88 EEPORT— 1891. 



tical point, of view. Exact experiments with osmotic cells, 

 whether of the natural or the artificial kind, are difiBcult to 

 carry out. It is fortunate therefore that the laws of osmotic 

 pressure lead up to two other generalisations, each of which 

 has given us a method for determining molecular weights that 

 is of greater value to the chemist, because practically easier, 

 than the theoretically simpler parent method. Parenthetically 

 I should explain that I am by no means following the chrono- 

 logical order of discovery. 



Starting with the laws of osmotic pressure, van't Hoff has 

 mathematically demonstrated that the vapour-pressure of a 

 solution must be lower than that of its pure solvent at the 

 same temperature, and that the relation between these two 

 pressures may be expressed by the following formula : — 



f = f \ i_ ^-^ \ , where/' is the vapour-pressure of the solu- 

 tion, / that of the pure solvent, n the number of molecules of 

 the substance in N molecules of the solvent, and s and s' the 

 specific gravities of solvent and solution respectively. If only 

 very dilute solutions be employed, s and s' are so nearly equal 

 that they may be left out of account, but this is not true of 

 stronger solutions. In the former case the equation becomes 



/'=/-!_ ^^1 ; so that one gramme-molecular weight of any 



substance dissolved in a hundred gramme-molecular weights of 

 any solvent lowers its vapour-pressure by ^ho ^^ i^^ value. It 

 follows from this that dilute solutions of different substances 

 in the same solvent which have the same osmotic pressure (or 

 are isotonic) have also the same osmotic pressure. Obviously, 

 then, measurements of vapour-pressure may take the place of 

 measurements of osmotic pressure for the determination of 

 molecular weights. Eaoult was the first to use the method ; 

 indeed, he did so before the theory of it had been explained. 

 But we owe the prettiest and simplest development of it to 

 Tamman and Walker. This consists in passing the same 

 current of air for some time through first the solution and 

 then the pure solvent, contained in modified Liebig's bulbs, 

 which are weighed separately. The loss of weight of the 

 solution is proportional to /', and that of the solvent to /— /', 

 while the sum of the losses is proportional to /. If, then, 

 we know the concentration of the solution, we have all the 

 necessary data for ascertaining the molecular weight of the 

 substance. 



The second generalization concerns the freezing-point. 

 When a dilute solution is cooled to the point at which the pure 

 solvent would freeze, it does not do so, but at a somewhat 

 lower temperature the solvent begins to separate out in the 



