Dr. F. Tinker on Osmotic Pressure. 437 



For this relationship to hold it is evident from equation [9] 

 that (i.) the heat of dilution ot the solution must be zero, 

 and (ii.) the partial pressure of the solvent inside the solution 

 shall be given by the equation 



77/ N 



7r l N -1- n 



The latter condition is only fulfilled if the solvent undergoes 

 no volume change during the process of solution {vide p. 433). 

 As is shown on p. 433, dilute solutions in general satisfy the 

 latter relationship. We must not, however, infer that all 

 dilute solutions are ideal. Equation [12] shows that they 

 are only ideal if they have no heat of dilution. In the case 

 of dilute sulphuric acid solutions, for instance (Q being 

 positive), the vapour pressures are abnormally low *, whilst 

 dilute aqueous phenolic solutions have a partial water vapour 

 pressure which is almost equal to that of pure water f. 



Conversely, we may define non-ideal solutions as those 

 which do not satisfy the relationship 



K- 



N 



p 1 N + n ' 



It is evident that departure from ideality in the cases we 

 have been dealing with are caused by.}: 



(i.) Volume changes of the solvent during the process of 

 solution ; these volume changes are caused by the 

 fact that the free space (and intrinsic pressure) of 

 the pure solute is generally different from that of the 

 pure solvent, so that the solvent has to accommodate 

 itself to the solute when the two are mixed together ; 

 and 



(ii.) Heat effects on dilution. The vapour pressure tends 

 to be abnormally high or low according as the solution 

 has a negative or positive heat of dilution. 



The general equation for the vapour pressure of non-ideal 

 solutions is [10]. 



* Cf. the figures given bv Regnault, Ann. Chim. Phys. (3) xv. p. 179 

 (1845) ; Sorel, Zeit. angew.'Chem. p. 272 (1889). 



t Schreinemakers, Proc. Roy. Soc. Amsterdam, vol. iii. pp. 1 & 701. 



X I- e. with solutions iu which the solvent and solute are neither 

 associated nor dissociated, and in which there are no solvates formed. 

 Evidently these latter effects, if they are present, will cause still greater 

 deviations from ideality. 



