes Debye forces into account—these results give no answer. The point is that the existing, perhaps undissociated, part plays no role here at all. However, the theory indicates a path which may lead, at least in principle, to the solution of this question, although there are many experimental difficulties along the way. Namely, we must seek such conditions under which the ionic forces disappear. The difference of conductivities measured under such conditions at finite and infinite dilution will then give a real measure of the amount of existing undissociated molecules. But before I speak...

to speak about these conditions, I should like to dwell somewhat on the definitions “dissociated” and “undissociated,” in order to obtain clear grounds for discussion. In the old theory of dissociation, one imagined that in a solution of NaCl there were, alongside the ions, real molecules, just as one would imagine the solid salt to be built up of molecules. But since it became known that the lattice of the solid salt is an ionic lattice, one may doubt the existence of real NaCl molecules in solution. However, we know from the vapor-density measurements of Nernst that the vapor of this salt is diatomic, so that the possibility of the existence of such molecular formations in solution is not excluded. These molecular formations are electrostatically incomprehensible; electrostatics would always lead back again to an ionic atmosphere. It is more likely that here we are dealing with discontinuous quantum-like changes, which have now become more accessible to understanding with the aid of quantum mechanics, thanks to the works of Heitler and London¹). Only such truly chemical molecules of definite composition can be regarded as molecules when one speaks of the degree of association. More substantial formations, bound electrostatically, in principle always obey the Debye theory. In this respect Bjerrum²), as he states in many places, recognizes his associated ionic aggregates only as calculable auxiliary quantities, and not as true chemical molecules. On the other hand, no one denies the existence of true chemical molecules in weak electrolytes, especially in organic salts, and the continuity of nature permits one to expect that similar formations in small amounts also exist in strong electrolytes. There is considerable unreliability inherent in attempts hitherto made, on the basis of experiments in which ionic forces act, to obtain, by taking the action of these forces into account, the degree of dissociation from changes in electrical conductivity not explainable by these forces. Not every deviation

¹) Cf., for example, the articles by London, Usp. Fiz. Nauk, vol. IX, no. 2, 1929. Ed.

²) N. Bjerrum, Ergebn. d. exakten Naturwissenschaften, 5, 125, 1926 (cf. Usp. Fiz. Nauk, 7, 269, 1927).

STRUCTURE OF ELECTROLYTIC SOLUTIONS

...from the Debye square-root law for the dependence on concentration can be laid at the door of the existence of an associated part; rather, this law represents only a first approximation for very dilute solutions. Therefore, in passing to concentrated solutions, the differential equations of Debye–Hückel and Onsager must be expanded further with respect to concentration. Such a calculation was carried out by Redlich¹) on the basis of the original Debye–Hückel equations. He came to the conclusion that for alkali-halide salts complete dissociation exists up to 0.1 molar solutions. But the accuracy of calculations based on the original Debye–Hückel equations, which include the electrophoretic ionic radius, is insufficient to exclude small degrees of association (of the order of one percent).

On the contrary, the following reasoning is entirely free of hypotheses; Onsager²) used it to estimate the true degree of dissociation, and, independently of him, somewhat later, Nernst³): if we have two salts with identical conductivity at infinite dilution and identical transference numbers, then for both salts all quantities entering into the ionic forces are equal. Therefore, the deviations in electrical conductivity that appear at high concentrations must be attributed to chemical changes. Onsager carried out such a comparison. The salts considered by him are not strictly identical and, though one may doubt whether the individual deviations of the alkali-halide compounds are not due to these small differences, the anomalous course of the curve for thallium salts stands beyond all doubt; for them it had long been known that in aqueous solutions they form complex compounds⁴). Nernst

¹) O. Redlich, Phys. ZS. 26, 199, 1925; 27, 528, 1926.
²) L. Onsager, Phys. ZS. 28, 295 Fig. 6, 1927.
³) W. Nernst, Berl. Ber. 19, I, 1928.
⁴) Whether neutral molecules or more highly charged ions arise with increasing concentration, which likewise lower the electrical conductivity owing to their greater Stokes resistance, is difficult to decide.

reached much higher concentrations and gives, for 0.1 molar solutions, the following degrees of association:

According to the old theory:

These numbers are based on the value of 98% dissociation of a 0.1 molar KCl solution obtained from the heat of dilution. Below are the degrees of association following from the old theory. In the following report the question will be discussed of how reliable are the degrees of association obtained from heats of dilution, by means of which the normalization of the upper numbers was first achieved. It is, however, accepted that the theory points out to us the path toward a direct determination; moreover, it makes it possible to indicate the conditions under which the ionic force disappears. Debye and Falkenhagen1, in two major papers that appeared this year, calculated the time required for the formation of the ionic atmosphere. Naturally, this problem is mathematically still much more complicated than the calculation of the distribution of the ionic atmosphere in the stationary state. The principal result is that the time of formation is of the order of \(10^{-10}/m\) sec (\(m\)—the molar concentration). If we apply an alternating voltage whose frequency is greater than this time, then it is already qualitatively clear that the relaxation time will be smaller and, for very rapid changes, will disappear completely. Since we imagine the ionic atmosphere to be at rest, it acts as a retarding factor when the ion departs and, to the same extent, as an accelerating factor when it returns to its former place. The electrophoretic force, on the contrary, is in essence independent of frequency, since the connection, through friction, between the ions and the lattice-like distribution that gives rise to the electrophoretic force has nothing to do with the time of formation of the atmosphere.

But knowledge of the relaxation time is also important for the voltage effect. When we pass to very strong fields, in which the velocity of the ion is of the order

1 m/sec, then after a time equal to a fraction of the time of formation of the atmosphere the ion is already completely outside its region, i.e. at large velocities the characteristic distribution is in general no longer formed, and both the relaxation force and the electrophoretic force disappear. Consequently, in the very strongest fields one measures a conductivity free from ionic forces. Of course, even here one cannot go infinitely far, if only because of spark breakdown; otherwise we would reach velocities at which, according to hydrodynamics, Stokes’ law would have to be modified. At velocities of 1 m/sec this correction, according to Oseen’s calculations, is 0.1%.

If you will permit me, in conclusion I shall schematically repeat once more how one may develop a completed picture of electrical conductivity, in the sense of finer phenomena, from the basic assumption of the existence of an ionic atmosphere and of the forces caused by it:

Differential equations of Debye–Hückel or Onsager for the stationary motion of ions

↓

Approximate integration: Ohm’s law and Kohlrausch’s square-root law

↙︎                                             ↘︎

Development with respect to concentration: deviations from the square-root law

Development with respect to the field strength: the field effect

Equations of Debye–Falkenhagen for the formation of the ionic atmosphere:

↓

Establishment of the relaxation time at high frequencies

Establishment of both forces at the highest field strengths.

III. E. Lange (Munich). New thermochemical and refractometric investigations in the field of strong electrolytes.

When the great investigator in the field of electrolytes, Svante Arrhenius (1)1, 41 years ago formulated his theory of electrolytic dissociation, which overturned everything, he certainly did not foresee that 40 years later, despite considerable successes in this field, the fundamental questions concerning the nature of electrolyte solutions would still be heatedly discussed. I should like to single out, besides him, several other names most characteristic of the various phases in the development of the theory. Van ’t Hoff (2) laid the foundations of the theory in which he taught us to apply the laws of ideal gases to the so-called ideally dilute solutions. Then came Arrhenius (1), whose doctrine that a more or less considerable part of the dissolved electrolyte decomposes into ions has, at the present time, retained its force only for the so-called weak, i.e. slightly dissociated, electrolytes, and leads to the application of the law of mass action in its original form to the dependence of the degree of dissociation on concentration. I shall also mention N. Bjerrum (3) and G. N. Lewis (4), who created thermodynamic concepts closely connected with the idea, advanced earlier by Sutherland (5), of interionic forces acting between the ions arising as a result of complete dissociation. Finally, P. Debye (6) must be mentioned, who, together with Hückel, was the first to succeed in developing for such practically completely dissociated electrolytes a quantitative theory fully applicable, at least in the region of very dilute solutions. At present the question is being investigated of how far the experimentally determined properties of solutions, above all moderately concentrated ones, can be explained solely on the basis of the notions of such interionic forces, or whether other factors must also be taken into account, in particular the existence of an undissociated part. Already Bjerrum (7)

thought that the activity coefficients could better be calculated by means of the concept of ionic association. Then C. Fajans (8), in a somewhat different form, arrived at the assumption of incomplete dissociation as a result of refractometric measurements. Still earlier, Nernst had expressed the same assumption on the basis of thermochemical measurements. To this category also belong the recently published works of Galban (10) on the absorption spectra of solutions.

I should like to single out from this extensive theoretical and experimental material two areas whose development belongs to recent times: the thermochemistry of electrolyte solutions, where the matter is chiefly the calculation and measurement of integral heats of dilution of more or less weak electrolyte solutions, which I shall discuss in the first part of my report.

In the second part I should like to dwell on certain optical investigations, above all those of Fajans and his co-workers (11), in which, on the basis of the dependence of molecular refraction in concentrated solutions on concentration, certain conclusions are drawn concerning their nature.

1. Thermochemical investigations.

As regards thermochemical measurements, in the case of integral heats of dilution one is dealing with those thermal effects which occur upon dilution to infinity of a solution, containing 1 mole of salt, of a definite initial concentration \(m\). According to Van’t Hoff, in general no heat of dilution should be evolved. Arrhenius reduces the entire heat of dilution to the heat of dissociation of the undissociated portion that existed at the initial concentrations. According to the Debye–Hückel theory, the entire effect measured in a certain completely dissociated electrolyte is determined by interionic forces. The general theoretical foundations of such a conception have already been sufficiently clarified in both preceding reports. I therefore wish subsequently to draw attention only

…to the most important consequences with respect to heats of dilution.

The situation is clearest in very dilute solutions, for example, for 1,1-valent salts below \(1/100\) molar. This concentration interval is called the limiting region. For aqueous solutions one can here obtain result (12), which at first seems strange: contrary to, or rather precisely as a consequence of, the forces of attraction between ions moving away from one another in the process of dilution, on the whole a positive heat of dilution is evolved. This can be explained vividly as follows: to increase the volume of the ionic system alone, starting from some definite concentration and proceeding to infinite dilution, energy of expansion is of course expended, which results in cooling of the system. But at the same time heat is developed in the dipolar medium surrounding the ions, since in the process of dilution the addition of water molecules to the solution leads to an increase of the hydration shells of the individual ions, i.e. to stronger hydration. And since the amount of heat thereby given off by the water molecules is, one may say almost accidentally, at room temperature greater than the negative energy of expansion, the result as a whole is a positive heat of dilution.

Confirmation of the qualitative requirement of the positive sign of the heats of dilution for very dilute solutions of such electrolytes which already at not very high concentrations give negative heats of dilution was not obtained in the work of Nernst and Ortmann (13), because of insufficient measurement accuracy. In a later work (14) this confirmation was obtained both by these authors and in investigations carried out at the same time by me together with Messner. Nernst and Ortmann (16) give, for the accuracy achieved with their improved calorimeter, in round numbers \(1/200\,000\) of a degree.

For a quantitative verification of the simple theoretical formula, the so-called limiting law, in which the radii of the ions are not taken into account, it is necessary as accurately as possible

to determine still smaller heats of dilution, sometimes reaching 3–5 millionths of a degree. In work carried out together with Layton (17), it proved possible to increase the accuracy of the differential calorimeter originally constructed together with Messner from 1–2 millionths of a degree to 0.5 millionth. This calorimeter (18) is shown schematically in Fig. 9. The two-liter Dewar vessel

Fig. 9.

is divided into two halves by a thermobattery filled with sealing compound, mounted on ebonite and consisting of 1,000 iron-constantan elements connected in series. By means of a mirror galvanometer it is possible to measure the temperature difference between the two halves of the calorimeter to one millionth of a degree. On each side there are metal pipettes, completely immersed in the contents of the calorimeter, in which the solution to be diluted is already present.

Mixing occurs when the upper and lower stoppers are opened simultaneously, since in this case the water serving for dilution and stirred by the agitator in each half of the calorimeter can also flow through the open pipette.

The experimental difficulties consist, essentially, in being able, after eliminating a number of sources of error, to bring the aforementioned thermometric sensitivity, which is capable of being increased still further, up to an equally high calorimetric sensitivity. External sources of error, which might have arisen from the medium surrounding the calorimeter, were eliminated by the fact that the water bath, completely surrounding the calorimeter, was always maintained, to an accuracy of \(1/1000\) of a degree, at the same temperature as the interior of the calorimeter. Within the calorimeter itself there could be sources of heat. For example, the temperature of the calorimetric liquid rises extremely slowly owing to the energy of friction, which was naturally reduced to the smallest possible value; owing to inertia, the temperature of the solution in the pipette, despite the good thermal conductivity through the metallic walls, always lags behind that of the contents of the calorimeter. Only because of this did a one-sided “zero effect,” equal to 6 millionths of a degree, result. This “zero effect” can be circumvented by producing it simultaneously and to the same degree in both halves of the calorimeter; thus on one side the solution was mixed with water, and on the other—quite symmetrically—water with water. To check whether the “zero effect” is in fact symmetrical and completely cancels, blind experiments were performed many times, in which water was mixed with water on both sides, or solution with the same solution. The remaining error on the average does not exceed 0.5 millionth of a degree. The position of the galvanometer was recorded for 3 seconds before and after the mixing and was graphically extrapolated to the moment of mixing.

Measurements of small heats of dilution were carried out in exactly the same way. It turned out that the heat of dilution of LiBr, reaching 2.5 millionths of a degree, can be determined

when performing individual experiments, to an accuracy of up to 0.5 millidegree, and to convert into calories with the aid of the corresponding electrical calibration through Joule heat.

From the large number of experimental data it would be desirable to select only certain results (19), which are

Fig. 10.

in close connection with the theoretical requirements imposed upon the limiting law.

1. First of all, the theoretical formula (13, 15, 18, 22)

\[ V_m = \frac{0.239}{10^7} \left( \frac{\sum \nu_i Z_i^2}{2} \right)^{3/2} \sqrt{ \frac{m N E^2}{D} } \sqrt{ \frac{8\pi E^2 N}{D k T \cdot 1000} } \left( 1+\frac{dD}{dT} \right) \ \frac{\text{calories}}{\text{mole salt}} \]

shows that in very dilute solutions the heat of dilution, determined by interionic forces, must increase proportionally to the square root of the initial concentration. The theoretical expression for the integral heat of dilution must thus have the form \(V_m=\text{constant}\sqrt{m}\). This requirement is met by the results of measurements for KCl (17), presented graphically in Fig. 10,

is confirmed, within the limits of the accuracy attained, approximately to within 5%, almost up to concentrations \(m/100\): the values of \(V_m\) with \(\sqrt{m}\) as abscissae have, both at \(12.5^\circ\) and at \(25^\circ\), an initially rectilinear course.

1. The theory requires that the heats of dilution of equivalent salts, for example of 1,1-valent salts, coincide in the \(\sqrt{m}\)-region at identical initial concentrations.

Fig. 11.

This requirement, as is seen from Fig. 11, is approximately fulfilled, within the limits of the accuracy so far attained, for certain salts, such as, for example, KF, KCl, CsCl, LiBr, etc. Of course, \(KNO_3\) already in a \(1/100\,m\) solution shows an evident deviation from the others. Nevertheless, at small concentrations its curve approaches the others so closely that one may suppose that at still greater dilutions it too reaches the \(\sqrt{m}\)-region and no longer differs from the other salts of the same valence. CsCl and KCl likewise approach, for example, KF, and indeed even at higher concentrations. Similarly, for multivalent salts, series of individual measurements agree approximately, for example for the 1,2-valent \(Na_2SO_4\) and the 2,1-valent \(Ca(NO_3)_2\) (15). Deviations from this theoretical requirement, for example in 2,2-valent salts, must probably be explained, just as for \(KNO_3\), by the fact that here the \(\sqrt{m}\) region has not yet been reached. More accurate experimental-

...verification of the equality of the heats of dilution of equivalent salts in the limiting region is being carried out at the present time.

1. The heats of dilution of salt solutions of equal molarity, but of different valence types, must in the \(\sqrt{m}\)-region differ by a quite definite, theoretically calculable factor. This is indeed found if, for example, we compare the 1,1-valent group (KCl, KF) with the 2,1- and 1,2-valent group \([\mathrm{Ca}(\mathrm{NO}_3)_2, \mathrm{Na}_2\mathrm{SO}_4]\). The theoretical ratio should be 5.2; the experimental ratio—approximately, by agreement—is 4.3. The existing discrepancy between theory and experiment must again be attributed to the fact that, for multivalent salts, the \(\sqrt{m}\)-region has not yet been reached.

2. Finally, as regards the absolute value of the constant \(K\) in the theoretical expression \(V_m = K\sqrt{m}\), it depends strongly on the temperature coefficient of the dielectric constant of the medium entering into the complete theoretical formula. The temperature coefficient of the dielectric constant of water, taken into account in the first approximation, is known, unfortunately, only with an accuracy of up to \(\pm 8\%\); hence, for the theoretical value of the heat of dilution, and also for the constant \(K\), fluctuations of \(\pm 30\%\) are obtained. For example, the theoretically expected heats of dilution at \(25^\circ\) lie between \(374\sqrt{m}\) and \(651\sqrt{m}\) (the dashed lines in Fig. 12 give the limits of the theoretical interval). Since the corresponding experimentally determined value for KCl gives \(376\sqrt{m}\), one can only say that the measured value does not lie outside the limits of the theoretical uncertainty.

Thus, for large dilutions, the experimental verification of the heats of dilution calculated according to Debye and Hückel leads in many respects to complete agreement with the theory. In other respects, these measurements, in view of the theoretical and experimental uncertainties, cannot be regarded as contradicting the theory.

The situation is less clear at somewhat higher concentrations. Here, in the theoretical formulae already

taken into account is the minimum distance to which two oppositely charged ions can approach. Gronwall, La Mer, and Sandved (20) were recently able to show that, in the region of the simpler phenomena of the depression of the freezing point, the theoretical data calculated with suitably chosen ion diameters agree well with the experimental results. On the same grounds one may, taking account of the sizes of the ions, conclude that the integral heats of dilution at higher concentrations should also no longer increase simply in proportion to the square root of the initial concentration. At what concentration the simple proportionality \(\sqrt[\,]{m}\) ceases, and how large the deviations from it are, depends entirely individually on the mean diameter of the given ion. Nevertheless, because of this, smaller heats of dilution would be obtained in comparison with the simple law \(\sqrt[\,]{m}\), but by no means negative ones. To explain the negative heats actually observed, it is therefore necessary to bring in still other possible explanations. Since the diameters mentioned refer to hydrated ions, and the hydrate shell must to some degree be subject to temperature influences, it is possible that the theory must take into account the temperature coefficient for the mean diameter (21). Thus, as Bjerrum (22)\(^1\) has shown, it is easy formally to explain the existence of negative heats of dilution. It is clear in advance that it is scarcely permissible at higher concentrations to carry out calculations simply with the dielectric constant of water and its temperature coefficient. Owing to this, additional terms could also appear, which might be invoked to explain the qualitative and quantitative deviations of the experimental heats of dilution from those calculated by simple theoretical formulas (16, 22). An important additional assumption, for explaining negative heats of dilution, was introduced by Nernst (23)\(^1\). Nernst proposed that, in the heat of dilution, there becomes notice-

\(^1\) See also the article by Semonchenko, “A Critique of the Electrostatic Theory of Solutions,” UFN, Vol. VIII, issue 5 (1928).

by them, besides the action of interionic forces, there is also the heat of dissociation of the undissociated part. He obtained, for example, for KCl at \(18^\circ\) up to \(2\%\), and for \(\mathrm{KNO_3}\) up to \(5\%\) of undissociated salt in a 0.1-normal solution.

These numbers are close in magnitude to the degrees of association given by Bjerrum (24). Nernst shows that between these degrees of association, calculated on the basis of heats of dilution, and certain peculiarities in the data on electrical conductivity and osmotic phenomena, a certain agreement can be found.

It may be said that there is a possibility of qualitatively understanding the course of the heats of dilution at higher concentrations from the assumption of a superposition of the heats of dissociation; in quantitative verification Nernst proceeds from certain approximate conceptions. Thus, moreover, the purely interionic effect at these concentrations can no longer be accurately calculated theoretically; he assumes, first, relying on measurements in LiCl, the proportionality \(\sqrt[3]{m}\) in the sense of the limiting law up to relatively high concentrations. In this connection it may be said that nothing of the sort can already be expected, owing to the influence of the finite sizes of the ions. Secondly, in calculating the heat of dissociation contained in the heat of dilution, whose dependence on concentration is given by the law of mass action \(Q(1-\alpha)=Kmf^2\alpha^2\), the activity coefficient \(f\) is assumed independent of concentration.

Although Nernst’s assumptions cannot be regarded as quantitatively proven, various data, including optical data, indicate that a rigorously carried out combination of the classical Arrhenius theory with the extended Debye–Hückel theory is passing beyond its initial theoretical stage.

2. Refractometric investigations.

From the very beginning, the theory of electrolyte solutions was based not only on thermodynamic and electrical criteria, but also on optical ones. Well known are those changes of colors which, under certain conditions, are undergone by...

many indicators, for example litmus, phenolphthalein. Such optical changes, visible to the naked eye, in many cases amount to the fact that, even upon simple dilution, undissociated molecules break up into free ions. It turns out, however, that strong electrolytes undergo upon dilution only a negligible change in color, i.e., in their absorption spectrum (27). With methods that are not especially precise these negligible changes may even be overlooked altogether. As is well known, Bjerrum, under the influence of these facts, came to the conviction that the group of strong electrolytes is practically dissociated entirely, and that the observed deviations, in the study of osmotic phenomena and electrical conductivity, from the data calculated according to the laws of ideal solutions can be reduced exclusively to the action of interionic forces. Together with the objections to this extreme theory already mentioned earlier, an important argument is also the fact that, with the aid of the most sensitive methods, it is sometimes possible to demonstrate a certain dependence of the optical properties of solutions on concentration. To this category belong, above all, the absorption measurements of Halban and Eisenbrand (11, 28) and the refractometric investigations of Fajans, Koner, and Geffcken (29). Of course, it must not be omitted from the outset that here the question concerns relatively high concentrations above 1 normal, at which the thermochemical data mentioned in the first part of my report are already theoretically inexplicable. In Halban’s investigations an important criterion for the existence of an undissociated part consisted in the following: suppose that both the undissociated molecules of the dissolved electrolyte and the free ions possess certain absorption spectra characteristic of them, and that the curves of the extinction coefficients of both limiting spectra intersect at some wavelength. If, upon further dilutions, an ever greater number of molecules dissociates into ions, then the absorption spectrum of the solution under investigation, referred to a mole, will pass from the spectrum of the molecules into the spectrum corresponding to the ions. The total extinction coefficient

will thus vary continuously for all wavelengths, with only one exception: where the two pure spectra would intersect upon dilution, no change in the molar extinction coefficient will be observed. Therefore the appearance of such exact multiple points of intersection in the course of dilution may, on the contrary, be regarded as strong confirmation of discrete molecular transformations. Halban and Eisenbrand believe that from their very accurate measurements of many strong electrolytes one may conclude, at least at medium concentrations and with a certain approximation, that such points of intersection exist. But the material available in this direction is still insufficient for a final decision of the question in the sense of the nonexistence of undissociated molecules in strong electrolytes.

Fig. 12.

Further optical confirmation of the assumption of the existence of an undissociated part is seen by Fajans in the results of refractometric measurements carried out by him with Koner and Geffcken (29). Although these measurements are closely connected with ideas concerning the deformation

atoms and ions, but let us point out at once that the results set forth can to a considerable extent be derived independently of this theoretical point of view and are obtained for the most part simply on the basis of the optical analogy between solutions of salts and acids.

For clearer understanding I shall first briefly relate some foundations of Fajans’ ideas on deformation1.

For this purpose we shall proceed from the values of molar refraction assigned to individual ions, as they are graphically represented in Fig. 13. These values of the molecular refraction \(R\) of free gaseous ions, obtained by Fajans and Joos (30), give a measure of the mobility of their electron shells in an electromagnetic field; the larger \(R\) is, the more strongly this shell is displaced. Comparing, for example, iodine with chlorine, we see that the molar refraction is the greater, the greater the diameter of the ion, and consequently the more freely the outer electrons are bound.

Fig. 13.

Fajans proceeds from the idea that the electron shell of anions is bound still more strongly by the approaching positive cation, and in this way explains why the molar refraction of an anion, for example Cl, becomes smaller on passing to HCl. It is clear here that the decrease in refraction is the greater, the more freely the electrons were bound, the greater the initial refraction of the anion itself was. For example, the refraction of the large free iodine ion decreases, on formation of hydrogen iodide, under the action of the strongly deforming and binding H-nucleus much more than the refraction of the smaller chlorine ion on passing to hydrogen chloride. In addition, the strengthening of the anion is the greater, the stronger the electric field of the active cation, i.e. the greater its positive charge and the smaller its radius.

In the latter case the cation can approach more closely the deformable anion. Experimental examples can also be cited for this case.

In contrast to this decrease in refraction upon deformation of the anion, the electron shell of the cation will, under the influence of the approaching negative anion, experience repulsion and weakening; the molar refraction of the cation will then increase somewhat, though on the whole less strongly. Naturally, this effect is again the more significant, the smaller in this case the active anion and the larger the passive cation.

The total changes in molar refraction shown in Fig. 13 in passing from free gaseous ions to the solid crystal show us that in reality both effects are superposed: the stronger negative effect and the usually weaker positive one. In large ions (iodine) there occurs, owing to strengthening, a strong decrease in refraction, which is the greater the smaller the cation. Conversely, in large cations (Rb), under the influence of small anions (F), the opposite positive effect becomes noticeable in the end, as a result of relaxation of the electrons of the cation; thus, for example, in KF and RbF as a whole a clear positive effect appears.

Let us return again to the discussion of the dependence of molar refraction on concentration in aqueous solutions of acids. Here we know in advance that, for example, $\mathrm{HClO_4}$ in a very dilute state (molar refraction $R=12.65$) is fully dissociated; in a 100% solution, i.e. in pure form ($R=13.20$), on the contrary, it is for the most part undissociated. Since the nucleus itself has no electrons and consequently no molar refraction, the effect given in Table 1 (column 5), corresponding to an increase in the molar refraction of hydrochloric acid by 0.6 units in passing from infinite dilution to the anhydrous acid, cannot be based solely on a distinctly negative partial effect of strengthening of the anion by the hydrogen nucleus. Rather, for aqueous solutions it is also necessary to take into account that each ion, before

Fig. 14.

The very smallest free hydrogen ion of all produces upon the surrounding water a strengthening action, thus diminishing refraction. To the freely hydrated H-ion there corresponds a negative refraction of 0.6 unit (column 2). If the H-nucleus is freed, at least in part, from its aqueous shell by binding with an anion

into a neutral molecule, then, owing to this, there occurs a positive change in the total refraction by the aforementioned 0.6 units, and this is added to the decrease, considered above, in the refraction of the anion as a result of its strengthening. Depending on whether the latter, corresponding to the strengthening of the anion, is numerically greater or less than the positive effect of 0.6 units upon dehydration of the H-nucleus, the total change will be either still positive or already negative. From the 5th column of Table I it is evident that the total change in refraction in aqueous solutions is strongly negative at increasing concentration, especially for the large, readily deformable halide ions. But in hydrochloric acid, which has a very slightly deformable anion, there is practically manifested only the positive effect from the water liberated by the H-ion.

The investigations of Fajans, Koner, and Geffcken, who used precise methods of measurement, show that in concentrated salt solutions as well there are observed small but distinct changes in molar refraction, as is evident, for example, from Fig. 14.

Experimentally, the refractive indices and densities of solutions above 2-normal were determined. The molar refractions of the dissolved salts calculated from these, after subtraction of the refraction of water, thus including the effect of hydration, were extrapolated to infinite dilution. The values obtained in this way proved, to within units of the second decimal place, to be composed quite additively of the separate values for free dissolved ions. In Fig. 14 are plotted the changes in the molar refraction of the dissolved salts at increasing concentrations relative to the values of the separate salts at infinite dilution, in hundredths. It is seen that, for example, for KF the molar refraction increases by 0.13 units; conversely, for NaJ it decreases by more than 0.3 units if one passes from infinite dilution to the concentration at saturation.

Let us compare this effect in salt solutions first with the already mentioned effect in acids and then with that which

Table I.

Dependence of the molar refraction of acid and salt solutions on concentration.

occurs in the formation of crystals from free ions. For this purpose let us first of all turn our attention to the 5th and 7th columns of Table I. In the 5th column are given the changes in the refraction of acids in passing from infinite dilution to the 100% acid; in the 7th column stand the values, quite corresponding to the first, of the changes for Na salts from infinite dilution to a 5-normal solution. From these two series of numbers it is clear that between both these changes of refraction there is a striking similarity in sign and in the relative changes of their magnitudes. Since for acids the cause of the change is obviously connected with the formation of undissociated molecules, Fajans draws from this the conclusion that the smaller differences in magnitude for Na salts as well, and naturally for all other electrolytes, can be reduced

to partial association into undissociated molecules. Hence it is clear that this is a purely qualitative conclusion by analogy, without taking into account the notions of deformation connected with it.

An indication in the same direction is also given by comparison of the effect in solutions of salts, Fig. 14, with the effect in the formation of crystals (Fig. 13). It is seen that, for example, NaJ and LiJ in both cases show a strong negative change (i.e., a decrease) of refraction, which occurs mainly from the strong passive stiffening of the large J-ion by the small K and Li ions. On the other hand, in KF a positive effect is observed in both cases.

These changes of refraction in the formation of a solid crystal and in naturally hydrated molecules show the same sequence; the similarity is especially manifested in other properties, for example in the relation between the lattice energy and the ionization energy of molecules in the vapor state. Likewise from comparisons of this kind Fajans concluded that the optical effects in solution are caused by the existence of such combinations of oppositely charged ions which are bound to one another directly, without an intermediate layer of water, and which we usually call the undissociated part.

One more objection would be possible—namely, that the change of refraction in salt solutions may be caused by interionic forces acting between ions through the water. Although such a possibility of explanation cannot be excluded in an entirely convincing manner, Fajans adduces a number of objections on the basis of which he regards this explanation as unlikely. One of these objections tends to show that the optical effects produced in solution by such ionic forces should be still smaller than the observational data. Let us, for this purpose, imagine the ions in a 5-normal solution of NaJ, in a first approximation, as distributed as in a crystal lattice; then the mean distance between lattices is equal to 5.5 Å, thus 1.7 times greater than in the solid crystal of NaJ (3.2 Å). Since, according to the experimental data, the decrease of the refraction of the anion, here the J-ion, occurs inversely pro-

proportional to the 4th power of the distance (31), then the decrease in refraction would be, at a 1.7-fold distance in vacuum, 8.3 times less than in the crystal; thus \(2.67 : 8.3 = 0.32\) (\(2.67\) is taken from Fig. 13).

This value, calculated in this way, must on other grounds be diminished still further, because in solution the attractive forces are strongly weakened by the water molecules situated between the ions, whereas in the crystal, naturally, nothing of the kind occurs. At the same time, of course, it is scarcely possible here to carry out calculations with the dielectric constant of pure water. But even if we calculate with the value \(D - 5\), estimated as too low, instead of \(8^\circ\), and it is clear that the exactly calculated value of the decrease in refraction must be much smaller, we obtain a fall of approximately \(-0.06\) units. This value, in comparison with the observed \(0.27\) (from Fig. 14), is much too small.

If we wished also to estimate the optical effect in the association of the hydration shell itself in the process connected with the dehydration of the ions, primarily the Na ion, then this could change the numerically small but positive part of the value \(-0.06\) only still further in the positive direction, and thus remove it still further from the measured value \(-0.27\). And Fajans thus comes to the conclusion that the effect in solutions cannot be caused by interionic forces acting through the water. As the probable explanation, therefore, there remains only the supposition that in concentrated solutions there exists, in appreciable quantities, an undissociated part in which there are no longer any water molecules between the ions. More precisely, of course, nothing can be said from this point of view about the nature of these molecules.

Combining the results of thermochemical and optical investigations, we arrive at the following conclusions: in very dilute solutions, measurements of heats of dilution indicate, in the main, the correctness of the Debye–Hückel theory; in other respects, for the present at least, until more exact theoretical data can be calculated, they

in no way argue against it. At high concentrations, deviations from the simple \(\sqrt{m}\) law occur, which are not unexpected. The assumption that, in solutions of strong electrolytes, there exist appreciable amounts of undissociated molecules has so far not been rigorously proved either by thermochemical or by optical criteria. But it seems that a number of facts speak in favor of this incomplete dissociation and thus provide the bridge—long sought and required on thermodynamic grounds—between strong and weak electrolytes.

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1. Cf. the article by K. Fajans, Uspekhi Fizich. Nauk, vol. V. ↩↩↩↩↩↩↩