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1.5.9: Chemical Potentials; Excess; Aqueous Solution

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    A given aqueous solution, at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) (\(\cong \mathrm{p}^{0}\)), contains a solute, chemical substance \(j\). If the thermodynamic properties of the solution are ideal, the chemical potential of the solute is given by equation (a).

    \[\mu_{\mathrm{j}}(\mathrm{aq} ; \mathrm{id})=\mu_{\mathrm{j}}^{0}(\mathrm{aq})+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{m}_{\mathrm{j}} / \mathrm{m}^{0}\right)\]

    For the corresponding real solution,

    \[\mu_{\mathrm{j}}(\mathrm{aq})=\mu_{\mathrm{j}}^{0}(\mathrm{aq})+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{m}_{\mathrm{j}} \, \gamma_{\mathrm{j}} / \mathrm{m}^{0}\right)\]

    Here \(\gamma_{j}\) is the activity coefficient. The excess chemical potential, \(\mu_{\mathrm{j}}^{\mathrm{E}}(\mathrm{aq})\) is given by equation (c).

    \[\mu_{\mathrm{j}}^{\mathrm{E}}(\mathrm{aq})=\mu_{\mathrm{j}}(\mathrm{aq})-\mu_{\mathrm{j}}(\mathrm{aq} ; \mathrm{id})\]

    \[\text { Then, } \mu_{j}^{E}(a q)=R \, T \, \ln \left(\gamma_{j}\right)\]

    Often an excess chemical potential \(\mu_{\mathrm{j}}^{\mathrm{E}}(\mathrm{aq})\) is written in the form \(\mathrm{G}_{j}^{\mathrm{E}}\). The latter notation stems from the fact that chemical potentials are partial molar Gibbs energies. In the case of the solvent, water(\(\ell\)), the corresponding equations for the chemical potentials in solutions having either ideal or real thermodynamic properties are given by equations (e) and (f).

    \[\mu_{1}(\mathrm{aq} ; \mathrm{id})=\mu_{1}^{*}(\ell)-\mathrm{R} \, \mathrm{T} \, \mathrm{M}_{1} \, \mathrm{m}_{\mathrm{j}}\]

    \[\mu_{1}(\mathrm{aq})=\mu_{1}^{*}(\ell)-\phi \, \mathrm{R} \, \mathrm{T} \, \mathrm{M}_{1} \, \mathrm{m}_{\mathrm{j}}\]

    \[\mu_{1}^{\mathrm{E}}(\mathrm{aq})=(1-\phi) \, \mathrm{R} \, \mathrm{T} \, \mathrm{M}_{1} \, \mathrm{m}_{\mathrm{j}}\]

    This page titled 1.5.9: Chemical Potentials; Excess; Aqueous Solution is shared under a Public Domain license and was authored, remixed, and/or curated by Michael J Blandamer & Joao Carlos R Reis via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.