Speyers

Speyers1 concludes that the relation between vapour pressure and molecular percentage composition is always represented by a straight line when the molecular weight of each substance is normal in both the liquid and gaseous states. The equation, where m is the molecular percentage of A, should then hold good.

Van Der Waals

Van der Waals 2 considers that the last-named relation is true when the critical pressures of the two liquids are equal and the molecular attractions agree with the formula proposed by Galitzine and by D. Berthelot,

Guthrie was clearly in error in taking percentages by weight, and Speyer has certainly made his statement too general, for there are very many cases known in which the relation does not hold, although both the liquids have normal molecular weights (for example, n-hexane and benzene, or carbon tetrachloride and benzene).

Kohnstamm's Experiments

In order to test the correctness of the conclusion arrived at by Van der Waals, Kohnstamm3 has determined the vapour pressures of various mixtures of carbon tetrachloride and chlorobenzene, the critical pressures of which, 34,180 mm. and 33,910 mm., are nearly equal, and he finds that the curvature is not very marked.

At the temperature of experiment, the maximum deviation from the straight line amounted to about 6 mm. on a total calculated pressure of 76 mm., or about 7.9 per cent. It is probable that in this case, the formula does not accurately represent the facts.

Closely Related Compounds

From a study of the alteration of volume produced by mixing various pairs of liquids together, F. D. Brown4 concluded that this change would probably be smallest in the case of closely related chemical compounds, and he obtained some indirect evidence in favour of this view ; it seems a fair assumption that for such mixtures this, and other physical relations, should be of a simple character.

1. Speyers, "Some Boiling Point Curves," Amer. Journ. Sci., 1900, IV., 9, 341.

2. Van der Waals, "Properties of the Pressure Lines for Co-existing Phases of Mixtures," Proc. Roy. Acad. Amsterdam, 1900, 3, 170.

3. Kohnstamm, "Experimental Investigations based on the Theory of Van der Waals," Inaugural Dissertation, Amsterdam, 1901.

4. F. D. Brown, " On the Volume of Mixed Liquids," Trans. Chem. Soc, 1881, 39, 202.

Experimental Determinations By Statical Method

Direct measurements of vapour pressures by the statical method have, however, in nearly every case been carried out with mixtures of liquids which have no very close chemical relationship, but Guthrie (loc. cit.) made such determinations with mixtures of ethyl bromide and ethyl iodide, and his results make it probable, though not certain, that the equation holds good for this pair of substances.

It is not known, however, whether the critical pressures of ethyl bromide and ethyl iodide are equal, though it is very probable that they may be.

Linebarger 1 has determined the vapour pressures of a few mixtures of each of the following pairs of liquids by drawing a current of air through them (p. 70): - benzene and chlorobenzene, benzene and bromo-benzene, toluene and chlorobenzene, toluene and bromobenzene. His results are in fair agreement with the above formula, but unfortunately the method, in one case at least (carbon tetrachloride and benzene), gave inaccurate results, and it is therefore impossible to place complete reliance on the experimental data. The critical pressures of these substances have been determined and those of the components of the mixtures are in no case equal.

Determinations By Dynamical Method

The vapour pressures of mixtures may be determined by the dynamical method ; the still is kept at a uniform temperature by means of a suitable bath, and the pressures are observed under which ebullition takes place. This method has been adopted by Lehfeldt (p. 64) and by Zawidski (p. 65), and the latter experimenter finds that mixtures of ethylene dibromide with propvlene dibromide give results in conformity with the formula

The critical pressures of these substances are not. however, known.

Again, the vapour pressures of mixtures may be determined indirectly from their boiling points under a series of pressures. The boiling points of each mixture are mapped against the pressures, or, better, the logarithms of the pressures, and from the curves so obtained the pressure at any required temperature can be read off.

In order to obtain the complete vapour pressure curve for two liquids at a given temperature, the boiling-point determinations for a considerable number of mixtures would have to be carried out through a wide range of pressure, but a less elaborate investigation is sufficient to ascertain whether or not the above formula is applicable.

Suppose that we determine the boiling points of mixtures containing, say, 25, 50 and 75 molecules per cent of the less volatile component, A, at a few pressures above and below 760 mm., in order to ascertain the boiling points under normal pressure with accuracy. If, then, we know the vapour pressures of each component at the three temperatures, we may calculate the theoretical vapour pressure of each mixture from the formula.

1 Linebarger, "On the Vapour Tensions of Mixtures of Volatile Liquids," Journ. Amer. Chem. Soc, 1895, 17, 615 and 690.