438 Dr. F. Tinker on Osmotic Pressure. 



2. The Phenomena of Osmotic Flow. 



Consider a semipermeable membrane having a thickness 

 sufficiently great for it to be regarded as a separate phase 

 in the osmotic system *. Let the pure solvent be on one 

 side of the membrane and the solution on the other. The 

 solvent tends to diffuse into the membrane from both the 

 pure solvent and the solution ; a pressure p 1 (say) tending to 

 be generated within the membrane by the pure solvent and 

 a pressure /?/ (say) by the solution. From equation [9] 



—, is given by the equation 



£-^-{=F.-5(>-W>*}'t* 



where ~dB 1 is the excess of the latent heat of vaporization of 

 the solvent from the pure solvent into the membrane over 

 the heat of vaporization of the solvent from the solution 

 into the membrane f . 



It is evident that the solvent will flow from the pure 

 solvent to the solution if the pressure p x generated in the 

 membrane by the pure solvent is greater than the pressure 

 Pi generated in the membrane by the solvent which is in 

 the solution. 



That this will almost invariably be the case under normal 

 conditions can be shown as follows. Developing equation 

 [13] we get 



Pl^PL = f N ^ _ *( I _ V^ !>lSL. 1 

 Pl ' [ N NV Vx-fti ) i 



= S\ Y 1 -b 1 j ( a PP rox 0> • • • L 1 ^] 



"6Bi 



since e^v does not usually differ very much from unity. 



Now, in practice, e^ is always positive, whether BBj is 

 positive or negative, for cJBj, which is usually negligible, is 

 of a much less order of magnitude than RT. Also (V 2 — b 2 + e) 

 is positive, except in the unlikely case in which the total 

 expansion (e) per solute molecule dissolved is negative and 

 actually greater than the free space (V 2 — lh) of the solute 

 itself. Hence p } — p x ' will almost invariably be positive, so 



* The actual colloidal membranes satisfy this condition. 



t The heat evaporation into the membrane is obviously not the same 

 as that into the vapour phase proper. It is clear, however, from the 

 general nature of the proof on p. 435 that the equations for p are similar 

 to those for p. 



