34 PROCEEDINGS OF THE AMERICAN ACADEMY. 



data are at present sufficiently complete to permit the testing of equa- 

 tion (54). 



V. Application to Electro-Chemistrt. 



Since the electrical work of a reversible cell is equal to the change of 

 free energy of the process taking place in the cell, the calculation of 

 electromotive force in many cases is possible by means of the general 

 equation (6). 



Tiie general formula for the electromotive force of a concentration cell 

 has already been given on page 29. 



Let us consider next the subject of a single potential difference be- 

 tween a metal and an electrolyte containing the ions of that metal. If 

 ^1 be the free energy of one gram-molecule of the metal, and '^o that of 

 one gram-molecule of its ions, then the electrical work in the electrolytic 

 solution of one gram-molecule is 



Now for '^2 we obtain from equation (5), modified according to page 27, 



^, = -R T\nr(v, - h) - T r^-^dT+ l),T + Wi,, 



where r is the correction for the particular solvent in which the ions are 

 dissolved, b^ the correction for the ions themselves, which will always be 

 negligible, c^.^ and |^2 are independent of the nature of the particular 

 solvent. Win is the internal energy of the ions, and if we represent by 

 5Ei the internal energy in the electrode, and by Uihe change of internal 

 energy in electrolytic solution, U= Wii — Wi2, and — SIo ™ay be re- 

 placed by U ■}- W.I- Then since ^i, 2Ei, c^^, fj2j are constants at con- 

 stant temperature, 



A= C-{- (RTlnrv.) + U, 



where C is a constant including the various terms mentioned above. If 

 we replace Vz by , where p is the osmotic pressure of the ions, we 



may write 



A= C-^ (RT\nBT)-RT\nl+ U=c-RT\n^+ U. 

 ^ ^ r r 



If for convenience we write c = R Tin P, 



A = -RTln~^+ U, 



