https://doi.org/10.1351/goldbook.15374
Volume \(V^{\rm{g}}\) of an amount \(n_{\ce{B}}^{\rm{l}}\) of a dissolved gas at a given standard temperature \(T^{^⦵\!}\) (usually \(\pu{273.15 K}\)) and given standard pressure \(p^{_{^⦵\!}}\) (\(\pu{1 bar} = \pu{0.1 MPa}\) or, in older literature, \(\pu{1 atm}\)) divided by the mass \(m^{\rm{l}}\) of the dissolving liquid containing an amount $n_{\ce{A}}$ of solvent at temperature $T$ and the given pressure \(p^{_{^⦵\!}}\).
Notes:
- There are two Kuenen coefficients, depending on whether the liquid is the equilibrium solution or the pure liquid, with mathematical definitions:
- Kuenen coefficient, solution reference \(S_{\ce{B}} = V^{\rm{g}}(T^{^⦵\!}, p^{_{^⦵\!}}, n_{\ce{B}}^{1})/m^{\rm{l}}(T, p^{_{^⦵\!}}, n_{\ce{A}}, n_{\ce{B}}^{\rm{l}})\)
- Kuenen coefficient, pure solvent reference \(S_{\ce{B}}^{\ast} = V^{\rm{g}}(T^{^⦵\!}, p^{_{^⦵\!}}, n_{\ce{B}}^{1})/m^{\rm{l}}(T, p^{_{^⦵\!}}, n_{\ce{A}})\) - The relations between the molality \(m_{\ce{B}}(p^{_{^⦵\!}})\) or mole fraction \(x_{\ce{B}}(p^{_{^⦵\!}})\) of dissolved gas and the Kuenen coefficients are \[\begin{array}{l} \frac{1}{x_{\ce{B}}(p^{⦵})} = 1 + \frac{1}{m_{\ce{B}}(p^{⦵})M_{\ce{A}}} = 1 + \frac{RT^{⦵}Z_{\ce{B}}^{⦵}(T^{⦵})}{p^{⦵}M_{\ce{A}}S_{\ce{B}}} \\ \frac{1}{x_{\ce{B}}(p^{⦵})} = 1 + \frac{1}{m_{\ce{B}}(p^{⦵})M_{\ce{A}}} = 1 + \frac{RT^{⦵}Z_{\ce{B}}^{⦵}(T^{⦵})}{p^{⦵}M_{\rm{A}}S_{\ce{B}}^{\ast}} \end{array}\] where \(M_{\ce{A}}\) is the molar mass the solvent and \(Z_{\ce{B}}\) is the compression factor of the gas.
- The Kuenen coefficient and the related quantities for expression of gas solubility: absorption coefficient, Bunsen coefficient, and Ostwald coefficient 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.