## Abstract

An expression for the chemical potential due to Kirkwood & Boggs is adapted to give rigorous expressions for Henry's coefficient (H) for the solubility of a gas in a liquid and for the temperature dependence of this coefficient, in terms of radial distribution functions (g) and a molecular coupling parameter. If the solute-solvent and solvent-solvent molecular interactions are similar in strength the expression for $T$ dln$H$/d$T$ reduces to $T\frac{\text{dln}H}{\text{d}T}=\frac{L}{RT}+(1+\alpha T)\ln \frac{p^{\circ}}{H}$ (i) where $L,\alpha \ \text{and}\ p^{\circ}$ are the molar latent heat, the coefficient of thermal expansion and the vapour pressure of the pure solvent. Equation (i) is closely obeyed by the simple systems Ar-CH$_{4}$, Ar-O$_{2}$ and Ar-N$_{2}$, though it becomes markedly less accurate when applied to the solubilities of common gases in liquids. This is to be expected since the solute-solvent and solvent-solvent intermolecular force fields are then very different. By assuming these force fields to be of the Lennard-Jones type and making simplifying assumptions relating g for the solute in the solvent to g for the pure solvent, the equation $T\frac{\text{dln}H}{\text{d}T}=\frac{L}{RT}+(1+\alpha T)\ln \frac{p^{\circ}}{H}-Q_{0}\left(1-\frac{\epsilon _{\alpha \beta}^{\circ}\ \sigma _{\alpha \beta}^{3}}{\epsilon _{\beta \beta}^{\circ}\ \sigma _{\beta \beta}^{3}}\right)$ (ii) is then obtained in which $Q_{0}=\frac{L}{RT}-1+\alpha T(1+\alpha T)\ln \frac{p^{\circ}V_{\beta}}{RT}$, where $V_{\beta}$ is the molar volume of the solvent, $\epsilon _{\beta \beta}^{\circ},\sigma _{\beta \beta},\epsilon _{\alpha \beta}^{\circ}$ and $\sigma _{\alpha \beta}$ are the Lennard-Jones force constants for the solvent-solvent and solute-solvent interactions respectively. This equation is found to predict $T$ dln$H$/d$T$ for gases dissolved in common liquids with sufficient accuracy to be of practical value. The equation $T\frac{\text{dln}H}{\text{d}T}=2-\alpha T+(1+\alpha T)\ln \frac{RT}{V_{\beta}H}$, valid at solvent reduced temperatures between about 0.5 and 0.65, is found in practice to provide a useful approximation to (ii) both for simple systems and for the permanent gases dissolved in common solvents. Expression (i) is shown to be related to an expression previously developed by Longuet-Higgins.

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