128 BUTLER 



and since 



we have 



ART. D 



p t/ ' Ma^^) w/ ' Ma^^^' 



(149) 



i.e., the fractional lowering of the vapor pressure is equal to the 

 ratio of the numbers of molecules of the solute and solvent. 

 Rearranging (149), we easily obtain 



i.e., the ratio of the vapor pressure of the solution to that of the 

 pure solvent at the same temperature is equal to the molar 

 fraction of solvent. This is Raoult's law.* It is to be par- 

 ticularly noticed that the molecular weight of the solvent which 

 appears in these equations is that in the vapor, while the 

 molecular weight of the solute is that in the solution. 



VII. The Values of Potentials in Solutions Which Are Not 



Very Dilute 



19. Partial Energies, Entropies and Volumes. We shall now 

 give an account of some extensions of the method of Gibbs 

 which permit the quantitative treatment of equilibria involving 

 concentrated solutions. The development of these extensions 

 and the working out of practical methods for the evaluation of 

 the potentials and other significant properties of solutions is 

 largely due to G. N. Lewis and his collaborators.! Much of 

 the work of these investigators has been concerned with solu- 

 tions of electrolytes, which are the subject of a separate article 



* CorriTpt. rend., 104, 130 (1887); Z. physikal. Chem., 2, 353 (1888). 



t Outlines of a New System of Thermodynamic Chemistry, Proc. 

 Amer.Acad.,43, 259 (1907); Z. physikal Chem., 61, 129 (1907). G. N. 

 Lewis and M. Randall, Thermodynamics and the Free Energy of Chemical 

 Substances, 1923. 



