446 Dr. F. Tinker on Osmotic Pressure. 



If instead of writing V x (i. e. the mol. vol. of the liquid 

 solvent) we write V (the volume of solution containing 



1 gm. mol. of solute = — Vi), and q for ^- Q, we get 



PV = RT + ? [22] 



This is the simple gas equation corrected for the heat of 

 dilution which has already been given by Bancroft *. In 

 this connexion it is to be noted that the osmotic pressure of 

 a dilute solution is given by the simple gas equation only 

 when the solution has zero heat of dilution. If the heat of 

 dilution is positive the osmotic pressure is abnormally high, 

 whilst if it is negative the osmotic pressure is abnormally 

 low. Bancroft, for instance, has shown that dilute solutions 

 of sulphuric acid in water, sodium in mercury, and resorcinol 

 in alcohol have osmotic pressures which are several times as 

 great as would be given by the gas law ; whilst Kahlenberg f 

 has demonstrated that solutions of cane-sugar, lithium 

 chloride, and certain other solutes in pyridine give osmotic 

 pressures which are only a fraction of what the simple gas 

 law would require them to be. 



It is apparent also from the method of deriving the pre- 

 ceding equation \_22~\ that the abnormalities in the osmotic 

 pressure of dilute solutions have their origin in abnormalities 

 in the vapour pressure, and hence ultimately in the difference 

 in the intrinsic pressures of the solvent and solution. Traube's 

 surface-tension theory is therefore of value in predicting 

 abnormalities in the osmotic pressure also. As a general 

 rule, if the surface-tension of a solution is low the osmotic 

 pressure would also tend to be low ; and vice versa. Hence, 

 in many cases, the apparent flow of the solvent from the 

 region of low surface-tension to high (supra, p. 440). 



(C) Compressibility Relationships at Osmotic Equilibrium. 



It has been pointed out previously that the application of 

 hydrostatic pressure to the solution causes both ir^pi, and p/ 

 to increase, owing to the fact that compression reduces ne and 

 brings the molecules inside the solution more closely together. 

 We can obtain the contraction at osmotic equilibrium as 

 follows : — 



The general equation connecting 7r x and tt/ is [5], viz. 



* Journ. Phys. Chem. x. p. 322 (1906). 

 t Ibid. x. p. 141 (1906). 



