THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 329 



tions of the constituent electrolytes remains undisclosed, the form of the 

 function may be determined. At the same time, the values of the poten- 

 tials of different electrolytes may be compared and relationships brought 

 to light which are of practical importance, even though their theoretical 

 significance may not be apparent. Our knowledge of electrolytes from 

 this point of view is restricted to aqueous solutions. In view of the fact 

 that many properties of electrolytic solutions are greatly modified in 

 solvents of lower dielectric constant, and since the similarity in the be- 

 havior of dilute aqueous solutions of different electrolytes is not often 

 found in other solvents, any generalization of the results obtained in 

 aqueous solutions must be made with caution. 



The Thermodynamic Method. The significance of the results ob- 

 tained from an examination of the thermodynamic properties of electro- 

 lytic solutions will be better understood if treated without reference to 

 detailed methods. Let us assume that we have a solution in which the 

 following reaction takes place: 



Mi + Mi +-= NI'^I' + **'**' + '" 

 The condition for equilibrium in such a solution is: 



(104) SnAf = Sn'JIf' . 



The potential sum for the constituents on either side of the reaction equa- 

 tion may be expressed by a function of the form: 



(105) 2nM - F(C 1} C 2) . . .C/AV ), 



where C 1} C 2 ,. . .C/A',. . . are. independent variables. If any of these 

 variables are not independent, a relation will evidently exist among them 

 by means of which they may be eliminated. So long as we are dealing 

 with a solution of a single electrolyte, the potential may obviously be 

 expressed as a function of the concentrations of the ions and the un-ion- 

 ized fraction; that is, we have: 



(106) 



Since a relation exists between the concentrations C + , C~ and C 7 it is 

 obvious that one of these variables is not independent. Since, in general, 

 it is not possible to determine the concentration of the ions and of the 

 un-ionized fraction in a solution of an electrolyte, the total concentration 

 of the salt may equally well be employed for practical purposes, in which 

 case: 



(107) 



