ELECTROCHEMICAL THERMODYNAMICS 721 



potential, rff, of a phase of variable composition is given by 



d^ = — r]dt + vdp + nidni + H2dn2 . . . + Undun, (28) 



an equation which is equivalent to equation [92] (Gibbs, I, 87) 

 if ni, n2, etc., are the numbers of mols of the components, 

 respectively, and m, ^2, etc., are the partial derivatives of ^ 

 with respect to ni, n2, etc. 

 From this we immediately find that, at constant composition, 



11 = - - (-> 



and 



'^l = .. (30) 



dp 



Further, from the fundamental equation relating f to Xt the 

 heat content function, we obtain 



( = x-tv = x + tf\. (31) 



From equation (17) we obtain for a reversible cell at constant 

 temperature and pressure the equation 



d^ = ±Ede. (32) 



As long as the various phases of the cell are sufficiently large so 

 that their compositions will not be appreciably altered by the 

 flow of a finite quantity of electricity e, then E will remain 

 independent of e, and equation (32) may be integrated. Let us 

 choose the path of integration to correspond with a chemical 

 equation involving a flow of N faradays. Let us denote the 

 faraday by F and employ the subscripts 1 and 2 to refer to the 

 states of the system before and after the process represented by 

 the given chemical equation. Further, let the symbol A denote 

 the increase in the value of a function during the given finite 

 process. We obtain 



Ar = r2 - n = r ^f = ± j^^' Ede = ± nef 



(33) 



