Dr. F. Tinker on Osmotic Pressure. 445 



Putting Yi=Y 1(a) — II£VY (o) , where ft is the coefficient of 

 compressibility of the solution and Vi' (a) is the mol. vol. 

 of the solvent at the atmos. press., we get 

 i«/i „*s RT dp' 



V l(a) Pi 



Integrating between the limits represented by the osmotic 

 pressure P and zero hydrostatic pressure *, and remembering 

 that Pi / ( p) = pi( a) ? w e obtain 



whence 



du-p\ udu = ^M 



dpi 

 Pi" 



i>-^p2 = ^log.^I. . . . [19] 



V 1 (a; Pi (a) 



This is the general equation connecting the osmotic pressure 

 with the vapour pressure of the pure solvent and solution 

 when both are at the atmospheric pressure. With the 

 exception that V/ is written for V 1? it is identical with the 

 equations given by Gibbs, Van Laar, and others. It holds 

 for all solutions irrespective of association of the solvent, 

 formation of solvates, &c, or of abnormalities in latent 

 heat, &c. 



Substituting the values of —, given in equation [10], we 



get for the type of solutions we have been dealing with 



P-i/3P 2 



- 7&°* i^r - st I 1 Y^hr ) S e 



RT, JN + 51 n( 1 V,-J,+6,a) RT , Q 

 = W^ {-8— nI 1 -^^)} + Vj"~ 



When the solution is dilate we have Vi' = Vi (see p. 433) ; 



the compressibility factor becomes negligible ; the ex- 



N-f- w 

 pression in brackets becomes equal — ~ — (pp. 433, 434) ; 



log e — ^ — = 1sj a Ppi'ox. ; so that the expression reduces to 



PV, = RT|+Q [21] 



* /. e. zero mechanical hydrostatic pressure, not counting the atmo- 

 spheric pressure. 



Phil. Mag. S. 6. Vol. 33. No. 197. May 1917. 2 H 



