1.14.2: Excess Thermodynamic Properties - Liquid Mixtures
A given liquid mixture at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) (\(\cong \mathrm{p}^{0}\)) contains \(\mathrm{i}\)-liquid chemical substances. The chemical potential of liquid component \(\mathrm{j}\) is given by equation (a) where \(\mu_{\mathrm{j}}^{*}(\ell)\) is the chemical potential of liquid component \(\mathrm{j}\) at the same \(\mathrm{T}\) and \(\mathrm{p}\).
\[\mu_{\mathrm{j}}(\operatorname{mix})=\mu_{\mathrm{j}}^{*}(\ell)+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{x}_{\mathrm{j}} \, \mathrm{f}_{\mathrm{j}}\right) \nonumber \]
Here \(\operatorname{limit}\left(\mathrm{x}_{\mathrm{j}} \rightarrow 1\right) \mathrm{f}_{\mathrm{j}}=1.0\) at all \(\mathrm{T}\) and \(\mathrm{p}\).
If the thermodynamic properties of the liquid mixture are ideal,
\[\mu_{j}(\operatorname{mix} ; \mathrm{id})=\mu_{\mathrm{j}}^{*}(\ell)+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{x}_{\mathrm{j}}\right) \nonumber \]
The excess chemical potential for liquid substance \(\mathrm{j}\),
\[\mu_{\mathrm{j}}^{\mathrm{E}}(\mathrm{mix})=\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{f}_{\mathrm{j}}\right) \nonumber \]
DSF