ΟΙ.

Log.

As the variation in the values of the simple distribution ratio in the foregoing table indicates, the benzoic acid exists partially as associated molecules in the benzene phase. The decrease in the value of 8 with increase in concentration is linear, as is shown by the curve in Fig. 1, where the values of logc × 103 are plotted

on the axis of abscissæ against the values of log× 102 on the axis of ordinates. With the exception of the values for the initial and final concentrations, all the points lie on a straight line.

In order to determine the degree of association, x, of the normal benzoic acid molecules in benzene, measurements were made of the freezing-point depressions of benzene produced by the same concentrations of benzoic acid employed in the foregoing distribution experiments. During the process of freezing, the solutions of benzoic acid were stirred by means of a platinumiridium stirrer operated by an electromagnet.14 The results of the freezing-point depression measurements are recorded in Table II.

14 Beckmann, E., Zeitschr. physik. Chem., 44, 174 (1903).

The values for the observed molar weight, given in the foregoing table, agree excellently with those determined by Beck

The concentration, z, of the undissociated molecules of benzoic acid in the aqueous phase may now be calculated by means of equation (19), from the data recorded in Tables I and II. Table III contains the values of z calculated by means of this equation. In the vertical columns, with the exception of the first, are represented the values of z which correspond to that total concentration, c, indicated by the numerals running horizontally along the

13

Beckmann, E., Zeitschr. physik. Chem., 2, 715∙ (1888).

VOL. CLXXX, No. 1075-6

top of the table. The numerals in the first vertical column represent the concentrations, c', with which a particular concentration, c, has been combined in order to calculate z. The values given for z in Table III have all been multiplied by 103. The numerals 2-10, correspond to those employed in Table I.

If the relation between the undissociated molecules in the aqueous phase and the normal and associated molecules in the benzene phase is correctly expressed by equation (19), it follows that the values for z in each vertical column should be constant. Although the values for z in the different columns of Table III vary slightly, they are sufficiently constant to substantiate the validity of the equation. It should be pointed out that small variations in the values for c and b, as determined by analysis, produce relatively large changes in the values calculated for 2. It is evident, therefore, that in order to obtain even approximately correct values for z it is necessary that c and b be determined with the highest possible degree of accuracy.

Values for the coefficient of the distribution of the normal molecules of benzoic acid between water and benzene at 6° are recorded in Table IV.

As is to be expected, with the exception of the values for the third and fourth concentrations, the mean values for the coefficient of the distribution of benzoic acid between water and benzene are fairly constant. By taking the average of the mean values

in the foregoing table, the value 1.134 is obtained for the coefficient of distribution,

In Table V are given the values of the dissociation constant of benzoic acid, which have been calculated by means of Ostwald's dilution law from the values of c and a contained in Tables I and III. All the values in this table have been multiplied by 105.

It will be seen that the calculated values for k in each column of Table V vary slightly and irregularly about the mean value. By taking the average of the means, the value 7.2 × 105 is obtained for the dissociation constant of benzoic acid in water at 6°. By means of electrical conductivity measurements, White and Jones 16 have found that the dissociation constant of benzoic acid in water is 6.2 × 10-5 at 0°, and 6.7 × 105 at 15.8°; while Salm "obtained the value 7.2 × 105 at 18° by a colorimetric method. It is evident, therefore, that, while the method described in this paper gives a value for the dissociation constant which is somewhat higher than that obtained by the conductivity method, the agreement between the values obtained by the two methods is sufficiently close to demonstrate that approximate values for the dissociation constant may be calculated from the distribution data by means of the formula derived in this paper. Although the distribution method for the determination of the dissociation

19

17

'White, G. F., and H. C. Jones, Amer. Chem. Journ., 44, 159 (1910).

Salm, E., Zeitschr. physik.Chem., 63, 83 (1908).

constant of electrolytes cannot compete with the conductivity method in most cases, on account of the relatively large experimental errors involved and the high degree of accuracy necessary, its use is suggested in those cases where the value of the dissociation constant of an electrolyte, as determined by the conductivity method, is found to undergo considerable variation with change in concentration.

SUMMARY.

1. A general formula has been developed for the calculation of the concentration of the undissociated molecules of an electrolyte in water by means of data obtained by the measurement of the distribution of the electrolyte between water and a second liquid phase. The formula takes into consideration the possibility of association of the electrolyte in the second liquid phase.

2. In order to test the validity of the formula, measurements of the distribution of benzoic acid between water and benzene have been carried out at 6°, and, from the data obtained, the concentration of the undissociated molecules of benzoic acid in the aqueous phase has been calculated. From these values, a mean value, 7.21 X 10-5, has been obtained for the dissociation constant of benzoic acid in water at 6°.

3. Although the foregoing value for the dissociation constant of benzoic acid in water is somewhat higher than that obtained by the conductivity method, the use of the distribution method for obtaining an approximate value for the dissociation constant of an electrolyte, in those cases where the value as determined by the conductivity method varies considerably with concentration, is suggested.

DEPARTMENT OF CHEMISTRY,

Swarthmore College,

Swarthmore, Pa.,

May 24, 1915.