POTENTIALS AT PHASE BOUNDARIES 189 



cations nor to that of the anions. If KCl is used, the oil phase will 

 contain either too much K+and too little Cl~, or perhaps the reverse. 

 There will be a tendency in the system to approach the true equi- 

 librium for each of the ionic species. Since because of this tendency 

 a separation of the ions is required, a difference of potential will 

 develop. And, furthermore, the separation will be accompanied 

 by the formation of an electric double layer of ions whose potential 

 will be such that the separating force will be counterbalanced by 

 the attraction between the two layers of ions. 



The calculation of this effect can be carried out in some such 

 manner as the following.^ Suppose that equilibrium having been 

 reached the concentrations of the electrolyte in the two solutions 

 are Ci and C2. Now the cations tend to distribute themselves in the 

 ratio of lio: where a is the true distribution coefficient of the cation 

 in question, and the anions likewise tend to distribute themselves 

 in the ratio of \:^. This tendency is opposed by the electrostatic 

 forces which develop because of this unequal distribution of ions. 

 When one mol of an ionic species migrates from solution 1 to solu- 

 tion 2 (in order to attain true equihbrium), then an electric current 

 is produced yielding work amounting to ttF. If the same replace- 

 ment or transposition of ions occurred mechanically (osmotically) 



C]Q: 



then the amount of work RT In — would be produced. We can 



C2 



thmk of this transition as occurring in two stages. First one mol 

 of cations is transferred from one medium in which its concentra- 

 tion is Ci into a medium of another kind where the concentration is 

 Cia. This process does not require any work. Now we dilute the 

 latter solution from concentration cia to C2 which requires the 



Cior 

 amount of work RT In — . The actual stable distribution which 



C2 



ensues must be so defined that 



RT , ci a 



■R = — In 



F C2 



By the same reasoning we arrive at the second condition, namely, 



RT , ci /3 



TT = — — — In 



F C2 



• As given by Michaelis; cf. footnote 3. 



