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XXXIV. The Vapour Pressures of Binary Liquid Mixtures : 

 Kinetic Theory based on JJieterici's Equation. By Frank 

 Tinker, M.Sc* 



IN a series of papers published at intervals during the last 

 sixteen years t? Dieterici has advanced a much more 

 fundamental equation of state than the better known Van der 

 Waals' expression. The equation in question, viz., 



« uRT , [1] 



v — b 



in which the constants a and b have a meaning similar to 

 that given them by Van der Waals, is based on the following 

 assumptions % : — 



(i.) The pressure ir within a fluid is given by the equation 



tt(u-&) = RT, [2] 



i. e., the product pressure X free space is given by the 

 perfect gas equation ; being independent of the size of 

 the molecules, or of the forces between the molecules, and 

 the same for all fluids at the same temperature. 



(ii.) The pressure at the surface of the fluid is always less 

 than that in the interior because of the inward pull exerted 

 by the forces of cohesion. Assuming that the boundary 

 pressure is proportional to the number of molecules which 

 have kinetic energy enough to overcome the inward pul], 

 Dieterici showed that this boundary pressure (p) is related 

 to the pressure within the fluid (V) by the exponential 

 equation 



p = 7re~wr, [3] 



where A is the work done by the molecule in reaching the 

 surface. Combination with equation [2] gives immediately 



RT _-A 



and making the further assumption that A is proportional 

 to the density of the fluid, and equal to - where a is a 



* Communicated by Principal Sir 0. J. Lodge, F.R.S. 



t Ann. Thy 's. u. Chem. xi. p. 700 (1899); Ann. der Physik [4] v. 

 p. 51 (1901) ; ibid. xxv. p. 269 (1908) ; ibid. xxxv. p. 220 (1911). 



"J; The assumptions aie also similar to Van der Waals', but are given 

 a different quantitative expression. The two equations become identical 

 at low and medium pressures. 



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