296 Mr. F. Tinker on' the Vapour Pressures 



constant for the substance in question, the equation [4] 

 becomes identical with equation [1]. 



Dieterici himself has shown that his equation gives ex- 

 cellent results when applied to critical data in the usual 

 way. Uecently others also have taken up the development 

 of the subject. In particular McDougall has lately demon- 

 strated * that the pressure of the saturated vapour over a 

 liquid is also given by the equation to a high degree of 

 accuracy. 



In view, therefore, of the interest which has been revived 

 in the causes for the deviations of the vapour pressures of 

 binary mixtures from the well-known law of admixture in 

 molecular proportions, and on account of the importance of 

 the question to the subject of osmotic pressure, it seemed 

 that it would be of interest to extend the application of 

 Dieterici's equation to such mixtures also. Van Laar has 

 already studied the subject from the thermodynamic side. 

 It will be seen from the treatment which follows that 

 Dieterici's equation leads to expressions for the partial and 

 total vapour pressures identical in form with those obtained 

 by Van Laar with the aid of the thermodynamic potential ; 

 but that the kinetic treatment enables the subject to be 

 developed further, and gives a very simple relationship 

 between the variation of the vapour pressure of the mixture 

 from the theoretical, and the variation of the latent heat of 

 vaporization from the theoretical value calculated by the 

 mixture rule. 



(a) Relation betiveen the Partial and Total Liquid Pressings 

 in a binary mixture and the relative molecular concen- 

 trations of the two components | . 

 Let X and Y be the two components of the liquid mixture, 



and let N molecules of X be mixed with n molecules of Y. 



* Journ. Amer. Chem. Soc. xxxviii. p. 528 (]916). Mr. McDougall 



shows that 





RT --^ RT --±- RT - 



1 v-i — b v 2 — o b 



where v r and v 2 refer to the specific volumes of the liquid and vapour 

 respectively, and where a and b have the values given by the equations 



1 1,1 Sv^vz Drp v 2 



- = - + -; a= — : KTloge— . 



t In what follows T use the term liquid pressure (w) to denote the 

 bombardment pressure exerted by the liquid molecules on either side of 

 a plane of unit area placed anywhere within the liquid. It is of course 

 different from the internal or intrinsic pressure due to cohesion. In 

 another place (' Nature/ vol. xcvii. p. 122 (1916)) I have also called it 

 the " diffusion pressure " to distinguish it from the latter. 



