THE NEW THEORY OF SOLUTIONS. 



411 



tions, and those of d'jd as derived from direct observations 

 of vapour-density. 



The accord between the two series of numbers leaves 

 little doubt that A = did. 



General conclusions. — The whole of Raoult's results may 

 therefore be represented by — 



{(P ~P')lPg\ x (100 M'/M) = d'jd (2). 

 If u be the number of o-ram-molecules of substance dis- 



o 



solved in N gram- molecules of solvent, n = g/M' and 

 N = 100/M (d jd) where M x did is the average molecular 

 weight of the solvent as calculated from its vapour-density 

 at the temperature of the experiment. We may therefore 

 write (2) as — 



(P-P')IP = n/N ' (3) 



and arrive at the remarkably simple empirical result that the 

 relative lowering of the vapour-pressure is equal to the 

 ratio of the number of gram-molectiles of dissolved sub- 

 stance to the number of gram-molecules of solvent present 

 in the solution. It is well to note that (3) can only hold for 

 dilute solutions as it leads to the erroneous conclusion that 

 when the solution is so strong that n = N, the vapour-pres- 

 sure of the solution is nil. For concentrated solutions, as 

 has already been stated, the equation — 



(P ~P')'P = n /( N + n ) 

 has to be employed to express the facts. 



Vapour-pressure and the gaseous laws.^K two solutions 

 in the same solvent have at the same temperature the same 

 osmotic pressure they must have the same vapour-pressure. 



