546 SCIENCE PROGRESS 



that the gas-equation PV = RT could be applied directly to 

 solutions, if " osmotic pressure " were substituted for " gas 

 pressure." This remarkable generalisation appeared to illu- 

 minate a vast range of difficult and puzzling phenomena and 

 at the time of its introduction it was widely believed that the 

 problems of osmotic pressure and of solutions had for the most 

 part been finally solved. 



Van't Hoff's conclusions were based on the measurements 

 which had been made by Pfeffer in the botanical laboratory at 

 Bonn about the year 1876. They were supported by a con- 

 sideration of cognate properties, such as the lowering of 

 vapour pressure and the depression of the freezing-point in 

 solutions, properties which had been studied by Raoult which 

 were now shown to be related thermodynamically to the 

 osmotic pressure. Using the somewhat scanty data then 

 available, Van't Hoff showed that Boyle's Law could be 

 applied to solutions, since (as Pfeffer had found) the osmotic 

 pressure was proportional to the concentration of the solute and 

 therefore inversely proportional to the volume to which it was 

 diluted in the solution. He next discovered the fact (which 

 had been overlooked by Pfeffer) that the small temperature 

 coefficient of osmotic pressure is identical with the corresponding 

 coefficient in gases, so that osmotic pressure is (like gas- 

 pressure) directly proportional to the absolute temperature. 

 Having thus proved that osmotic pressure could be expressed 

 by the equation PV = RT, he calculated from Pfeffer's data the 

 value of the constant for a gramme-molecular proportion of sugar 

 and found that it was identical with the constant of the gas- 

 equation PV = RT. This equation could therefore be used 

 equally well to calculate the pressure of a gas or the osmotic 

 pressure of a solution. 



The validity of the equation in the case of solvents other 

 than water and of solutes other than sugar was deduced from 

 the substantial identity, in the case of twelve solvents, of Raoult's 

 " Molecular lowering of the vapour pressure " with figures 

 calculated from the formula K = M/100 (K = molecular lowering, 

 M = molecular weight) and of Raoult's " Molecular depression 

 of the freezing-point " with figures calculated from the formula 

 t = o'02T 2 /W (t = mol. depression, T = abs. temp, of f.p., W = 

 latent heat of fusion) in the case of five solvents. As both 

 formulae were based on the assumption that osmotic pressure 



