THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 343 



centrations. It has been shown that this form of the curve is general and 

 that in solutions of non-aqueous solvents the deviations from Ghosh's 

 equation are much greater than in water, and therefore are far in excess 

 of any possible experimental error. 25 



Ghosh has likewise treated other properties of electrolytic solutions. 

 In view of the fact that his theory fails to account satisfactorily for the 

 relation between the conductance and the concentration of electrolytic 

 solutions, it is unnecessary to consider these properties here. 



c. Milner's Theory. Of the various theories proposed to account for 

 the properties of electrolytic solutions, that of Milner is perhaps the most 

 noteworthy, since it is comparatively free from arbitrary assumptions. 

 Milner 26 has calculated the virial for a system of positively and nega- 

 tively charged particles by statistical methods, and therefrom has calcu- 

 lated the influence of the ions on the freezing point of solutions. 26 * He 

 found, in effect, that the virial of a system of charged particles has a 

 finite value, from which the osmotic pressure of the solution may be 

 deduced, and therefrom the freezing point. 



In the following table are given values of the van't Hoff factor i for 

 potassium chloride in water calculated by Milner, together with the values 

 of i determined by Adams directly from freezing point measurements. 



TABLE CXXXIV. 



COMPARISON OF MILNER'S VALUES OP i, WITH THOSE EXPERIMENTALLY 



DETERMINED. 



C 0.005 0.01 0.02 0.05 0.1 



?: Milner 1.962 1.947 1.926 1.885 1.838 



*Adams 1.961 1.943 1.922 1.888 1.861 



As may be seen from the table, the calculated values of i are in excel- 

 lent agreement with those determined by Adams. Milner's values are 

 based on the assumption that the electrolyte is completely ionized, the 

 observed freezing point depression being due entirely to the interaction 

 of the ions. If an ionization value were assumed corresponding to that 

 given by the ratio A/A , the values of i, as calculated by Milner, would 

 be lower than those observed. Milner has accordingly suggested that, 

 within these ranges of concentration, strong electrolytes are completely 

 ionized. If this is so, the change in the conductance of electrolytes must 



Kraus, loc. cit. 



Milner, Phil. Mag. 23, 551 (1912) ; ibid., 25, 742 (1913). 



*" Compare, Cavanagh, Phil. Mag. 43, 606 (1922). 



