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ION–ION INTERACTIONS 231

Fig. 3.4. The free energy of ion–ion interactions is
the electrostatic work of taking an imaginary assembly of
discharged ions and charging them up to obtain a solution
of charged ions.

constituting the electrolyte. Generally, however, the desire is to isolate the contribution
to the free energy of ion–ion interactions arising from one ionic species i only. This
partial free-energy change is by definition the chemical-potential change arising
from the interactions of one ionic species with the ionic assembly.
To compute this chemical-potential change rather than the free-energy
change one must adopt an approach similar to that used in the Born theory of
solvation. One thinks of an ion of species i and imagines that this reference ion alone
of all the ions in solution is in a state of zero charge (Fig. 3.5). If one computes the
work of charging up the reference ion (of radius ) from a state of zero charge to its
final charge of then the charging work W times the Avogadro number is equal
to the partial molar free energy of ion–ion interactions, i.e., to the chemical potential
of ion–ion interactions:

Fig. 3.5. The chemical potential arising from the
interactions of an ionic species i with the electrolytic
solution is equal to the Avogadro number times the elec-
trostatic work of taking an imaginary solution in which one
reference ion alone is discharged and charging this refer-
ence ion up to its normal charge.