1.10.22: Gibbs Energies- Salt Solutions- Solvent
A given salt solution contains a 1:1 salt \(j\) (e.g. \(\mathrm{NaCl}\)) in which the salt, chemical substance \(j\), completely dissociates into ions. In other words, the total molality of solutes equals \(2 \, m_{j}\). By definition the chemical potential of water in this aqueous solution, \(\mu_{1}(\mathrm{aq})\) (at fixed temperature and pressure, the latter being ambient and hence close to the standard pressure \(\mathrm{p}^{0}\)) is given by equation (a).
\[\mu_{1}(\mathrm{aq})=\mu_{1}^{*}(\ell)-2 \, \phi \, \mathrm{R} \, \mathrm{T} \, \mathrm{M}_{1} \, \mathrm{m}_{\mathrm{j}} \nonumber \]
For the corresponding ideal solution, \(\phi = 1.0\) at all \(\mathrm{T}\) and \(\mathrm{p}\), Hence,
\[\mu_{1}(\mathrm{aq} ; \mathrm{id})=\mu_{1}^{*}(\ell)-2 \, \mathrm{R} \, \mathrm{T} \, \mathrm{M}_{1} \, \mathrm{m}_{\mathrm{j}} \nonumber \]
Just as for solutions containing neutral solutes, the minus sign in equation (b) means that added salt stabilizes the solvent in an ideal solution; \(\mu_{1}(\mathrm{aq} ; \mathrm{id})<\mu_{1}^{*}(\ell)\).
For water in an aqueous salt solution containing salt \(j\), molality \(\mathrm{m}_{j}\), where each mole of salt forms \(v\) moles of ions with complete dissociation, the chemical potential of the solvents is given by equation (c).
\[\mu_{1}(\mathrm{aq})=\mu_{1}^{*}\left(\ell ; \mathrm{p}^{0}\right)-\mathrm{v} \, \phi \, \mathrm{R} \, \mathrm{T} \, \mathrm{M}_{1} \, \mathrm{m}_{\mathrm{j}}+\int_{\mathrm{p}(0)}^{\mathrm{p}} \mathrm{V}_{1}^{*}(\ell) \, \mathrm{dp} \nonumber \]
For the ideal dilute solution, \(\phi =1.0\). Here \(\mu_{1}^{*}\left(\ell, \mathrm{p}^{0}\right)\) is the standard chemical potential of water at temperature \(\mathrm{T}\). Alternatively we may switch the reference chemical potential for the solvent to the pure liquid at the same pressure [1,2].
\[\mu_{1}(\mathrm{aq} ; \mathrm{T} ; \mathrm{p})=\mu_{1}^{*}(\ell ; \mathrm{T} ; \mathrm{p})-\mathrm{v} \, \phi \, \mathrm{R} \, \mathrm{T} \, \mathrm{M}_{1} \, \mathrm{m}_{\mathrm{j}} \nonumber \]
Footnotes
[1] For relevant Tables see;’ R. A. Robinson and R. H. Stokes, Electrolyte Solutions, 2nd edn.(revised), Butterworths, London, 1965, Appendix 8.
[2] The impact of salts on osmotic coefficients is illustrated by the properties of aqueous solutions containing alkylammonium salts.
- S. Lindenbaum, J. Phys.Chem.,1971, 75 ,3733; and references therein.
- G. E. Boyd, A. Schwartz and S. Lindenbaum, J. Phys.Chem.,1966, 70 , 821; and references therein.