186 HYDROGEN ION CONCENTRATION 



where Ci is the concentration of hydrogen ions in the water, and ki 

 is that concentration of H-ions in the same solvent against which 

 the potential would be zero. At electrode II the potential is 



Co 



TTo = RT In — 



with the corresponding meaning for C2 and k2. 



The difference between these two electrode potentials is, therefore, 



(I) 



This potential difference can become equal to zero when 



2L - hi 



C2 ka 



But since — represents a constant value, therefore, the ratio - 



must also be constant, i.e., when any acid is distributed in any con- 

 centration between an aqueous and an oil phase with the establish- 

 ment of an equilibrium, the ratio of the H-ion concentrations in the 

 two phases will remain constant. It can be equally well shown that 

 when chlorine electrodes are taken instead of hydrogen electrodes 

 the ratio of Cl-ion concentrations in the two phases will remain the 

 same whatever chloride in whatever concentration be involved. 

 Briefly stated : it can be shown that any given ionic species must be 

 distributed between an aqueous and an oil phase in accord with its 

 unalterable distribution coefficient. But this is not possible, as can 

 be demonstrated both practically and theoretically. The theoretic 

 proof of this impossibihty can be given in the sense of Nernst's 

 theory as follows: If we first assume that every ion-species, as well 

 as any other molecular species, has a definite distribution coefficient, 

 then it should certainly be different for the various ion-species. 

 Therefore, in the case of HCl, the H-ions will have a different dis- 

 tribution coefficient from that of the Cl-ions, and the two phases 

 must have different distributions with respect to H- and Cl-ions. 

 But for electrostatic reasons this is impossible. Neither can the 

 true distribution correspond to the specific coefficients of the CI- or 

 H-ions, but it must He somewhere in between these. And, hkewise, 

 this true distribution must be different in an HCl solution from 



