Associated Substances

Zawidski included in his investigation some pairs of substances, of which the molecules of one component are associated in the liquid state (water), or in both the liquid and gaseous states (acetic acid), and he concludes that his formula can be employed for such mixtures, provided that in calculating the values of m and 1 - m we take the average molecular weight of the associated liquids under the conditions of the experiment. As a rule, however, the experimental data at present available are only sufficient to afford a rough estimate of the average molecular weight of an associating substance when mixed with another liquid.

Rosanoff's Formulae

In recent years M. A. Rosanoff and his co-workers have carried out a series of excellent experimental and theoretical researches on distillation ; and in 1914 Rosanoff, Bacon and Schulze1 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.

They found that, in the cases examined, if a set of values of were plotted against the corresponding values of log [pA(l -m)/pbm], the result was a straight line passing through the origin of the co-ordinates, which indicated that the simplest possible relationship exists between the two quantities. This apparently general law is expressed by the equation

The authors state that this equation is not in conflict with the thermodynamical 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.

From Zawidski's measurements of the vapour pressures of mixtures of carbon tetrachloride and benzene at 49.99° they obtain the equation.

P = 268.075 + 80.853M - 43.826m2 + 16.531m3 - 13.695m4, according to which a mixture containing 91.65 molecules per cent of carbon tetrachloride has a vapour pressure of 30843 mm., which is a maximum, the vapour pressure of pure carbon tetrachloride being 308.0 mm. The existence of a mixture of maximum vapour pressure is thus confirmed (pp. 84, 89, 92), and the calculated molar percentage of benzene, 8.35, agrees well enough with the values previously found. For carbon tetrachloride (a) and benzene (b)

1 J. Amer. Chem. Soc., 1914, 36, 1993.

Therefore log10 [pA(1 - m)/pbm] =0.122115 -0.132383M +0074900m2 - 0.082734m3.

The observed and calculated results are given below.

Table 35

The agreement is good, and it is also very satisfactory in the case of ethyl iodide and ethyl acetate and of chloroform and acetone, which form mixtures of maximum and minimum vapour pressure respectively. The agreement in the last case is specially noteworthy for there can be little doubt that acetone forms complex molecules to some extent. For chloroform and acetone the equation is log10 [pA(l - M)/pBM] = -0.199592-M4361m + 3.66677m2-2.07687m3; and the results are given on following page.

Table 36

The case of benzene and toluene has already been considered (p. 85).