330 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



If the value of the potential sum *2nM may be experimentally determined 

 at different concentrations, the form of the function F(C S ) is empirically 



known. If the experimental values of DnJlf are correct, then the values 

 of F(C S ), as determined by different methods, must necessarily be in 



agreement. This result has been verified by Lewis and Randall, 10 * as 

 we shall see below. When mixtures of electrolytes are employed, the 

 expression for the potential obviously becomes a function of a greater 

 number of variables. In the case of a salt in the presence of another salt 

 with a common ion, the potential becomes a function of two variables; 

 and in that of a salt without a common ion, of three variables. We 

 should not expect, therefore, that the values obtained for the potential 

 sum in mixtures could be directly compared with those obtained for the 

 same electrolytes in a pure solvent. The methods which have been 

 adopted by investigators in this field, however, have consisted essentially 

 in expressing the potential of an electrolyte in a mixture as a function 

 of a single variable. This method consists in introducing a variable 

 defined by an equation of the form: 



(108) C m =F(C 1 , C 2 ,...). 



This function is given such a form that the value derived for the poten- 

 tial sum in the mixture, on introducing C m as variable, corresponds with 



that of a solution of the pure substance when the same variable is intro- 

 duced. If such a function exists, then we are led to conclude that the 

 potential sum for a given electrolyte in solution is dependent, not upon 

 the concentrations of the various substances involved, but upon some 

 other single parameter. 



The potential of an electrolyte as a function of its concentration may 

 be determined directly by means of the electromotive force of concentra- 

 tion cells. More indirectly, the potential may be obtained from the 

 vapor pressures of these solutions and from other related properties, such 

 as the freezing point, boiling point, etc. If the experimental determina- 

 tions are correct, the values of the potentials derived from the measure- 

 ment of these different properties must necessarily be in agreement with 

 one another. 



Lewis and Randall " have compared the available experimental data 

 for aqueous solutions in this way, and have found them to be in excellent 

 agreement. This implies the correctness of the methods employed in cal- 

 culating the various thermodynamic quantities, as well as the accuracy 



loa Lewis and Randall, J. Am. Chem. Soc. 43, 1112 (1921). 

 11 Idem, loc. cit. 



