A. K. Kalle.

Determination of the Vapor Pressure of Certain Acids of the Fatty Series by the Electrical Conductivity Method

(An experimental study from the physicochemical laboratory of the Tomsk Technological Institute).

(With 7 drawings and diagrams appended to the article).

INTRODUCTION. To determine the pressure of saturated vapors, as is known, there exist three principal methods: the static method, the dynamic method, and the method based on the study of isotherms. The first two methods make it possible to determine both comparatively small and large pressures of saturated vapors; the last, however, gives accurate figures only at comparatively large values of the vapor pressure of the substance under investigation. However, at very small vapor pressure, reaching only a few millimeters of mercury, and especially at fractional parts thereof, all these methods for the most part give the most contradictory data. Therefore, for determining small vapor pressures, many so-called “indirect” methods of determination have been proposed. Among such methods one must mention the classical method of Pfaundler (1), given by him especially for determining the vapor pressure of mercury; it is based on the fact that a current of air passing over mercury carries with it mercury vapor, which is caught in a U-shaped vessel filled with silver leaf. The increase in weight of this vessel, equal to \(q\), determines the weight of mercury in the passed volume of air \(V_g\), determined with the aid of a gas meter. Applying the laws of Boyle–Mariotte and Gay-Lussac, and denoting by \(t_1\) the temperature of the gas in the gas meter, the total pressure of the gases by \(P\), and the pressure of water vapor at temperature \(t_0\) by \(B\), Pfaundler obtained the following formula, determining the vapor pressure \(p\) of mercury, expressed in millimeters of mercury:

\[ p = 85185 q \cdot \frac{(t + zt_1) P}{V_g (P - B)} . \]

In the present work I had in view determining the vapor pressure of saturated vapors of formic, acetic, and propionic acids in such a way that, knowing the vapor pressure of any one acid, known on the basis of reliable literature data—for example, acetic acid at \(18^\circ\)—one could obtain it also for other temperatures, without using the frequently only approximately correct laws of Boyle and Gay-Lussac. Moreover, with regard to the acids selected for study, I could apply Dalton’s law (14), which states that “the vapor pressures of saturated vapors are the same for all liquids equally distant from the normal boiling point”; therefore, knowing the vapor pressure at a definite temperature for any one acid, it would be possible to determine it for other acids as well. Generally speaking, having investigated the function \(p = f(t)\) for one acid, one cannot, of course, determine this dependence for any other; but, in particular, as the investigations of Schmidt (13) have shown, for six acids—formic, acetic, propionic, normal and iso-butyric, and iso-valeric acids—Dalton’s law is quite applicable.

Therefore, in the present work I made use of the circumstance that, for the acids taken, the amounts carried over with a constant current of air are proportional to their vapor pressures.

To determine the amount of acids carried over, I used the determination of changes in the electrical conductivity of water poured into an absorption vessel.

This method made it possible to determine the amount of acids carried over without removing the absorption vessel from the thermostat, at definite intervals of time, and thus to introduce a repeated check of the vapor pressure at a given temperature. A diagram of the apparatus is given in Fig. I.

Explanations for the diagram:

A — water-supply tap.
B — mercury manometer of constant level.
C — column and tube (1 meter long) with soda lime.
D — water pump.
E — bottle for water drainage with a constant level.
F — manometer with a tap.
G — vessel for equalizing pressure.
H₁ and H₂ — bottles with H₂SO₄ for removal of moisture.
I — manometer with xylol for equalizing pressure.
K — mercury manometer with mirror reading.
L — vessel for the liquid under investigation.
M — apparatus for determining electrical conductivity.
N — clamp for admitting the air current into vessels L and M.

Procedure

First of all, the same air-current pressure was always established; this was monitored by means of manometers. Then the liquid under investigation was poured into vessel L through a funnel with a drawn-out tube, in such a way as not to wet the walls lying above the level of the liquid; distilled water was poured into vessel M, its \(k\)—specific electrical conductivity—was determined, and, marking with a stopwatch the beginning of passage of the air current, clamp H was opened; after 40 minutes this clamp was closed in order to determine the change in electrical conductivity in vessel M, and thereafter this determination was repeated every 10 minutes. The electrical conductivity was determined in the usual way with the aid of a previously calibrated Wheatstone bridge and an accurate rheostat by Köhler; as the source of alternating current, a small inductor with a high tone was used. As the vessel for determining electrical conductivity, vessel M (see Fig. I), made by me for this work, was used. Two such vessels were used, of which one—“A”—had a capacity equal to 0.1404, and the other—“B”—equal to 0.07775; the electrodes in these vessels had been previously platinized.

Construction of the electrical thermoregulator

As an electrical thermoregulator, I devised the following device, which made it possible to maintain the temperature in the thermostat with an accuracy up to 0.01°; this thermoregulator can easily be made by anyone using simple means, provided that the temperature required in the thermostat does not differ very much from room temperature, i.e. within approximately 16°—25°; of course, when water cooling is used, it is also suitable for temperatures down to 10°. The arrangement of this thermoregulator is shown in Fig. II. An ordinary toluene regulator R (without upper branches) is connected through mercury

with one of the wires leading to the carbon lamp L, immersed in the thermostat; the other wire from the lamp goes to the platinum pin \(t\), set at such a height that, when the temperature in the thermostat rose to a definite point, a short circuit occurred between the pin \(t\) and the mercury of the regulator, and practically no current any longer passed through the lamp; the electric current in this case had to be taken through a lamp rheostat (4–5 lamps); on the other hand, to avoid strong spark discharges between the pin \(t\) and the mercury, both wires from the lamp were connected to a condenser, and a layer of paraffin oil was poured onto the mercury. When the temperature in the thermostat fell below the specified value, the contact between the mercury and the pin \(t\) was broken, and then the lamp L was again lit automatically.

Determination of the relationship between concentration and the specific electrical conductivity of the acids taken.

In order to pass from the observed specific electrical conductivities to concentrations, it was most convenient to obtain the graphical dependence of these quantities at a given temperature. In view of the fact that the vessel for determining electrical conductivity was always kept at \(18.00^\circ\), it was sufficient to determine this dependence only at this temperature.

1) Formic acid.

For formic acid there are observations by Otten (2) for comparatively concentrated solutions from 4.94% to 100%, at \(18^\circ\); then, for more dilute solutions, observations by Jahn and Schröder (15), and, finally, determinations by W. Ostwald (3) at \(25^\circ\), made by him for determining the dissociation constant of this acid. With the aim of checking the proper operation of my apparatus, I made several determinations of the specific electrical conductivity of HCOOH solutions at \(18^\circ\) and \(25^\circ\). These data are placed in Table I.

Table I.

HCOOH solutions. The capacity of the vessel is equal to 0.2840.

Ostwald (3) gives, at 25°, the dissociation constant as \(2.05 \cdot 10^{-4}\). By plotting my data and Otten’s on the diagram (see Fig. III), it was possible to determine graphically, from the given specific electrical conductivity, the concentration of formic acid obtained.

2) Acetic acid.

To determine the concentration of \(\mathrm{CH_3COOH}\) from its specific electrical conductivity at 18°, I used the work of Kohlrausch (12), which gave, at this temperature, a series of determinations of the equivalent electrical conductivity. Using the formula \(K = \lambda \eta\), where \(\eta\) determines the number of gram-equivalents in \(1\ \mathrm{cm.^3}\) of solution, I obtained the following table, on the basis of which the diagram was constructed (see Fig. IV).

Table II. \(\mathrm{CH_3COOH}\) at 18°.

3) \(\mathrm{C_2H_5—COOH}\)—propionic acid.

The relationship between specific electrical conductivity and concentration for this acid is given in the work of Jahn (4), whence \(K_{18}\,10^4\) was also calculated.

Table III. \(\mathrm{C_2H_5COOH}\) at 18°.

Here \(Y\) denotes the dilution in liters; these data are plotted on the diagram in the same Fig. IV.

In addition, I carried out a preliminary experiment: whether the electrical conductivity of the acid in the absorption vessel changes when air is blown through it. The result, as is seen from Table IV, was negative. The acid was—\(\mathrm{CH_3COOH}\), 10% (approx.).

Table IV.

To obtain identical conditions in the different experiments, it was necessary that the level of the liquid under investigation in vessel L, where the substance evaporates, remain constant. To introduce a correction for the liquid level, two experiments with acetic acid at 15° were performed; in the second experiment, 0.5439 g more acetic acid was taken than in the first. The electrical conductivity of the water (specific) was equal to \(6 \cdot 10^{-6}\). The figures in the table are with corrections.

I experiment. \(\mathrm{CH_3COOH}\) at 15°. Vessel “A.”

Table V.

II experiment. \(\mathrm{CH_3COOH}\) at 15°. Acid greater by 0.5439 g.

Table VI.

From these two experiments it may be concluded that, when the amount of CH$_3$COOH was increased by 0.5434 g, its percentage content in the absorption apparatus increased on average by 0.008%. In the subsequent experiments this correction was introduced to the level, but its magnitude was still smaller, since in experiments lasting even several hours the acids usually evaporated by no more than 0.1 g.

III experiment. CH$_3$COOH at 10°.

Table VII.

IV experiment. CH$_3$COOH at 18°.

Table VIII.

V experiment. CH$_3$COOH at 22°.

Table IX.

VI experiment. \(\mathrm{CH_3COOH}\) at \(0^\circ\) (the same for the liquid and solid acid).

Table X.

In Fig. V the dependence between the time of blowing air through and the concentration of the acid obtained in the absorption apparatus is given graphically. On the basis of the principles indicated in the introduction, and also taking, as the mean from the observations of Ramsay (6), Kahlbaum (11), Richardson (9), and Schmidt (10), the vapor pressure of \(\mathrm{CH_3COOH}\) at \(18^\circ\) to be equal to 10 millimeters of mercury, I obtained the data given in Table XI.

Table XI. \(\mathrm{CH_3COOH}\).

At a single glance at Fig. V, representing the results of the first six experiments carried out with vessel “A,” one is immediately compelled to note that the increase in concentration in the absorption apparatus over equal intervals of time is not quite the same, as it ought to have been, but increases all the time. This is fully explained by the fact that tube T (Fig. I) inside is little by little covered with the acid evaporating from L; consequently the evaporating surface delivering acid to the absorption apparatus also gradually increases, and this influence is especially pronounced for the most volatile acid and at high temperature. In Fig. VI the data obtained for \(\mathrm{CH_3COOH}\) are plotted graphically, and there are also entered the values obtained by Landolt (8) and by others of the authors mentioned above. The above-mentioned harmful influence of tube T was almost eliminated by using vessel “B,” of smaller capacity, into which it was sufficient for the determinations to pour 10 cm\(^3\) of water (50 cm\(^3\) were poured into vessel “A”), so that the change of concentration in it was much more significant and the influence of tube T had little importance. In the three experiments of mine cited below, the determinations were already carried out with vessel “B” and, as is seen from Fig. VII, here the increase in concentration already proceeded proportionally to time.

VII experiment. HCOOH at 18°.

Table XII.

VIII experiment. CH₃COOH at 18°.

Table XIII.

IX experiment. C₂H₅COOH at 18°.

Table XIV.

To the article by A. K. Kalbe, “Determination of the Vapor Pressure of Certain Acids of the Fatty Series by the Electrical Conductivity Method.”

Fig. 1.

To the article by A. K. Kalle: “Determination of the vapor pressure of certain acids of the fatty series by the electrical-conductivity method”

![Diagram with labels: “To condenser,” “KOH solution,” “Toluene,” “Part of the thermostat with electric thermoregulator.”]

Fig. 2.

Part of the thermostat with an electric thermoregulator.

Fig. 3.

![Graph labeled “oil,” with vertical scale 0 to 5.0 and horizontal scale \(K \cdot 10^4\).]

To A. K. Kal’ts’s article, “Determination of the elasticity of the vapors of certain acids of the fatty series by the electrical-conductivity method.”

Fig. 4.

\(CH_3COOH\) at various temperatures.

Vertical axis: percentage content.

Curve labels: \(22^\circ\), \(18^\circ\), \(15^\circ\), \(10^\circ\), \(0^\circ\).

Fig. 5.

To A. K. Kale’s article: “Determination of the vapor pressure of certain acids of the fatty-acid series by the electrical-conductivity method”

Fig. 6.

Fig. 7.

On the basis of these data, we obtain for the vapor pressure of HCOOH at \(18^\circ\) the value 33 millimeters of mercury. Landolt’s observations (8) give 31.4 mm at \(20^\circ\), and Schmidt’s (10), 33 mm. Similarly, for propionic acid we obtain the pressure of its saturated vapors at \(18^\circ\) equal to 1.9 mm. Schmidt’s observations (10) give 1.5 mm at \(10^\circ\), and 3.0 mm at \(20^\circ\).

In conclusion, some applications of this method may be indicated. For example, by filling vessel M with a solution of \(\mathrm{Ba(OH)_2}\) and passing through it a uniform current of room air, one can readily determine the \(\mathrm{CO_2}\) content in it from the change in electrical conductivity; the sensitivity of this method is so great that the combustion of a single Bunsen burner is already clearly reflected in the change in electrical conductivity. Obviously, the same method is also applicable to the determination, in general, of acidic gases such as \(\mathrm{SO_2}\), HCN, etc.

On the other hand, using air with a definite \(\mathrm{CO_2}\) content as the titrating medium, this method may conversely be applied to the peculiar electrometric titration of alkalis.

Conclusions

1. A method has been developed for determining the vapor pressure of volatile electrolytes, suitable for determining very small pressures.

2. The suitability of this method has been tested in the determination of the vapor pressure of formic and propionic acids at \(18^\circ\), as well as of acetic acid at \(0^\circ\), \(10^\circ\), \(15^\circ\), and \(22^\circ\); at the same time, the dissociation constant of formic acid at \(18^\circ\) was verified.

3. A simple method is indicated for constructing an electrical thermoregulator for maintaining, with an accuracy of up to \(0.01^\circ\), a specified temperature in a thermostat, differing only slightly from room temperature.