LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY, 



277 



Finally we must determine bow the activities of the components of a 

 mixture vary when the composition is changed at constant temperature 

 and pressure. In order to solve this problem we may employ the ap- 

 paratus shown in Figure 2. A contains a mixture of Xi and X2. Ei is 

 a membrane permeable only to Xi, E2 one permeable only to X2. In Bi 

 and B2 are" ideal solutions of Xi and X2. The two pure ideal solvents 

 lie above the pistons, Fi and F2, which are permeable only to these 

 solvents. D is a piston which exerts a constant pressure on A. The 

 pressure at Ci and C2 Avill also be held constant. We may perform the 

 following isothermal cycle of reversible operations, starting with ATj 

 mols of Xi and A^2 niols of X, in A, and none of these substances in Bi 

 and B2, the pistons Fi and F2 being at Ei and E2. 



(1) Keeping the pressures on Fi and Fo constant and at such values, 

 ITj and n,, as to maintain equilibrium with the mixture in A, raise 

 these two pistons at such 



rates that as Xi and Xj 

 pass into Bi and B2 the 

 remaining mixture in A 

 still keeps its original com- 

 position. Finally, when all 

 the mixture has disap- 

 peared from A there will 

 be A"i mols of Xi in Bi 

 where it exerts the os- 

 motic pressure Hi, and oc- 

 cupies a volume which we 

 will call Vi, and there will 

 be i\'"2 mols of Xo in Bo, 

 volume ^^2- 



(2) By simultaneous movements of the pistons Fi and F2 change the 

 volumes in Bi and Bo to ]\ — d Vi and V^ — d T,. The osmotic pres- 

 sures will change to Di -1- dn^ and Ha -f dlls- T!ie solutions in Bi and 

 Bo are now able to exist in equilibrium, not with the original mixture, 

 but with a mixture containing Xi and Xg in another proportion, say A"i 

 mols to ]S\ — (^-^"2 mols. 



(3) Form a mixture of this composition in A by lowering the pistons 

 Fi and Fo. This operation will be just the reverse of (1), except that 

 Xi and X2 enter the mixture in the constant proportion, not of jS\ to 

 i\"o but of Ki to X2 — dX^ At the end of this process all of Xi and 

 all but dNi of Xo will have passed into A. 



(4) Finally force into A the remaining dN2 mols of Xo, whereby the 

 whole system returns to its original condition. 



A 



D 



FlGUKE 2. 



the osmotic pressure being ITo, and the 



