92 J. van't Hoff on the Function of Osmotic Pressure 



which, from de Vries' physiological researches (Eine Metlwde 

 zur Messung der Turgorkraft, p. 512), exhibit equal osmotic 

 pressure when they contain an equal number of molecules in 

 a given volume. 



VII. Second Confirmation o/Avogadn/s Law in its Application 

 to Solutions. — Molecular lowering of Vapour-pressure. 



The relation between osmotic pressure and the pressure of 

 a vapour in contact with liquid, which is easily developed 

 on thermodynamical principles, yields, from Raoult's recent 

 observations, a satisfactory proof of the analogy under consi- 

 deration. 



We shall begin with a general law, of which the previous 

 matter of this thesis is quite independent: — Isotonism(i. e. equal 

 osmotic pressure — from IV09 and to^o?, stretching) in solutions 

 made with the same solvent, implies equality of vapour-pressure. 

 This statement is easily proved by a reversible cycle, keeping 

 temperature constant. Imagine two solutions exhibiting 

 equal vapour-pressure, and introduce a small quantity of one 

 in the state of vapour into the other in a reversible manner, 

 i. e. by means of cylinder and piston. The vapour-pressures 

 are equal, hence this transference takes place without expen- 

 diture of work ; and also, on restoring the original condition, 

 no work is expended. But if the solvent be transferred back 

 through a semipermeable diaphragm, separating the two 

 solutions, then equal osmotic pressure must exist, else the 

 transference could not take place without expenditure of 

 energy. 



If this fundamental conception be applied to dilute solutions, 

 accepting the laws which have been explained in the preceding 

 pages, the simple conclusion follows, that if a solvent contains 

 equal numbers of molecules of dissolved substances, the 

 vapour-pressure is the same. This is merely Raoult's law 

 (Comptes rendus, lxxxvii. p. 167 ; xliv. p. 1431) of the con- 

 stancy of molecular diminution of vapour-pressure, obtained by 

 multiplying the relative diminution by the molecular weight of 

 a one-per-cent. solution ; i. e. with the difference between the 

 vapour-pressures of the solvent, before and after addition of 

 dissolved substance. The equality of molecular diminution of 

 vapour-pressure depends on the solutions containing equal 

 numbers of molecules, a close proportionality between the 

 lowering of the vapour-pressure and the concentration being 

 assumed. With ether, for example, the value fluctuated 

 between 0*67 and 0*74 (mean 071) for thirteen substances 

 dissolved in it. 



