442 Dr. F. Tinker on Osmotic Pressure. 



magnitude and direction of osmotic flow is ultimately deter- 

 mined, partlv by the relative concentrations of the two 

 solutions, partly by their relative heats of dilution, surface- 

 tensions, intrinsic pressures, &c, and partlv by the relative 

 magnitude of the volume changes which the solvent 

 undergoes during the process of solution. If, on the one 

 hand, we eliminate surface-tension and intrinsic pressure 

 differences, &c, by working with two ideal solutions on 

 opposite sides of the membrane, the direction of flow is 

 invariably from the weaker solution to the stronger one. 

 If, on the other hand, we eliminate concentration differences 

 and work with two non-ideal dilute solutions of equal 

 strength, the direction of flow is (as shown above) from the 

 solution having the lower heat of dilution, surface-tension, 

 intrinsic pressure, &c, to that having the higher value of 

 these quantities ; in fact, Trail he's theory of osmosis holds 

 good. Whilst if we eliminate both concentration and 

 surface-tension differences, &c, by working with two equally 

 strong non-ideal solutions having equal heats of dilution, 

 the direction of flow will be towards the solution in which 

 the solvent has undergone the greater expansion during the 

 process of solution. 



3. The Conditions at Osmotic Equilibrium. 

 Consider again the case in which pure solvent and solution 

 are separated by a semi-permeable membrane which is thick 

 enough to be regarded as a separate phase in the osmotic 

 system *. Let the pure solvent be under the atmospheric 

 pressure a, and the solution under such a hydrostatic pressure 

 P that the solvent and solution are in osmotic equilibrium. 



(a) Relationship between the Pressure of the Solvent in the 



various parts of an Osmotic System, the latter being at 



Equilibrium. 



It is evident that, when a system is at osmotic equilibrium, 



the pressure (/0i' (P) ) generated inside the membrane by the 



solution must be equal to the pressure (p l{a) ) generated by 



the pure solvent, just as the vapour pressures proper of pure 



solvent and solution are equal at osmotic equilibrium f. 



* Footnote (*) on p. 438. 



t Thomson & Pnynting, ' Properties of Matter,' p. 191 . A. W. Poiter, 

 Proc. Roy. Soc. A. lxxix. p. 519 (1907), ibid. A. Ixxx. p. 457 (1908). The 

 ultimate proof of both the theorems mentioned is very simple. If the 

 pressure were not uniform in either the membrane or in the vapour phase 

 proper, a process of diffusion would take place. The fact that work could 

 be obtained from the process can be made to contradict the second law of 

 thermodynamics. 



