478 



J. H. van't Hoff on the Origin 



the water-vapour passes in the same direction, but only 

 until the pressure reaches that measured by Mitscherlich. 



It is even possible to make a calculation founded on this 

 interdependence. The force with which Mitscherlich dealt is 

 small because it acts on the attenuated vapour, whilst that of 

 Pfeffer is large because it refers to the concentrated water. 

 Thus we have: — 



Pfeffer : Mitscherlich = 1000 : ^0-08956^(1 + ^\ 



so that we can calculate Pfeffer' s force from the diminution 

 of vapour-pressure (freezing-point) . 



Temperature. 



Osmotic Pressure. 



000239 T. 



o 



6-8 



0-664 



0-668 



15-5 



0-684 



0-689 



22 



0721 



0-704 



32 



0-716 



0-728 



36 



0-746 



0-737 



The above proportionality is not quite exact. The accurate 

 formula is obtained if the work which the attraction for the 

 water can perform is made the starting-point ; this is inde- 

 pendent of the fact whether the water as such, or its vapour, 

 is transferred. Hence we get the relation for 18 kilos water, 



2TI. ^ = JLpy ; 

 Pi 423 



where p w and pi represent the pressure of the water and the 

 solution respectively, P the osmotic pressure in kilos per 

 square metre, and Y the volume in cub. centims. of 18 kilos of 

 water. 



This formula reproduces Pfeffer's results very exactly. It 

 also lends itself for the determination of the pressure when p 

 only is known ; so that we have the solution of Mitscherlich's 

 problem in regard to the water of crystallization, for obviously 

 this attraction for water corresponds to that of a solution 

 having an equal maximum vapour-pressure. Hence we get: — 



