On the Osmotic Theory of Solutions. 



599 



diffusion. In the ordinary theory o£ diffusion, as developed 

 originally by Nernst *, the motion o£ the solute under the 

 influence of osmotic pressure differences is considered. A more 

 rigorous theory (especially when strong solutions are in ques- 

 tion) must deal with the osmotic pressure differences (differ- 

 ences in the ordinary osmotic pressure and in its complement) 

 which cause the solute and solvent particles to stream past 

 one another ; regarding the matter from this point o£ view 

 we shall deduce thermodynamically an exact expression for 

 the forces which act on the two sets of particles. 



Fig. 1. 



General case for a solution of two volatile 

 (or involatile) components f . 



We will distinguish the two com- 

 ponents as solute and solvent. 



Let the three columns, represented in 

 fig. 1, be at a constant temperature 

 throughout and be subjected to the 

 influence of gravity. AB is a column 

 of solution, CD and EF are columns of 

 pure solvent and pure solute, respectively. 

 The membranes C\ are permeable to the 

 solvent only, while E L are permeable to 

 the solute only. 



Let the relative positions of the upper 

 surfaces of the three liquids be such that 

 at any given level the vapour-pressure J 

 due to the solvent in the solution is the 

 same as that due to the pure solvent, and 

 similarly for the vapour of the solute. 

 Evidently, under these conditions^ the 

 three liquids can be in equilibrium. 



* Zeit. Phys. Chem. vol. ii. (1888) p. G13. 



t The equations can be extended so as to include any number of 

 components. 



% The vapour-pressures are only introduced into the argument so as to 

 give a clear mental picture of the equilibrium subsisting between the 

 liquids. The calculation, however, is quite independent of vapour- 

 pressures and is applicable to solutions neither of whose components is 

 volatile : it is perfectly valid if one or more of the liquids are limited 

 upwards by a piston, by means of which a pressure or even a tension 

 could be imparted, provided always that the pressures are so arranged 

 that the three liquids are in osmotic equilibrium with one another. 

 It may be mentioned here that the final results apply to any solution 

 extended upwards indefinitely ; the extension downwards may or may 

 not have a limit according to the physical " constants" of the solution. 

 The results also apply to any mixture of molecules, whether of gases, 

 vapours, or liquids. 





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