https://doi.org/10.1351/goldbook.15349
Fugacity (\(\tilde{p}_{\ce{B}}\)) of a gaseous component (\(\ce{B}\)) in equilibrium with a liquid or solid mixture containing \(\ce{B}\) is directly proportional to the activity (\(a_{\ce{B}}\)) of the component in the mixture \[\tilde{p}_{\ce{B}} = \tilde{p}_{\ce{B}}^{\ast} f_{\ce{B}} x_{\ce{B}}\] where \(f_{\ce{B}}\) is the activity coefficient of \(\ce{B}\) referenced to Raoult’s law at mole fraction \(x_{\ce{B}}\) and \(\tilde{p}_{\ce{B}}\) is the fugacity of pure \(\ce{B}\).
Note: An ideal mixture is defined by replacing fugacities with partial pressures and setting the activity coefficient equal to unity \[p_{\ce{B}} = p_{\ce{B}}^{\ast} x_{\ce{B}} = y_{\ce{B}}p\] The total pressure, \(p\), is then simply the sum of the partial pressures of all components.