Chemical Potential to the Theory of Solutions, 939 



The relation between this lowering effect and the compen- 

 sating pressure increase is shown by the following equation, 

 which may be derived from equation (4) by means of 

 equation (1), 



/o(o, p„ e) -Ms, Poj 6) = n(«, Po , 0) p (,, p ^p +a,e). (5) 



The Thermody mimical Theory of Vapour-Pressure. 



If the pure liquid solvent and its vapour are in equilibrium, 

 the surface of separation being plane, the pressure of the 

 system is determined as a function of the temperature by the 

 equation 



/ o (o,n o ,0)=F o (n o , 6) (6) 



where F (II , 6) is the chemical potential of the solvent 

 vapour at a pressure II and temperature 6. 



If the solution and the solvent vapour are similarly in 

 equilibrium, the pressure is determined as a function of the 

 temperature and concentration by the equation 



/,(«, n, 0)=F o (n, 0) (7) 



If V(#, 0) denotes the specific volume of the solvent vapour 

 at a pressure x and temperature 0, we have 



^Itt*. 6) =V(«, 6). 



Hence we have, from equations (6) and (7), 



/• (o, n , &) - Jo (s, n , 8)= \ v(«, d)dz-(n -n)P (s, n»rr . e). 



.... (8) 



Since V(.r, 6) is always greater than P (s, x, 0), IT — II is 

 always positive, i. e. the effect of the addition of the solute 

 is to lower the vapour-pressure. 



The lowering of the vapour-pressure and the osmotic 

 pressure are both closely related to the lowering of the 

 chemical potential of the solvent. A relation between the 

 two will be deduced in the next section. 



The Relation between the Conditions of Osmotic Equilibrium 

 and Vapour-Pressure, 



If we suppose that in the case of osmotic equilibrium 

 between the solution and the pure solvent the latter is under 



