448 Dr. F. Tinker on Osmotic Pressure. 



or in words, the free space within a dilute solution having 

 no heat of dilution is equal to RT times the coefficient 

 of compressibility. This relationship is important, for it 

 enables the " free space " within a dilute solution to be 

 calculated very easily. Since the pure solvent is the 

 limiting case of a dilute solution, and has perforce no 

 heat of dilution, it will be seen that the above relationship 

 should hold absolutely for pure liquids. It is to be noted, 

 however, that the coefficient of compressibility must be 

 taken at atmospheric pressure and not at relatively high 

 pressures *. 



We can now use equation [25] for obtaining the general 

 equation for the osmotic pressure in terms of the con- 

 centrations, volume change on solution, and the coefficients 

 of compressibility /3 b j3 2 , and for the pure solvent, pure 

 solute, and solution respectively. 



From equation [20], viz. 



p Vl ' (0) (i-^p) 



by substituting 



( Yj - b,) = &RT, V 2 - b 2 = &RT, 



and V/ (a) = Y Hu) -^ {(V, - b$- (j,-b,+e a ) } 



(cf. equation [71), 

 we get ' L J 



p { v «-^(A-A-l5?)}{' i -H 



= et log . I N>«_g ( ft " ft+ M ) I + Q. 



l and 2 are both usually very small, so that we can count 

 A— 2 as zero without appreciable error. 

 The equation then becomes 



It is clear also that with all but the strongest solutions we 



* As is well known, the coefficient of compressibility varies con- 

 siderably with the pressure. 



