324 HEAT. 



is proportional to the number of molecules of solute present, whatever 

 their nature. When we have to multiply by c, where c is nearly 2, it is 

 taken to imply that the molecules of salt are for the most part dissociated 

 each into 2. When we have to multiply by a number nearly 3, it is 

 taken to imply that the dissociation is from one into three molecules and 

 so on. 



For very dilute non-electrolytic solutions n, the number of salt 

 molecules, is very small compared with N, the number of solvent molecules, 

 and we may put 



a n 



(4) 



Substituting in (1), p. 320, we get for the osmotic pressure 



n /K\ 



N 



If we put the relation between the pressure o> and the density ir of 

 hydrogen as 



(T 



we may put that for any rarefied vapour of molecular weight M as 



=2-ne 



<r M 



whence P = T' < 6 > 



Further, if s is the density of the salt in the solution or the number 



of grammes per c.c., and if S is its molecular weight, then _ is the number 



S 



of gramme molecules per c.c. Similarly ~ is the number of gramme 

 molecules of the solvent per c.c. if the solution is sufficiently dilute. 



5-5*4 



and substituting in (6) we get 



Comparing this with - = ^R# we see that the osmotic pressure P is the 



pressure which the salt would exert if it were gaseous, and of the density 

 at which it actually exists in the solution. This most remarkable result 

 was first obtained in a very different way by Van t'Hoff, and is known 

 as Van t'Hoff's law of osmotic pressure. We shall give some account of 

 his theory later. 



