556 Dr. T. M. Lowry on Osmotic Pressure from 



migrating from the membrane back into the solution. This 

 would lead to a disturbance of the equilibrium between the 

 solvent and the liquids on either side, and would be sufficient 

 to produce an osmotic flow and a consequent osmotic pressure. 



Deduction oe 1 the Gas-Formula from the Kinetic 

 Theory of Osmotic Pressure. 



Of the theories of osmotic pressure that have hitherto been 

 put forward, that of van 't HofT is the one that leads most 

 directly to a simple quantitative explanation of the phenomena. 

 Poynting, in developing his theory quantitatively, considered 

 that solute molecules and stable compounds of solvent and 

 solute would merely alter the effective surface of the liquid 

 without changing the relative rates of evaporation and con- 

 densation ; only in the case of labile compounds was it consi- 

 dered possible that the rate of evaporation might be checked 

 without altering the raie of condensation; on this basis a 

 quantitative explanation was only possible on the imprac- 

 ticable assumption that all ordinary solutes are loosely mono- 

 hyd rated in aqueous solutions. The more recent theory that 

 osmotic pressure depends on a disturbance in the equilibrium 

 between simple and polymerized solvent molecules, e. g. y 

 nH 2 < > ^ H 2>l O w (Armstrong, Proc. Roy. Soc. 1906, A. 

 lxxviii. pp. 264-271), has also, as yet, failed to yield a quan- 

 titative interpretation of the pressures produced. 



The quantitative interpretation of the kinetic theory of 

 osmotic pressure follows at once from Nernst's proof of the 

 relationship between osmotic pressure and vapour pressure 

 ( k Theoretical Chemistry/ pp. 124-129). Thus if N be the 

 number of gram-molecules of solvent, and n the number of 

 gram-molecules of solute in unit volume of the solution, the 

 validity of the gas-formula for osmotic pressure is readily 

 deducible from the equation 



where p is the vapour-pressure of the solvent, and p T that of 

 the solution *. If the simple assumption is made that the 

 molecules of solvent are uniformly distributed in the surface 

 layer, and that the spacing or packing is the same as in the 

 pure solvent, it follows at once that the rates of evaporation 

 from unit surface of solvent and solution will be in the ratio 



* The value of N is determined by the molecular weight of the solvent 

 as it exists in the vapour, and not by its molecular weight in the liquid 

 state. 



