Young — On Brown's Formula for Distillation. 669 



It will be seen that the agreement is very close for the mixture richest in 

 benzene, but that it. becomes less close as the percentage of benzene decreases. 

 At the worst, however, the agreement is fair. 



Duhem (1887-1894) and Margules (1895) independently proposed the 

 equation 



d log Pa _ d log p B 

 d log M d log (1 - m) 



.or the relation between the molar composition of the liquid mixture and the 

 partial pressures p A and p B of "the components in the vapour, and the 

 formulae of Lehfeldt and of Zawidski are based on this equation. 



In recent years M. A. Eosanoff and his co-workers have carried out a series 

 of excellent experimental and theoretical researches on distillation ; and in 

 1914 Eosanoff, Bacon, and Schulze (J. Amer. Chem. Soc, xxxvi, 1993) pointed 

 out that the method of Margules, which depends on the graphic measurement 

 of the slope of the total pressure-curve at its two ends, is liable to yield 

 inaccurate results. 



They, therefore, sought to formulate a general relationship, even if only 

 empirical, between the total and partial vapour-pressure curves, 



dT 

 They found that, in the cases examined, if a set of values of ^— were 

 J dm 



plotted against the corresponding values of log [p A (1 - M)/p B M], the result 



was a straight line passing through the origin of the coordinates, which 



indicated that the simplest possible relationship exists betweeir the two 



quantities. This apparently general law is expressed by the equation 



dV 



g£ = (l/K) log [p A (1 - M)/_p E M], 



where 



l/K = (P A -P B )/(logP A -logP B ). 



Therefore 



g = [(P A - P E )/(l0g P A - log P B )] log [p A (1 - M) /jfcM] .... (I) 



The authors state that this equation is not in conflict with the thermodyna- 

 mieal equation of Duhem and Margules, and they show that it faithfully 

 reproduces the experimental results in all types of cases, even when mixtures 

 of maximum or minimum vapour-pressure are formed. 



Eosanoff, Bacon, and Schulze (loc. cit.) have determined the vapour- 

 pressures of mixtures of benzene and toluene at 79-70°, and find that the data 

 are almost perfectly reproduced by the formula 



P = 288-438 + 466-519M - 56'464m 3 + 100-281M 3 - 49-971M 4 , (II) 



where m is the molar fraction of benzene in the liquid mixture. 



5 l 2 



