417 



three-phase mixtui-e sepcarated hy a rneinbrane fVoin pure hexane 

 would absorb hexane, hut separated fVoni llie pure water it would 

 expel water. So the thermodynamic potential of the water in the 

 three-phase mixture is greater than that of pure water; that of hexane 

 would be smaller than that of pure hexane on the said assumption. 

 If hexane and water is brought together each under its own vapour- 

 pressure, three-phase equilibrium sets naturally in. In this a rise 

 occurs in the thermodynamic potential of the water. 



The thermodynamic potential of one component in a binary mixture 

 is indicated by : 



\d.vJpT 

 If in a pure substance .4 a little of a second substance B is 

 dissolved, the thei-modynamic potential of A is changed by an 

 amount : 



fdZ\ fd"Z\ f d''Z\ 



dM^H, = -r- dp — w[—j\ d.x — x\ --— dp 



or 



For a dilute solution this value becomes: 



dM^ II , = rdp — MR Td.v. 



This value is zero for osmotic equilibrium and the osmotic pressure 



is indicated by : 



MRT 

 dpo= dx (1) 



V 



If now the change of the external pressure is considered when 

 a little of B is dissolved in A under the vapour-pressure in such 

 a way that the obtained solution is again under its own vapour 

 pressure, then : 



/'d'Z\ 



^1 <^P — l'^^ — '^-'i) -!—„ d^x' 

 \d.v,-J,>T 



Hence the change in external pressure amounts to : 



For dilute solutions the gas volume v^ may be substituted for?;,^, 

 if the temperature does not lie in the neighbourhood of the critical 

 temperature; hence: 



dp — ^'~^' MRTdx, (2) 



27 

 Proceedings Royal Acad. Amsterdam. Vol. XVI. 



