THERMODYNAMICAL SYSTEM OF GIBBS 



127 



(c) Lowering of the Vapor Pressure of the Solvent by an 

 Tnvolatile Solute. Consider a mass of the solution in equilibrium 

 with the vapor, in which the quantity of the solute is in- 

 appreciable. At constant temperature we have, for a variation 

 of the solution, 



dp = + ^ • (^/xi' + 7- • dn^', (145) 



and for a variation of the vapor 



m/ 



dp = + -jj- ■ dm 



(146) 



In order to preserve equiHbrium, dm' = dm", so that, sub- 

 stituting the value of dm given by (146) in (145) and putting 



W2' , At 



m 



and writing 



7" = ^^' 



mi 



// 



= 71 



etc., 



we obtain 



or 



At 

 dp = ~, dp + j^^ dy2 , 



7i 



71' 



— dp = 

 Thus, by integration, 



7i 



// 



At 



71' - 71" M2^^^ 



^72'. 



7i' 



At 



Po-P = :;T3^-]^)-72, 



(147) 



(148) 



where po is the value of p when 72' = 0. Since 71" is small in 

 comparison with 7/, we may write, approximately. 



Po - p = 



7i 



n 



At 



71' M2(^> 



72 





