LEWIS. — FREE ENERGY AND EQUILIBRIUM. 35 



or, since ^ = v Cq tt, where v is the valence of the ion, Cq the electricity 

 carried by a gram-molecule of a univalent ion, and tt the electromotive 



force, then RT^p U 



17 = In-^-f — , (5o) 



in which P differs from the electrolytic solution pressure of Nernst in 

 that it is at constant temperature the same, no matter what the solvent 

 may be in which the ions are dissolved, while the value of the Nernst 

 solution pressure holds good only for water solutions, r represents the 

 particular volume correction of the solvent. 



An interesting type of cell is one in which two similar electrodes are 

 in contact with solutions of an electrolyte containing the electrode ion in 

 two different solvents ; as, for example, zinc, zinc sulphate in water, zinc 

 sulphate in alcohol, zinc. When a current passes through this cell, the 

 total change consists in the transfer of zinc sulphate from one solvent to 

 another. The free energy change in a cell of this type may be found 

 from equation (6), modified as in equation (46), 



A = RT\n'^^,+ U, (56) 



where i\ and v/ are the molecular volumes of the positive and negative 

 ions respectively, in the first solvent ; v,, and v^', in the second solvent. 

 Now v/ =^ g Vi , where ^ is a whole number or a simple fraction ; also, 

 V2 = g V2- Therefore, 



^ = i?7^1n^V^+ U=2RTln'^^+ U. (57) 



If ra represents the number of gram-molecules transferred from one 

 solvent to the other when the quantity of electricity, v^o, passes through 

 the cell, then 



veoTT = 2 ;» i? T'ln-^' -f m U. 



Let m U ^= q, then 



. = ^i?rin^^ + ^. (58) 



From the equation of Helmholtz, 



and comparing (58) and (59) it is evident that 



ll = l^E\n'-^\ (60) 



a I V Co riVi 



