698 RICE ART. L 



Therefore 



ri^dt + sda -Y QdV = Q 

 or 



da = — r]s dt — q dV, 



i.e., at constant temperature, 



da- 



i7 = - ^' 



Gibbs' own proof just carries through the same steps for the 

 "surface" of the solution, the component being the hydrogen ion 

 whose quantity in the electrolyte is supposed just to neutralize 

 the charge on the mercury (the apparent difficulty about the 

 sign has already been explained) and the chemical potential of 

 the ion is supposed to alter by the amount /3 6F where 5F is the 

 alteration of the electric potential of the solution and /3 the 

 reciprocal of the electrochemical equivalent a. Let us turn our 

 attention for a moment to this latter assumption. 



69. Ouggenheim's Electrochemical Potential of an Ion 



If one conceives an ion to be transferred from one solution to 

 another (in both of which it is an actual component) across the 

 interface, we can easily prove in the same manner as that in 

 which Gibbs derives his equations [687], [688], that 



V + om' = V" + afx", 



where the electrochemical equivalent a is a positive quantity 

 for cations and negative for anions. We can write this in the 

 form 



where /3 is the reciprocal of a, the "chemo-electrical" equivalent 

 as we might call it. Actually it is the quantity n + fiV which 

 is the physically important and significant "intensity factor" in 

 the expression for the energy transferred from one phase to the 



