412 Mr. F. G. Donnan on Raoult's Law of 



where f— original vapour-pressure, /' = reduced pressure, 

 n= number of molecules of dissolved substance, and N = 

 number of molecules of solvent. The factor k never deviates 

 far from unity, and for solutions of medium concentration it 

 is sensibly equal to unity, so that for such solutions we have 



/-/ = n 

 / N + n* 



This is the usual form in which Raoult's Law is applied. 

 This equation has been theoretically deduced from the known 

 laws of osmotic pressure by Van't Hoff and by Arrhenius. 

 The following is an attempt to deduce it from the kinetic 

 molecular theory. 



Suppose we have a liquid in equilibrium with its vapour 

 at a certain temperature t. Let the corresponding vapour- 

 pressure be/. We shall suppose the liquid and its vapour 

 to be contained in a closed vessel, and we shall also suppose 

 the temperature to remain constant, so that no permanent 

 disturbance of equilibrium due to a permanent change of 

 temperature need be considered. For this purpose we may 

 imagine the walls of the containing vessel to be perfect 

 conductors of heat, and suppose the vessel surrounded by a 

 very large reservoir at constant temperature t. 



This equilibrium of the liquid with its vapour is regarded 

 as conditioned by a mutual and equal exchange of molecules. 

 A certain definite number, a, of molecules escape per second 

 from the superficial film of the liquid and pass into the 

 vapour, while the same number, x, pass per second from the 

 vapour into the liquid. Although the escape of any one 

 particular molecule from the liquid into the vapour, and vice 

 versa, is in itself a fortuitous occurrence, yet, owing to the 

 very great number of molecules, a constant average is main- 

 tained and equilibrium preserved. 



This is the usual view of liquid-vapour equilibrium, on the 

 kinetic hypothesis. 



Considering the vapour, x will, cceteris parnbus, be propor- 

 tional to the number of molecules per unit volume — that is, 

 proportional to the density, and therefore to the pressure. 

 Thus we may write x = cf, t being constant. The number of 

 molecules in the liquid remains constant. Call this nnmber 

 N. Now suppose we dissolve in the liquid n molecules of a 

 substance which exerts no appreciable vapour-pressure at the 

 temperature t, i. e. whose molecules, for some reason or other, 

 cannot escape at this temperature from the superficial film 

 into the outer space. We have now a modified state of 

 affairs within the liquid, It is allowable to suppose, as 



