938 Mr. S. A. Shorter: Application of the Theory of 



In the special case where 5 = the function P becomes equal 

 to the specific volume o£ the pure solvent, and if we adopt a 

 similar notation for the mean value of this latter quantity 

 we have 



t<0, P ^p 2 , 6) = v{0, w, 6) { i_fl,(&+£?_„) ] . . (3) 



where y5 is the compressibility of the pure solvent. 



The Thermodynamical Theory of Osmotic Pressure. 



Consider the pure solvent at a pressure p in equilibrium 

 with the solution at a pressure p, the two being separated by 

 a membrane permeable to the solvent only. The chemical 

 potential of the solvent must have the same value in the 

 solution as it has in the pure liquid state. Hence we have 



Mo, Pih e)=Ms,p,0). 



Since the chemical potential of the solvent decreases with 

 increase of concentration, and increases with increase of 

 pressure, p must be greater than p Q . The difference p —p is 

 determined as a function of s,Pq, and 6 by the above equation. 

 We will denote this difference by Cl(s, p , 0), or by 12 simply, 

 when it is not necessary to specify the particular values of 

 the variables. The above equation may be written in the 

 form 



/o(0,;>o, 0)=/oO,/>o + n, 0) . ... (4) 



The quantity H(s, p Q , 6) is usually called the osmotic pressure 

 of the solution. This term is rather misleading, since given 

 values of the temperature and concentration do not fix the 

 value of O. It is necessary to specify in addition the pure 



solvent pressure. The value of _r — 0(s, p , 6) is easily 



opo 



calculated. If an increase Ep in the pure solvent pressure 



causes an increase SO in the osmotic pressure, we have 



/o(o,jpo+$po, o )=/<>(*, po+M+n+BQ, o). 



Hence we have 



^— 12(5, p , V) = p ( H . — I- 



opo -L o[S, J> , u) 



The theory of chemical potential shows clearly that 

 osmotic pressure cannot be regarded as a specific property of 

 the solution. The osmotic pressure is simply the increase of 

 pressure necessary to counteract the lowering effect of the 

 addition of the solute on the chemical potential of the solvent. 



