OSMOTIC AND MEMBRANE EQUILIBRIA 201 



chemical potentials of ionic species are determinate and, in 

 fact, equal to the corresponding linear combinations of the 

 electrochemical potentials, the condition for this being that the 

 linear combination corresponds to a combination of ions with 

 zero net electric charge. The physical meaning of this is simply 

 that the potential of a combination of ions with zero net electric 

 charge is determined completely by the chemical composition 

 in the bulk of the phase and is independent of its electrical state. 



17. Ideal Solutions of Ions. At very high dilutions of ions 

 aU equilibria are given correctly by assuming that the electro- 

 chemical potential [^u,] of the ionic species <Si is of the form 



[Mi] = Mi*(0 + V^ni - \Kiv) + At log Ni + ZiFV, (75) 



where )U»*(0 is for a given solvent a function of the temperature 

 only, Vi* and Vi*{\ — Kip) are the partial molar volumes of the 

 ionic species Si at zero pressure and at the pressure p respectively, 

 Ni is the mol fraction of the species Si, and Zi its valency. 

 Finally V depends on the "electrical state" of the system, that 

 is, on the distribution of electric charges at the surface of the 

 phase, and has the same value for all ionic species. Solutions of 

 ions behaving in accordance with (75) are called "ideal." In 

 analogy with ideal solutions of uncharged species it is natural 

 to define the chemical potential m of the ionic species Si by 



/i.- = Mi*(0 + PVi*(l - hiP) + At log Ni, (76) 



and to call V the electric potential of the phase. 



18. Non-ideal Solutions of Ions. Since all ionic solutions 

 tend towards ideahty at infinite dilution, it is most convenient to 

 treat non-ideal solutions by the introduction of activity coeffi- 

 cients fi just as in the case of non-ideal solutions of uncharged 

 species. We therefore write formally 



[m] = fjii*it) + pvi*(l - ^Kip) + At log Ni 



-hAthgfi + ZiFV, (77) 



where Mi*(0 is for a given solvent a function of the temperature 

 only; y,* and Vi*{l — Kip) are the values of the partial molar 



