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1.14.2: Excess Thermodynamic Properties - Liquid Mixtures

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    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

    This page titled 1.14.2: Excess Thermodynamic Properties - Liquid Mixtures was last modified on Mon, 20 May 2024 07:02:53 GMT and is shared under a Public Domain license and was authored, remixed, and/or curated by Michael J Blandamer and Joao Carlos R Reis via source content that was edited to the style and standards of the LibreTexts platform.