The Expansion of Gases on Mixing, Especially at Very Low Pressures. I. Its Relation to the Empirical Calculation of the Fugacities in Gaseous Mixtures

From plots of the expansion of a gas in a mixture, (${\overline{v}}_1-v_1$), or of the expansion of gases on mixing to form a mole of mixture from the pure gases at constant temperature and pressure, ($\Sigma x_1{\overline{v}}_1-\Sigma x_1{v}_1$), as functions of the pressure, it is clear that these quantities do not vanish at zero pressure. These expansions do not vanish for mixtures of ethylene and argon, ethylene and oxygen, nitrogen and hydrogen, and nitrogen and methane, in which cases the limiting values are, according to the existent data, finite and positive. Values for zero pressure can be calculated from a "linear combination of constants" in the equation of state for the mixture, which values in all cases but the first are evidently suitable end-points for the extrapolation to zero pressure. In the case of argon and ethylene the calculated points are not so suitable, but are reasonably good. In this case, the Lorentz formula for the mutual co-volume fits very well and the corrections on the Lewis and Randall rule for argon and ethylene have been calculated to 50 atmospheres from curves drawn according to the Lorentz formula. In a number of cases the corrections differ by 1 percent from those calculated by previous investigators, who assumed the expansions to vanish at zero pressure. The empirical calculation of fugacities from the pressure data of gaseous mixtures is in general improved by, if it does not in fact require, some knowledge of the expansions at zero pressure.