for the degree of dissociation, obtained by conductivity or freezing-point methods, are employed. In the present communication a general formula has been developed by means of which it is possible to calculate the ionic concentrations of an electrolyte in aqueous solution from data obtained from the measurement of the distribution of the electrolyte between water and some second liquid phase. In the development of this formula it has been assumed that in aqueous solution the electrolyte obeys the dilution law, and that, in accordance with Nernst,11 there is a constant distribution coefficient for the undissociated molecules of the electrolyte between the two liquid phases. THEORETICAL. When a substance is shaken up with two non-miscible solvents it is distributed between them in a definite manner 12 which depends upon its solubility in each of the solvents. The distribution coefficient, the ratio in which the solute is distributed between the two phases, depends not only upon the solubility of the solute, however, but also upon whether the molecular complexity of the solute is the same in the two solvents. When the molecular complexity is the same in both solvents the distribution coefficient is constant for a given temperature; but when the solute has a different molecular complexity in the two phases the simple distribution ratio varies with the concentration at a constant temperature. The symbols employed in the remainder of the paper are as follows: C, the total concentration of the solute in the aqueous phase in normal moles per litre; b, the total concentration of the solute in the second phase in normal moles per litre; a, the degree of dissociation of the solute in the aqueous phase; x, the degree of association of the solute in the second phase; n, the complexity of the associated molecules in the second phase; ô, the ratio, q, i.e., the simple distribution ratio; the two phases; Berthelot, M., and E. Jungfleisch, Ann. chim. Phys. [4], 24, 396 (1872); Jakowkin, A. A., Zeitschr. physik. Chem., 18, 585 (1895); Ostwald, W., Lehrbuch, 2. Aufl., 1, 811. 12 K2, the constant governing the equilibrium existing between the normal and associated molecules in the second phase, and k, the dissociation constant of the simple molecules in the aqueous phase. If, at a constant temperature, a binary electrolyte is shaken up with water and a second solvent in which it dissolves with the formation of simple and associated molecules, then, after a short time, the following equilibria will exist: (1) between the ions of the electrolyte and the un dissociated molecules in the aqueous phase; (2) between the normal molecules in the aqueous phase and the normal molecules in the second liquid phase; (3) between the normal and associated molecules in the second liquid phase. The first of these equilibria is governed by Ostwald's dilution law: anion concentration X cathion concentration a2c2 k (1) concentration of the undissociated molecules (1 – abc The second equilibrium is governed by the equation, conc. of normal molecules in aqueous phase c(1 – a) Ki= conc. of normal molecules in second phase b(1 – x) The third equilibrium is governed by the equation, conc. of normal molecules in second phase b(I – x) K2= (3) conc. of associated molecules in second phase bx (2) Let the concentration of the undissociated molecules in the aqueous phase be z, i.e., C(I – a) = 2. Then from equation (2) it follows that Kib(1 – x), (4) and by combining equations (3) and (4) = = K,K:"\ 6x = Kijbx. (5) On multiplying equation (4) by K, and equation (5) by Kį, we obtain K32 = K K3[6(1 – x)], (6) and Kız = K KsVbx · (7) [ Z z' = K (10) By dividing equation (9) by equation (10), we obtain 6(1 – x) + 1 bx (11) b'(1 – x') + 1 b'x' Therefore, B'(1 – x') + 1 b'x' (12) b(1 – x) + bx On putting b'(1 – 2') + 1 b'z' p= (13) 6(1 – x) + vox equation (12) becomes (14) Since in the aqueous phase the concentration of the anions or cathions is equal to the total concentration minus the concentration of the undissociated molecules, i.e., ac = ( - ((1 - a) = (-2, equation (1) may be written (0 – 2) (c' – 2') (15) z' = zp. On substituting in equation (16) the value given for z' in equation (14), we obtain (C--)_ (c' – zp), (17) Vap whence : d'-CVP. (18) On substituting in equation (18) the value given in equation (13) for p, we obtain b'(1 – x') + b'x' (19) b(1 – x) +Vox -V By means of the general equation (19) the concentration of the undissociated molecules in the aqueous phase may be calculated, even when the solute is present in the second phase as a mixture of normal and associated molecules. When association of the normal molecules in the second phase does not incur, i.e., when x = 0, equation (19) reduces to If, on the other hand, the association of the molecules in the second phase is complete, i.e., if x = 1, equation (19) becomes It is evident from equation (19) that, when the solute is present in the second liquid phase as a mixture of normal and associated molecules, it is necessary that the degree of association, x, of the normal molecules be known, in order to calculate the concentration, 2, of the undissociated molecules in the aqueous phase. The degree of association of the normal molecules in the second liquid phase may be obtained by means of measurements of the freezing-point lowering produced in the second solvent by the solute. The degree of association is given by the equation, M. м. (22) M.(1 - 1) where Mo represents the molar weight calculated from the observed freezing-point lowering, and Mt the molar weight calculated from the chemical formula of the solute. EXPERIMENTAL VERIFICATION OF EQUATION (19). In order to test the validity of equation (19), determinations have been made of the distribution of benzoic acid between water and benzene. Since it has been shown,13 in the case of some electrolytes, that the distribution ratio varies with temperature, the distribution of benzoic acid has been measured at 6 +0.1°, a temperature which lies very close to the temperature at which the x values for benzoic acid in benzene have been determined by the freezing-point method. Thiophene free benzene (Kahlbaum zur Analyse) was used in the distribution experiments. The benzene solutions of benzoic acid were mixed with an equal volume of “conductivity water, and the mixture placed in suitable bottles, which were agitated in a thermostat for several hours, at the end of which time the bottles were removed from the agitation apparatus and allowed to stand in the thermostat until complete separation of the two liquid phases had taken place. Portions of the aqueous and benzene layers were then removed and analyzed with standard sodium hydroxide solution which was prepared from pure metallic sodium. Table I gives the results of the distribution measurements made with benzoic acid at 6o. TABLE I. 15 Hantzsch, A., and A. Vagt, Zeitschr. physik. Chem., 38, 705 (1901). |