298 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



equilibrium requires that the total potential shall be the same throughout 

 the system. The total potential is defined by the equation: 



(88) M' = M + P, 



where M' is the total potential of a given molecular species, M is its 

 thermodynamic potential, and >P is the potential due to the external 

 forces. The thermodynamic potential may be expressed as a function of 

 the concentration by means of the equation: 



(89) M = RTlogC + i + J, 



where i is a function independent of concentration, while J is a function 

 which, in general, involves all the independent variables of the system. 

 For a concentration cell operating between the concentrations C x and 

 C 2 , we have: 



(90) (M + + M-) 2 (M + + M-) = W, 



where M + and M~ are the thermodynamic potentials of the ions of a 

 given electrolyte and W is the work performed by the cell when one 

 equivalent (or mol) of the electrolyte is carried from the first solution to 

 the second. Introducing Equation 89, and writing for W its value in 

 electrical units, we have: 



(91) -rEF = RT log^ + (2J.) 2 - (27^, 



Uj O 1 



where 2,7- = J + + J~> F is the electrochemical equivalent, E the elec- 

 tromotive force, and r the number of equivalents of electricity flowing 

 per equivalent of electrolyte transferred. The value of r depends upon 

 the number of charges v associated with a molecule of the electrolyte 

 and the nature of the electrode process. For a concentration cell with 

 transference, 



(92) ' r v/N, 



where N is the transference number of the ion to which the electrodes 

 are impermeable. For cells without transference, N = 1. The electro- 

 motive force E is that due to the transfer of the electrolyte alone, and, 

 if other processes are involved, the measured electromotive force must 

 be corrected for these processes before introducing into Equation 91. 

 At higher concentrations, in view of the fact that the ions are hydrated, 

 solvent will be carried from a solution of one concentration to that of 

 another. This process involves work and the electromotive force, as 

 measured, must be corrected accordingly. In general, since the relative 



