44 MOLECULAR WEIGHT AND POLYMERISM 



column of vapour AB ; accordingly, the saturation pressure 

 of the solution which obtains at A must be less than that of 

 the solvent, by say A^>. But just as the diminution 

 of vapour pressure corresponds to the column of vapour, 

 so the osmotic pressure corresponds to the column of liquid 

 resting on a b, and if both be referred to the same area, the 

 change of vapour pressure is to the osmotic pressure as 

 the weight of any volume of vapour is to that of the same 

 volume of liquid. Taking, for simplicity, a kilogram- 

 molecule M of vapour, if its volume is v litres, then by 

 applying Avogadro's law to the vapour and solution we get 



pv = PV, so that v V, 

 P 



where p and P are respectively the vapour pressure and 

 the osmotic pressure, and V is the volume in litres of 

 a kilogram-molecule of the dissolved substance. If the 

 composition of the solution is given as n molecules of 

 dissolved substance to N molecules of solvent, one dissolved 



N 

 molecule ??i occurs in in + M kilograms of solution (here 



the molecular weight of the solvent is taken as M, as 

 determined from the vapour density, but without any 

 assumption as to the real value of that quantity in the 

 liquid). If N is great, as in dilute solutions, the weight 



NM 



may be taken as - ; this is accordingly the weight of the 



volume V of solution, and that of v is - - 



p n 



Hence we have the relation 



PNM ,, 



P : A p = ~ - :M 

 pn 



or 



A n 



This is a somewhat modified form of Raoult's law. The 

 latter refers to the so-called molecular lowering of vapour 



