https://doi.org/10.1351/goldbook.15377
Volume \(V^{\rm{g}}\) of an amount \(n_{\ce{B}}^{\rm{l}}\) of a dissolved gas calculated at given temperature \(T\) and pressure \(p\) divided by the volume of the dissolving liquid of volume \(V^{\rm{l}}\) and containing an amount \(n_{\ce{A}}\) of solvent at the same temperature \(T\) and pressure \(p\).
Notes:
- There are two Ostwald coefficients, depending on whether the liquid is the equilibrium solution or the pure liquid, with mathematical definitions:
Ostwald coefficient, solution reference \[L_{\ce{B}} = V^{\rm{g}}(T,p,n_{\ce{B}}^{\rm{l}})/V^{\rm{l}}(T,p,n_{\ce{A}}, n_{\ce{B}}^{\rm{l}}) = c_{\ce{B}}^{\rm{l}}/c_{\ce{B}}^{\rm{g}}\] Ostwald coefficient, pure solvent reference \[L_{\ce{B}}^{\ast} = V^{\rm{g}}(T,p,n_{\ce{B}}^{\rm{l}})/V^{\rm{l}}(T,p,n_{\ce{A}})\] - The relations between the molality \(m_{\ce{B}}(p)\) or mole fraction \(x_{\ce{B}}(p)\) of dissolved gas and the Ostwald coefficients are \[\begin{array}{l} \frac{1}{x_{\ce{B}}(p)} = 1 + \frac{1}{m_{\ce{B}}(p)M_{\ce{A}}} = 1 + \frac{RTZ_{\ce{B}}}{V_{\ce{A}}p_{\ce{B}}L_{\ce{B}}} \\ \frac{1}{x_{\ce{B}}(p)} = 1 + \frac{1}{m_{\ce{B}}(p)M_{\ce{A}}} = 1 + \frac{RTZ}{pV_{m,\ce{A}}L_{\ce{B}}^{\ast}} \end{array}\] where \(V_{\ce{A}}\), \(V_{m,\ce{A}}\) are the respective partial molar volume and molar volume of the solvent and \(Z_{\ce{B}}\) is the compression factor of the gas.
- The Ostwald coefficient and the related quantities for expression of gas solubility, the absorption, Bunsen, and Kuenen coefficients, appear frequently in the older literature of gas solubility determination. However, the modern practice, recommended here, is to express gas solubility as molality, mole fraction, or mole ratio.