274 PROCEEDINGS OF THE AMERICAN ACADEMY. 



If a mixture contains Xj and X2 in the proportion of N't, mols of the 

 former to ^^2 of the latter, the relation of the partial molecular volumes, 

 V 1 and -v 2 is readily seen. If we add to an infinite quantity of the 

 mixture iVj mols of Xj, the mixture will increase in volume by NiVi. 

 Then adding N^ mols of X2 the volume increases by AVv Altogether 

 we have done nothing more than add one mol more of the original mix- 

 ture. The total change of volume must therefore equal v, the volume 

 of one mol of the mixture. Hence, 



A'lFi + ^^2^2 = v. X 



From equation IX we have the following two equations for the two 

 constituents : 



BT' 



\ dP )t,n~ 

 \ dF )t,n~ 



RT 



Adding these two, we obtain the important equation, 

 'A^iain^i + N.d\xiL\ v 10 



(:■ 



dP )t,n RT 



XI 



The influence of temperature upon the activity of one of the con- 

 stituents of a mixture may also be determined with the aid of the 

 apparatus of Figure 1. Starting with the piston F at E, we may per- 

 form the following cycle of reversible operations, keeping the pressure 

 constant upon both D and C. 



(1) At the temperature 7" raise the piston F until 1 mol of Xi passes 

 into B, where it occupies the volume v'. The pressure on F is kept at 

 such a pressure, 11, that the activity of Xi is always the same in B as 

 in A. 



(2) Lower the temperature to 7" — dT, moving the piston F so that 

 none of Xi passes through K The volume of B is changed to v' — dc? 

 and the osmotic pressure to IT — d^. 



^° The equation is written in this form rather than in the more conventional 

 form, 



-.(^i..--=(m,=^.' 



in order to emphasize the peculiar significance of the term N-^d In |i + N«d In lo- 

 in general we shall see that the equations of a mixture may be obtained from 

 tliose of a pure substance by substituting tliis series of terms in place of (?ln|. 



