ELECTROCHEMICAL THERMODYNAMICS 725 



which have arisen. Consequently, any further advance must 

 rest upon some extra-thermodynamical discovery, for example, 

 some empirical law. We have found that by a suitable mech- 

 anism, we may obtain the change in chemical potential of an 

 ionizing component from the study of a process represented by 



HCl(m2) -^HCl(wi). 



If we let niz vary and keep mi constant, at unit value, or at an 

 arbitrary standard value, then we can measure the change in 

 the quantity, ni' — ni", with the concentration. If this is done, 

 we find that as m2 approaches zero, ni" changes with the con- 

 centration at constant temperature according to the law 



m' - Ml" = 2Rt log — ' 



m2 



or, since both /xi' are 2 Rt log mi are fixed, 



Ml" = 2Rt log W2 + /, (40) 



where 7 is a function of t and p only. Since the electrical 

 process involves the transfer of both hydrogen and chloride ions, 

 the factor 2 occurs in the expression on the right. This is the 

 form of the expression derived from the perfect gas laws. It is, 

 therefore, the equivalent of van't Hoff's law for dilute electro- 

 lytes. This experimental discovery of van't Hoff, coupled with 

 the ionic theory of Arrhenius, marked the beginning of a very 

 extended experimental investigation of solutions of electrolytes. 

 As a result, it was soon found that, in the cases of solutions of 

 strong electrolytes, wide departures from this law occur. 



Without any addition to the fundamental thermodynamic 

 theory, we may numerically overcome this difficulty by insert- 

 ing a term which serves to measure the deviation from van't 

 Hoff's law. Thus, 



m" = 2Rt log Ui, -{■ I = Rt log a^aci + I, 



or 



n" = 2Rt log ma + 2Rt log y + I, (41) 



