1.10.9: Gibbs Energies- Solutes- Cospheres
The chemical potential of solute \(j\) in aqueous solution, molality \(\mathrm{m}_{j}\), at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) (which is close to ambient) is given by equation (a).
\[\mu_{\mathrm{j}}(\mathrm{aq})=\mu_{\mathrm{j}}^{0}(\mathrm{aq})+\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{m}_{\mathrm{j}} \, \gamma_{\mathrm{j}} / \mathrm{m}^{0}\right) \nonumber \]
In developing an understanding the of factors which contribute to \(\mu_{\mathrm{j}}(\mathrm{aq})\), a model for solutions developed by Gurney is often helpful [1].
A co-sphere is identified around each solute molecule \(j\) where the organization of solvent molecules differs from that in the bulk solvent at the same \(\mathrm{T}\) and \(\mathrm{p}\). In a solution where the thermodynamic properties of the solute \(j\) are ideal, there are no solute-solute interactions such that the activity coefficient \(\gamma_{j}\) is unity. In real solutions the fact that \(\gamma_{j} \neq 1\) can be understood in terms of co-sphere---co-sphere interactions together for salt solutions strong charge-charge interactions.
The model [2] identifies two zones. Zone A describes solvent molecules close to the solute molecule, the number of such solvent molecules being the primary hydration number. Zone B describes the solvent molecules outside Zone A. Their organization differs from that in the bulk solvent as a consequence of the presence of solute molecule (or, ion) \(j\). Zone C lies beyond zone B where the organization of solvent is effectively the same as that in pure solvent at the same \(\mathrm{T}\) and \(\mathrm{p}\). There is merit in not being too pedantic concerning the definitions of zones A, B and C.
For real solutions co-sphere----co-sphere interactions are accounted for using for example the term \(\left[\partial \ln \left(\gamma_{\mathrm{j}}\right) / \partial \mathrm{p}\right]_{\mathrm{T}}\) in the equation describing the partial molar volume \(\mathrm{V}_{\mathrm{j}}(\mathrm{aq})\) for solute \(j\) in a real solution.
Footnotes
[1] R. W. Gurney, Ionic Processes in Solution, McGraw-Hill, New York, 1953.
[2] H. S. Frank and W.-Y. Wen, Discuss. Faraday Trans.,1957, 24 ,756.