4 i4 SCIENCE PROGRESS. 



tains one gram-molecule of dissolved substance is NM/w/i. 

 On introducing V into (5) we obtain — 



PV = -o8iqT. 



Raoult's results, therefore, lead to the conclusion that in 

 dilute solution dissolved substances obey gaseous laws. 

 Equations (4) and (5) make it possible to calculate the 

 values of the osmotic pressure from vapour-pressure 

 observations, and the entire discussion makes it evident 

 that vapour-pressure observations support the idea which 

 has not yet been confirmed by direct experiment that 

 osmotic pressure is independent of the nature of the 

 solvent. 



Equation (5) can only apply to very dilute solutions, as 

 it involves the assumption that p and p' differ by so little 

 that the density of the vapour may be taken to correspond 

 with the pressure p. If we avoid this assumption by taking 

 note of the actual fall of pressure on passing from CD to 

 AB, the vapour being assumed to obey gaseous laws, we 

 obtain — 



P = (-0819 P T/M)x (log,///) (6). 



It is interesting to note that if we substitute for P the cor- 

 responding gaseous pressure this equation may be reduced, 

 as Ostwald has shown, to — 



(p - p')ip = «/(N + n), 



or the expression derived empirically by Raoult for strong 

 solutions and which is therefore in harmony with theoretical 

 considerations. 



As has been mentioned the relationship between vapour- 

 pressure and osmotic pressure was first established by 

 van't Hoff in 1886. His mode of treatment consists 

 essentially in equating the amount of work required to 

 remove a definite amount of solvent from a solution by 

 causing it to pass through a semi-permeable wall to amount 

 required to remove the same quantity by evaporation at the 

 same temperature. By this method van't Hoff and Gouy 

 and Chaperon (1888) have arrived at relationships which 

 are essentially the same as those given above. 



