LEWIS. — THERMAL PRESSURE. 



161 



For the solvent, 



P = (3 -a. 

 Combiaing these we obtain, 



dP=d(3 — da + rf/3'. 



For equilibrium, when the escaping tendencies of the solution and solvent 

 are the same, 



dft — da = 0. 



Hence the equation for osmotic equilibrium is, 



dF=d(3'. 



But dP = c?n, the osmotic pressure, and 



{dn) R T 



d(S' = 



from equation (10) ; hence 



dn 



(dn) RT 



the equation of van 't Hoff. 



The conclusion that a certain osmotic pressure, and an equal change in 

 the external pressure, together have no effect upon the tendency of a 

 solvent to escape into some other phase may be verified in au interesting 

 way. 



In Figure 4 let A represent a pure liquid X ; 



B, a solution in X, whose osmotic pressure is 11 ; 



C, the vapor of X ; and D, an inert, insoluble 

 gas exerting a pressure equal to IT. M and 

 M' are two membranes permeable to X alone. 

 Since the gas pressure in D is equal to the 

 osmotic pressure 11, X will not pass through the 

 membrane M, therefore none of X will distil 

 from solution to solvent or vice versa, for sucli 

 a distillation would form a cyclic process con- 

 tradicting tlie second law of thermodynamics. 

 Hence the vapor pressure over a solution is 



the same as that over the pure solvent when the solution has an additional 

 external pressure applied, equal to its osmotic pressure. The effect of 

 the thermal pressure of a solute upon the vapor pressure of a solvent 

 may be regarded, therefore, as due to a stress upon the surface of the 

 solution acting like a diminution in external pressure of the same 

 magnitude. 



VOL. XXXVI. — 11 



