﻿Molecular Thermodynamics. 239 



when m is constant (at constant temperature and pressure) 

 and therefore equal to m we get 



f=M„|> M + Jlog (1 +-, C)1 



+ 2wJ^-RJ logc,-iog(l + m O)T]+M G, . . (20) 



which is equation (52) of the first of these papers, from 

 which the " second approximation " equations were obtained. 



It is, of course, not possible to say how, in the most 

 general case, m will depend on the concentrations of the 

 various solutes, but an interesting case, of probably very wide 

 application, may be treated and will at the same time serve 

 as an illustration. 



This is the case where m can be written, with sufficient 

 approximation, as a series of ascending integral powders of C, 

 the total solute concentration. 



This can be shown to be the case, for instance, when the 

 various solvent-molecular species behave as perfect solutes 

 (in the true sense, — not in the sense of the Raoult-van't 

 Hoff laws). 



Some simple cases have been investigated, but the detail 

 need not be given here. It will suffice to say that in the 

 simplest case, for example where the solvent consists of two 

 molecular species, m and (2 m ), the one the doublet of the 

 other, we find that ~m can be expressed as 



m = m [l + 6{m C) + V (m C) 2 ], 



where the values of 6 and y depend, of course, on the 

 proportions in which the two species are present in the pure 

 solvent, but in any case cannot exceed §• and -3-g respectively 

 (these maxima not being simultaneous). 



We may carry this expansion of m, which is formally 

 convenient for our purpose, to one further term of which 

 only the order of magnitude will matter, 



in 



.=l + 0(- Q C) + V (m Cy + Z(m C^ . . (30) 



the last term being, as we shall find, altogether negligible if £ 

 is no greater than about y 1 ^. 



Approximating on the assumption that 6 and r) are of the 



