190 GUGGENHEIM art. e 



Hence 



where [vh] is defined by 



(33) 



and is equal to the partial molar volume of the species Sh at 

 the given temperature and at a pressure equal to the mean 

 of the pressures p' and p" on either side of the membrane. 

 Formula (32) is exact for membrane equilibrium as regards the 

 species Sh between two ideal solutions in the same solvent, 

 whether Sh denote the solvent species or one of the solute 

 species. 



7, Non-ideal Solutions. The range of concentrations over 

 which solutions remain ideal varies very much according to the 

 nature of the solvent, the nature of the various solute species 

 and the temperature. It is however generally accepted that in 

 the neighbourhood of infinite dilution all solutions become 

 ideal. This provides a convenient thermodynamic treatment 

 of solutions that are not ideal. 



In analogy with (26) we may write formally for any species 

 Sh, whether solvent or solute, 



HH = tih\t, p) + At log Nhfhy (34) 



where in^H, p) is for a given solvent independent of the compo- 

 sition. In general /;, is a function of temperature, pressure and 

 composition, but has the simplifying property that for given 

 temperature and pressure its value approaches unity as the 

 dilution approaches infinity. It is called the activity coefficient 

 of the species Sh and is a measure of the deviation of the solution 

 from ideahty so far as the species Sh is concerned. 



Since ix}^{t, p) is by definition independent of the composition, 

 and we are assuming that in the neighbourhood of infinite 

 dilution the solutions become ideal, it follows that /xa''(^ v) must 



