the Lowering of .Vapour-Pressure. 413 



before, that a molecules per second get an opportunity of 

 escaping from the liquid, since there is nothing to alter this 

 condition of things, as the molecules of the dissolved sub- 

 stance move freely about like those of the solvent. But, 

 assuming a homogeneous composition of the solution, the 



N 

 theory of chances shows that only the fraction ^ of the x 



molecules which get suitable opportunities will be molecules 

 of the solvent, and therefore able to escape. Thus we have 



now only ^ x molecules escaping every second from the 



liquid. 



Accordingly the previous mobile equilibrium is disturbed, 

 for the liquid will now be gaining molecules, and the vapour 

 losing them. 



This will continue until the rates at which the liquid and 

 vapour gain molecules again become equal. The value of the 



N 

 fraction ^- , however, changes during this process, inas- 

 much as N becomes N + v, where v is increasing and repre- 

 sents at any moment the number of molecules gained by the 

 liquid (we must suppose that the film of pure solvent thus 

 formed is dispersed and homogeneity secured by agitation of 

 the liquid). Thus when equilibrium is again attained we 



N + v 

 shall have ^= x molecules escaping from the liquid into 



the vapour per second, and vice versa. If/' is the new vapour- 

 pressure, we have now 



N + n -r- v J ' 



where v has now its final value, i. e. the total number of 

 molecules gained by the liquid. If we divide the members of 

 this equation by the members of the previous equation, we 

 obtain : — 



N + v _f 

 N+n-tv~ f> 



whence 



n = f-f 

 N + n + v / ' 



Now if the solution is dilute, ~ — - will be a small fraction and 



