Formula Of Duhem And Margules

The formula arrived at by Duhem, and, later, by Margules, may be written: where p1 and p2 are the partial pressures of the vapours of the two liquids A and B, and m and (1 - m) their molecular fractional amounts in the liquid mixture, taking the normal molecular weights as correct.

1 Duhem, " On the Vapours emitted by Mixtures of Volatile Substances," Ann. de l'Ecole Normale Sup., 1887, [3], 4, 9 ; " Some Remarks on Mixtures of Volatile Substances," ibid., 1889, [3], 6, 153 ; " Solutions and Mixtures," Trav. et Mem. de la faculte de Lille, 1894, III. D. ; Traite elementaire de mechanique chimique, 1899.

2 Margules, " On the Composition of the Saturated Vapours of Mixtures," Sitzungsber. der Wiener Akad., 1895, 104, 1243.

3 Lehfeldt, "On the Properties of Liquid Mixtures," 3 Parts, Phil. Mag., 1895, [V.], 40, 397 ; 1898, loc. cit. ; 1899, [V.], 47, 284.

4 Loc. cit.

5 Bancroft, "The Phase Rule," 1897.

Fig. 32. - Ethyl alcohol and benzene.

Lehfeldt's Formula

Starting from this equation, Lehfeldt adopts the formula, where t = ihe ratio of the masses of the two substances in the vapour, q the ratio in the liquid and K and r are constants. For r, Lehfeldt gives the equation :where Iia and Iib are the vapour pressures of the pure liquids at the temperature of experiment; S is the ratio of the number of molecules of the two substances in the vapour; A and B are the normal molecular weights of the components.

Margules has pointed out that, when r < 1, the equation t = Kqr leads to infinite values of dp/dM when m=0 or M = l, which does not agree with the facts, but Lehfeldt finds that the equation holds very well for mixtures which do not contain a very small proportion of either component, provided that the molecular weights of both sub-stances are normal in the liquid as well as in the gaseous state. For associating liquids the formula does not hold good at all.

Benzene And Carbon Tetrachloride

As an example we may consider the case of mixtures of benzene and carbon tetrachloride, for which Lehfeldt gives the formula: log t = 0.065 + 0.947 log q.

[In Tables 32 and 33 the molecular composition is given instead of the composition by weight.]

Table 32

In the above equation log t = log q when log q = 1 .2264, that is to say, when mass of CCl4/mass of C6H6 = 16.84. In other words, there would be a mixture of minimum boiling point, containing 5.6 per cent by-weight or 10.5 molecules per cent of benzene.

Generally, if K is positive and r is less than unity, there must be a particular value of q for which log t = log q, and there must therefore be a possible mixture of constant boiling point.

Relation Between Brown's And Lehfeldt's Formulae

In the equation t = Kqr, when r = l, t=Kq, or Brown's law holds good. Lehfeldt himself gives for mixtures of toluene and carbon tetrachloride the formula which agrees almost exactly with that given on

Carbon Disulphide Ana Metnylal

As an example ot two substances, the molecular weights of both of which are presumably normal, but which form a mixture of maximum vapour pressure considerably higher than that of either component, we may take carbon disulphide and methylal, examined by Zawidski.

In Table 33 are given the observed molecular percentages of carbon disulphide and those calculated by means of the formula log t = 0.036 +

0.619 logq.

Table 33

The agreement is not very good, and there appears to be evidence of curvature.