46 MOLECULAR WEIGHT AND POLYMERISM 



with the aid of thermo-dynamics, insisting again that the 

 law of the lowering of vapour pressure infers nothing as 

 to the molecular weight of the liquid solvent. 



Thermo-dynamic deduction of the laiv of diminution of 

 vapour pressure. Let the solution contain da kilograms of 

 dissolved substance in one kilogram of solvent, the former 

 possessing the molecular weight m; withdraw from it, 

 osmotically and reversibly, i. e. with the aid of cylinder and 

 piston, so much solvent as contains one kilogram-molecule 

 of dissolved substance, with expenditure of work 



where dP is the osmotic pressure in kilograms per square 

 metre produced by the absorption into the solution of da 

 per kilogram, and Fthe volume in cubic metres in which 

 one kilogram-molecule is dissolved. 



The amount of solvent withdrawn is to be restored 

 reversibly by evaporation and condensation. In the first 

 place we gain a quantity of work (i) by reversible evapora- 

 tion at p and T ; next a second quantity by expansion of 

 the vapour till the pressure has fallen to p dp, that of the 

 solution. This work, for the kilogram-molecule M of 

 vapour, is 



Avdp = iT^; 



Wlr 



consequently, for the mass -7- with which we are concerned, 



da 



2 Tdp m 

 p Mda 



Finally the vapour is to be condensed in contact with the 

 solution at p dp and T, in which process the work gained 

 in (i) is used up. Since this cyclic process has been carried 

 out at constant temperature, it cannot be accompanied by 

 a conversion of work into heat, or vice versa, so that the 



