Dr. F. Tinker on Osmotic Pressure. 435 



It is evident that either of these conditions will be satisfied 

 but rarely. In the case of dilute solutions (in which V/ = V x ) 

 equation [7] indicates that the total volume change 



ne=n{(V 1 -6 1 )-(V 2 -6 i! )}. 



There will thus be an expansion or contraction on mixing- 

 according as (Vi— &i) is greater or less than (V 2 — b 2 ) *. 



(b) The Partial Pressures of the Solvent and Solute 

 in the Vapour Phase, 



By combining the Dieterici equation with the foregoing 



results we can arrive at the laws obeyed by the solvent and 



solute in any other phase with which the solution is in 



contact and into which either (or both) solvent or solute 



can diffuse. The equation connecting the pressure of the 



solvent and solute in any phase with the pressure inside the 



solution can be written as 



_ AL 

 2>' = 7r'e RT ? [8] 



where p' an ^ ' 7T ' are partial pressures in the phase and 

 solution respectively, and A' is the work done in transferring 

 a molecule from the solution to the phase in question. 



We thus have for the partial pressure of the solvent p ± ' 

 in any phase (say the vapour phase)! 





V x 7T-,e ET 77-, ^*: 



*- , = — = — \e rt 



Pi , A i IT. 



^ e '"^ [9] 



BA X being the excess work performed by " evaporating " 

 one molecule of the solvent from the solution into the phase 

 over the work performed when the solvent is "evaporated" 

 from the pure solvent. 



We can extend the applicability of equations [8] and |_9] 

 by first proving that g)A x is approximately equal to the heat 

 of dilution Q of the solution. 



Let the pure solvent and the solution be separated from 

 one another by the phase in question f. A molecule of 

 solvent can be conveyed from the pure solvent to the 



* In the absence of solvation and association and dissociation changes 

 this deduction should be capable of experimental test. The fact that 

 physical factors only can cause total volume change invalidates many 

 determinations of the formulas of the " hydrates " formed during solution 

 from the volume changes which take place on mixing. 



+ It is immaterial what this phase is. It may be either a vacuum 

 (the vapour phase proper), a colloidal membrane, or another liquid or 

 solid in which the solvent and solute are soluble. 



