Super solubility from the Osmotic Standpoint. 257 



3rd Operation. — Keeping both pressures constant, drive 

 back mass m of solvent from right to left. The work term 

 on the left is 



£ /?£ °1 \ _ fi l~- /— ^? ^2 , <^\ £2 /_°j_ ^2 ^0*2 Yl 

 Va ~~ Ci 2 ' ' P La \dp "dc 2 dp dp)~e l \CiC 2 dp <^p/J 



and that on the rio-ht is 



4£A Operation. — Without transference through the mem- 

 brane, reduce the pressures to their original values. This 

 operation contributes no terms in mhp. 



Equating the work done by the external forces to zero, we 

 get 



w 



Rememberin 



Co 

 — -0-2=1/.! 



g that 



1 1 - 



O-Tl 



0£l ^£? 1 



dc 2 dp J' 





c)Pi/dp= 



is reduces to 



■ (u 1 — Si)lu x 



dc 2 

 dp 



and ~d Pi/B c 2 = s-rfui . 

 c 2 (cr 2 — s 2 ) 





(1) 



A similar result for the conjugate osmotic pressures and 

 crystals of the solvent is obtained by performing the same 

 cycle on a system under suitable imaginary conditions. 



(7) In this connexion it may not be out of place to point 

 out that an exact relation, giving the change of solubility 

 with temperature when the pressure on the solution is con- 

 stant, may be obtained ; Cohen *, quoting Braun f , gives 

 the following thermodynamical relation between the pressure 

 and temperature coefficients of solubility — ' 



dco I dc a L 



!/. 



2 «^2 



dtl dp (o- 2 — s 2 )t* 



where t is the temperature and L the heat of solution. 

 Substituting (1) in this expression, we get 



dt c 1 u 1 t'd'P 1 /~dc 2 ' ■ ' " " ' w 



(8) A corresponding cycle can be applied to partially 

 miscible liquids. Before doing so, it is necessary to show 



* Zeit. Phys. Chem. vol. lxxv. p. 262. 

 t Zeit. Phys. Chem. vol. i. p. 261. 



Phil. Mag. S. 6. Vol. 24. No. 140. Aug. 1912. 8 



