274 PROCEEDINGS OF THE AMERICAS ACADEMY. 



If a mixture contains X, and X., in the proportion of X } mols of the 

 former to X of the latter, the relation of the partial molc-ular volun 

 c, and '-., is readily seen, [fwe add to an infinite quantity of the 

 mixture -V, mols of X 2 , the mixture will increase in volume by .V,,-,. 

 Then adding X. mols of X 2 the volume increases by X.'-._>. 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, 



X l r l + \.,T-, = v. X 



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

 constituents ■. 



V W Jt,.y~ 



V dP ) T ,N 



BT 



Sl- 



ur 



Adding these two, we obtain the important equation, 



V 8P ) T ,x~ 



r r 



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 ] 

 form the following cycle of reversible operations, keeping the pressure 

 constant upon both D and C. 



(1) At the temperature '/'raise the piston F until 1 mol of \i pi 

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

 such a pressure, II, that the activit}' of X x is always the same in B as 

 in A. 



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

 none of Xi passes through E. The volume of B is changed to v' — rfe* 

 and the osmotic pressure to H — </U. 



10 The equation is written in this form rattier than in the more conventional 

 form, 



v /£!Bji\ , N jdlnjA __v_ 

 Nl \ dP )t.s- *H dP h,*-RT' 



in order tn emphasize tlie peculiar significance of the term .V,^ln|, Y.y/lnfj. 

 In general we Bhall see that the equations "f a mixture may lie obtained from 

 those of a pure BUhstance by substituting this series uf terms in place of <;ln{. 



