Though the paralleHsm is not perfect, these results show that, within 

 the Hmits of the methods available at the time, the osmotic pressure of a 

 cane sugar solution is equal to the pressure of a gas at the same tempera- 

 ture and containing the same number of molecules as there are solute mole- 

 cules in unit volume. 



Starting with cane sugar, van't Hoff showed that approximately the 

 same relation could be calculated for other dissolved substances such as 

 invert sugar, malic acid, tartaric acid, citric acid, magnesium malate and 

 citrate, all of which de Vries had shown to be isotonic in equimolecular 

 concentrations. This offered confirmation for Avagadro's law as applied 

 to dilute solutions. 



From the above work van't Hoff made the important deduction that 

 the osmotic pressure of a solution is equal to the pressure which the dis- 

 solved molecules would produce if they existed as a gas in the volume oc- 

 cupied by the solution. This kinetic view of osmotic pressure has been 

 termed the bombardment theory (Glasstone, 1940) or the solute pres- 

 sure theory (Meyer and Anderson, 1939) of osmotic pressure. Ob- 

 viously, as van't Hoff pointed out, his deduction applies only to very dilute 

 solutions ; theoretically, it would apply only to solutes that obey Henry's law 

 and to solvents whose vapors are perfect gases ; practically, as expressed 

 in van't Hoff's equation, it holds fairly well for aqueous solutions of non- 

 electrolytes below 0.1 M in concentration. 



Refinement of the Osmotic Pressure Law: — In addition to the 

 solute pressure theory some advocate a solvent pressure theory (Meyer 

 and Anderson, 1939), whereas others advance the vapor pressure theory 

 (Callander, 1908). To one familiar with modern views of molecular 

 kinetics, it should be clear that the diffusion pressure of solute and solvent 

 molecules in a solution as well as their vapor pressures should all be inter- 

 related. And, theoretically at least, changes in concentration should alter 

 pressures not in proportion to the ratio of solute molecules to a fixed vol- 

 ume of solvent as is implied by van't Hoff's law, but in relation to the 

 mol fraction of solute in the solution (Lewis, 1908). 



Assuming that the vapor of the solvent obeys the gas laws, the relation 

 between the osmotic pressure of a solution and the vapor pressure is as 

 follows : 



P„V = RTlnA ^^^ 



P 

 where 



Pq = osmotic pressure of the solution, 



V = the partial molecular volume of the solvent under standard pressure, 

 p = vapor pressure of the solvent above the solution, 

 Po = vapor pressure of the pure solvent. 



