Thermodynamical Theory of Ternary Mixtures. 957 



where Vi is the specific yolume of C» in the pure state. From 

 equations (9), (10), (11), and (54) we can readily deduce the 

 following relations between the different osmotic pressures: 



"^ +Si ^ + ^o^ =0 - • • • (55) 



v - 



Br . 3i\ , Br 2 



+ 5^!^- \-s 2 v 2 ^— =0. . . . (56) 



OS>2 OS 2 OS 2 



ri B^ =r ^-- • (57) 



We will next consider the connexion between osmotic 

 equilibrium and vapour pressure. 



We will first deduce a few qualitative relationships from 

 general considerations. Consider the system water (C ), 

 •alcohol (Ci),and potassium chloride (C 2 ). The further addi- 

 tion of potassium chloride raises the partial pressure of the 

 alcohol *. Suppose now that the ternary mixture is separated 

 ■from pure alcohol by a membrane permeable to alcohol, equi- 

 librium being maintained by a suitable osmotic difference of 

 •pressure. The further addition of potassium chloride will 

 raise the chemical potential of the alcohol, so that if the 

 pressures are kept constant, alcohol will pass from the mixture 

 to the pure alcohol. To prevent this the original osmotic 

 difference of pressure would have to be diminished. 



Speaking generally, we may say that if the further addition 

 of C 2 raises (lowers) the partial pressure of d, it lowers 

 (raises) what may be termed the osmotic pressure of C and 

 C 2 in the solvent medium CV If the addition of C 2 lowers 

 the osmotic pressure, the addition of C must raise it. 



Quantitative relationships between osmotic pressure and 

 vapour pressure may be obtained from equations (28) and 

 (54). Thus we have the equations 



JJD^-V^ (58) 



^--^BV • • • • (59) 



connecting the osmotic pressure with the partial pressure of 

 the component to which the membrane is permeable. 



Equations connecting the osmotic pressure w T ith the partial 

 pressures of the components to which the membrane is im- 

 permeable may be obtained fjrom the above equations by 



* Kablukow, Solomonow, and Galine, loc. cit. 



