The Empirical Calculation of the Fugacities in Gaseous Mixtures. II. Its Relation to the Tangents on Certain Thermodynamic Diagrams. Approximate Equations For Some Important Thermodynamic Properties of Gas Mixtures

The thermodynamic account of the behavior of mixtures of real gases at constant temperature may be resolved into two problems: (1) The $p-v-T$ relationships for pure gases, as embraced in equations of state; and (2) The behavior of gases on mixing at constant temperature and volume, as expressed for example by the excess ${\overline{v}}_1-v_1$ of the partial molal volume of a gas in the mixture over its volume when pure at the temperature and pressure of the mixture. In part 1 it was shown that the limiting value of ${\overline{v}}_1-v_1$ at zero pressure is finite and positive and can be calculated with considerable success by a linear combination of constants previously tested at higher pressures. We are consequently in a position to calculate the limiting value of the tangents in certain thermodynamic diagrams, and equations are here given for so doing. These include a group of functions of the energy, entropy, heat content, and the $t-p$ and $t-v$ thermodynamic potentials, as well as a smaller group of functions of the fugacity and equilibrium pressure. The former group takes advantage of the resolution into two problems mentioned above. It is a noteworthy result that their limiting tangents depend only on the cohesive pressure $A$ term of the equation of state. From the limiting values of the tangents there have been derived, by approximate integration, equations explicit in the pressure for the change of energy, entropy, heat content, $t-p$ and $t-v$ thermodynamic potentials on mixing gases at constant temperature and pressure. From a consideration of the relative accuracy of calculation demanded in the two parts of the resolution it is believed that these approximate equations should furnish, in connection with adequate equations of state, satisfactory thermodynamic calculations for pressures not too high. It is shown that the variation of the mass action function $K_p$ with composition at constant temperature and pressure depends at low pressures chiefly on the cohesive pressure $A$ constants of the gases involved.