397 



for the equilibrium between the electrons in the metal and in the 

 coexisting electrol^'te is: 



(i"'sh=«-''^'s=(msK^„-FVj, (1) 



in which(Ho,y and(MöJ indicate the molecular thermodynamic 



potentials of the electrons in the metal and in the coexisting elec- 

 trolyte for the case that the potential difference = 0, Vs and Vj, 

 being the electric potentials of the metal and of the electrolyte, so 

 that F Fs and F V i denote the molecular electrical potentials of 

 the electrons in these two phases. 



It now follows from this equation that when we omit the index 



Ar=0: 



r.s-Fx=A:=- '' (2) 



r 



As it was our purpose to derive an equation for the potential 

 difference in which not only the concentration of the electrons in 

 the electrolyte occurs, l)ut also that in the metal, the splitting up 

 of the molecular thermodynamic potential into a concentration-free 

 term and into a concentration member, viz. : 



(i = n'^RTlnC (3) 



has been applied both to the electron in the electrolyte and to the 

 electron in the metal. We then get : 



L = -^ ^^ . ... (4) 



F 



If we now put : 

 we get : 



^^-^'o^^RTlnK', (5) 



L^^lu^p^ . (6) 



F {6l) 



the electron equation, derived by Smits and Aten, for the potential 

 difference. 



When we now again return to equation (5), and add R TlnSs to 

 the two members, we get : 



lü^ + RTln {ds) = RT In K'e {(^s) + (^'^L (7) 



o 



or 



RTlnK'fj^{as) = (Ji6g~(i'üf^ (8) 



We get for the potential difference of 2 different melals: 



