THE NEW THEORY OF SOLUTIONS. 413 



vent, and let the vessel contain a quantity of a solution of 

 a non-volatile indifferent substance. When equilibrium is 

 established between solvent and solution the level of the latter 

 AB will be at a definite height H above CD the level of the 

 solvent, and if p be the density of the solution its osmotic 

 pressure P will be Hp. Now, in order that this condition 

 of equilibrium may remain undisturbed, the solution must 

 neither gain nor lose liquid by evaporation, that is, the 

 vapour-pressure of the solution at the level AB must be 

 equal to the pressure exerted by the vapour of the solvent 

 at the same level. If this were not the case it could be 

 shown in the manner already indicated that a continuous 

 isothermal circulation of solvent would ensue. But if/ be 

 the vapour-pressure of the pure solvent or the pressure of 

 the vapour at the level AB, the pressure/' at the level CD 

 and thus the pressure of the solution will be less than p by 

 the pressure exerted by a head of vapour equal to H. Con- 

 sequently if d be the density of the vapour, p — p' = Hd, and 

 since P = Hp we have — 



P/(/-/)=pM (4)- 

 We may now express d in terms of M the molecular weight 



of the solvent. The mean pressure of the vapour lies, of 



course, between p and p'; since, however, the solutions are 



dilute and p and p' differ but slightly, we may take p to 



be the pressure of the vapour. If further the vapour be 



assumed to behave as a perfect gas, pv — "0819 T where v 



is the volume in litres occupied by M gr. of vapour. Thus 



d = M/v = Mp/'o8ig T and therefore — 



P = (-0819 pT/M) x \(p -p')lp). 



Now Raoult has shown that (p — p')jp = n/N, hence — 



P = -0819 7i P T/NM (5). 



Here NM is the weight in grams of the amount of solvent 



which contains n gram-molecules of dissolved substance. 



If we neglect the weight of the dissolved substance and if 



we assume that the density of the solvent is the same as 



that of the solution, 1 the volume V of solution which con- 



1 Since the litre is employed as the unit of volume, p will not be the 

 ordinary density of the solution, i.e., the weight of 1 c.c, but the weight 

 of 1 litre. 



