444 Dr. F. Tinker on Osmotic Pressure. 



(b) The Magnitude of the Osmotic Pressure. 



As is well known*, the application of hydrostatic pressure 

 to a solution increases the vapour pressure of the latter, and 

 when a pressure equal to the osmotic pressure is put on the 

 solution, the vapour pressures of the solvent and solution 

 become equal to one another. We may therefore define the 

 osmotic pressure as the hydrostatic pressure which, when 

 applied to the solution, will raise the vapour pressure up to 

 that of the pure solvent, and which incidentally will also 

 bring the pressure generated inside the membrane by the 

 solution up to that generated by the solvent. This definition 

 is, of course, merely a slight extension of the usual definition 

 that the osmotic pressure is the hydrostatic pressure which 

 (when applied to the solution) stops the osmotic flow. 



Taking the above definition as the basis, we can now 

 arrive at the magnitude of the osmotic pressure very simply 

 by making use of the relationship between the vapour 

 pressure of a liquid and the hydrostatic pressure to which it 

 is subjected which was first obtained by Sir J. J. Thomson 

 for pure liquids f and extended by A. W. Porter to solutions 

 in general \ . 



, 1 . . , . dTl V rim 



Porter s relationship is -= — , = -, lb 



1 dp i s L J 



where II = hydrostatic pressure. 



pif = partial vapour pressure of solvent at pres- 

 sure n. 

 v — sp. vol. of vapour at pressure II. 

 s = sp. vol. of the solvent in the solution at 

 pressure fl. 



(i. e. the loss in vol. when 1 gm. solvent 

 is removed from the solution.) 



Multiplying both v and s by the molec. wgt., and assuming 

 that the vapour obeys the simple gas law, we have 



dU = RT 



dpi ~ pi'Yi, 



where V/ is the molec. vol. of the solvent in the solution 

 under the hydrostatic pressure IJ, whence 



RT dp. 



jn _RT dpi 



* Supra, also, p. 439. 



t 'Application of Dynamics to Physics and Chemistry/ p. 171, 



\ Proc. Hoy. Soc. A. lxxix. p. 519 (1907). 



