414 Raoult's Law of the Lowming of Vapour-P ressure. 



v will be very small in comparison with N + n. So that we 

 may write, in accordance with Raoult's Law : — t 



n J-f 

 N + n / 



n 

 For concentrated solutions, v will be greater and ^- will 



not be a small fraction, so that in this case it is just possible 

 v will have an appreciable effect, in which case v\e should 

 have 



= k 



N + n / ' 



where k is less than unity. But as v will evidently never 

 become of much importance in comparison with N + rc, h will 

 never desdate far from unity, as Raoult observed. 



In the above investigation, v stands for the number of 

 molecules gained by the liquid. But it is evident v is con- 

 nected with the change of vapour-pressure. At first, number 

 of molecules per unit volume of vapour =>/. Denoting time 



by t, the rate at which the liquid gains molecules =—\~. 



Hence the number of molecules gained by the liquid from 

 volume V of vapour in time t is expressed by 





i £dt = YX(/-f) = v. 



Thus we have : — 



N+n+v\c/-/T i ' 



This expression assumes that the whole volume V remains 

 saturated. 



Assuming that the fundamental equation of the kinetic 

 theory of gases is applicable to the space occupied by the 

 vapour (and the liquid surface acts towards the vaporous 

 space just as if it were an immovable wall), it is easily seen 

 that 



X=— , 

 m 



where m — mass of a molecule, and v = velocity of mean 

 square of the molecules (the pressures / and /' being measured 

 in absolute units). 



