https://doi.org/10.1351/goldbook.15317
Volume \(V^{\rm{g}}\) of an amount \(n_{\ce{B}}^{\rm{l}}\) of a gas dissolved at a given standard temperature \(T^{^⦵\!}\) (usually \(\pu{273.15 K}\)) and given standard (partial) pressure \(p_{\ce{B}}^{_{^⦵\!}}\) (\(\pu{1 bar} = \pu{0.1 MPa}\) or, in older literature, \(\pu{1 atm}\)) divided by the volume of the solvent \(V^{\rm{l}}\) containing an amount \(n_{\ce{A}}\) of solvent at temperature \(T\) and the given total pressure \(p^{_{^⦵\!}}\).
Notes:
- There are two Bunsen coefficients, depending on whether the liquid is the equilibrium solution or the pure liquid, with mathematical definitions:
- Bunsen coefficient, solution reference \(\alpha_{\ce{B}} = V^{\rm{g}}(T^{^⦵\!}, p^{_{^⦵\!}}, n_{\ce{B}}^{1})/V^{\rm{l}}(T, p^{_{^⦵\!}}, n_{\ce{A}}, n_{\ce{B}}^{1})\)
- Bunsen coefficient, pure solvent reference \(\alpha_{\ce{B}}^{\ast} = V^{\rm{g}}(T^{^⦵\!}, p^{_{^⦵\!}}, n_{\ce{B}}^{1})/V^{\rm{l}}(T, p^{_{^⦵\!}}, n_{\ce{A}})\)
where \(n_{\ce{B}}^{\rm{l}}\) is the amount of dissolved gas in the liquid solution. - The relations between the molality \(m_{\ce{B}}(p^{_{^⦵\!}})\) or mole fraction \(x_{\ce{B}}(p^{_{^⦵\!}})\) of dissolved gas and the Bunsen coefficients are \[\begin{array}{l} \frac{1}{x_{\ce{B}}(p^{_{^⦵\!}})} = 1 + \frac{1}{m_{\ce{B}}(p^{_{^⦵\!}})M_{\ce{A}}} = 1 + \frac{RT^{^⦵\!}Z_{\ce{B}}^{^⦵\!}(T^{^⦵\!})}{p^{_{^⦵\!}}V_{\ce{A}}\alpha_{\ce{B}}} \\ \frac{1}{x_{\ce{B}}(p^{_{^⦵\!}})} = 1 + \frac{1}{m_{\ce{B}}(p^{_{^⦵\!}})M_{\ce{A}}} = 1 + \frac{RT^{^⦵\!}Z_{\ce{B}}^{^⦵\!}(T^{^⦵\!})}{p^{_{^⦵\!}}V_{m,\ce{A}}\alpha_{\ce{B}}} \end{array}\] 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 Bunsen coefficient and the related quantities for expression of gas solubility; absorption coefficient, Kuenen 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.