Carbon Compounds in Concentrated Solutions. 223 



of the mixture is reduced to one-half of p, and let us dissolve 

 in this complex solvent the same quantity of solute as we 

 should have dissolved in the simple solvent in making a molec- 

 ular weight determination, using the same weight of complex 

 solvent as we should use of simple solvent. Then 



_ wM p'/2 _ wM. p 

 m ~W (p-p')/2 ~ W f^pf 



This is what is supposed to be the case with water or with any 

 other solvent whose molecules are complex. The complex 

 molecules are altogether inert. They play the part of the inert 

 liquid in the above complex solvent, and all we need know is 

 the molecular weight of the solvent in the vapor state. 

 Put (1) in the form 



N~^y "n + p' 



>\W +1 )= 1 J' ^ 



Integrating 



_ RT 2 dp 



p dT 



which is the second law of thermodynamics applied to vapori- 

 zation, and remembering that under these conditions, dp/dt 

 is negative, we get 



p _ Q' T-T„ 



P' R T,T 



Substituting in (5) we have 



/n \_Q'T~T 



l \N + 7~K T,T ' 



where Q f is the heat of vaporization of one gram-molecule 

 of solvent from the solution, the quantity of solution being so 

 great that no change in concentration is produced when the 

 gram-molecule is removed, T x is the boiling point of the solu- 

 tion, T that of the pure solvent, and R is the gas constant. 



This equation is available for determining the molecular 

 weights according to the boiling point method, or to determine 

 the latent heat of vaporization of the solvent. It will answer 

 for all purposes to which van't Hoffs formula is put and is 

 altogether independent of the osmotic theory. 



A corresponding equation^ easily obtained in terms of heat 

 of. fusion and freezing temperatures. 



Rutgers College, December, 1901. 



