The Osmotic Pressure of Solutions. 133 



where p x is the vapour pressure of the solid at T, and the 

 •other letters have their former signification. 



We also have 



^ T = ^-(c - Cl )(T -T), 



where w = latent heat of fusion for 1 gr. mol. solvent at T . 



T = melting point of solvent. 



c and c x = capacity for heat for 1 gr. mol. liquid and solid 

 solvent respectively. Call. (c -c^) = c and we get 



- »._, (T .. TH si-.^. 



Integrating this equation between the limits T and T, 

 and remembring that at T 



we get 



. Pl JT T-T /T-T TYl 



lo ST £L w °^r- <-T~ log TjJ 



T 



after expanding log T and neglecting terms after the second 



this becomes : 



<-$.-3$*i&n • • • • <s » 



Now at the freezing point of a solution its vapour pressure 

 is the same as that of the solid solvent at the same 

 temperature. 



Call the freezing point of the solution F. At F, therefore, 

 .p=pi, and therefore 



At F, therefore, we have from equations (2) and (3), by 

 putting T = F and writing the quantities on the right hand 

 side of (2) equal to those on the right of (3) with negative 

 sign, and after making all reductions, 



, Jf T -F C /T -F\ 2 M dqi 



