Dr. F. Tinker on Osmotic Pressure. 433 



Substituting in equation [2] we have 



N + « n/ n Vo — & 2 + e\ 



7T 2 ft // \ \ 2 — 2 t 



Equations [2], [3], [4], [5], [6] are general, and hold 

 whatever volume changes may take place in either the 

 partial volumes or the total volume. 



Equations [2] and [3] show that the partial liquid 

 pressures of the solvent and solute are determined partly by 

 their respective molar fractions and partly by the changes 

 in molecular volume which take place on mixing. 



The most important particular case is the one in which 

 we get the partial pressure of the solvent given by the 

 relation 



7T,' N fc 



TTl 



N+N ' 



It is evident from equation [2] that the relationship can 

 hold only if V 1 -6 1 = F = V 1 / -6 1 , L e. if V/=Vi ; in other 



i 

 words, the partial vapour pressure ratio — for the solvent 



N 7ri 



is equal to the molar fraction ^ only when the molecular 



volume of the solvent undergoes no change by the process 

 of solution. It can be shown, however, that all dilute 

 solutions under normal conditions obey the relationship 



< N 



ir i N + n 

 more or less approximately f. Consider, for instance, a litre 



* As will be shown later, the simple osmotic laws for dilute solutions 

 hold only when the above relationship holds. 



+ It is important to note the limitation of "normal conditions." 

 The partial pressures, both inside the solutiou and in the vapour phase 

 proper, &c, vary with the hydrostatic pressure placed on the solution. 

 It will be shown subsequently that with ideal solutions, for instance, 

 at osmotic equilibrium, xn' and xr, are equal instead of tt x being greater 

 than 77-/ .as under normal, conditions. 



