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ION–ION INTERACTIONS 311

The equilibrium sanctions the use of the law of mass action

where the a’s are the activities of the relevant species. From (3.152) it is seen that
is the reciprocal of the ion pair’s dissociation constant.
Since is the fraction of ions in the form of ion pairs, is the concentration of
ion pairs, and is the concentration of free ions. If the activity coefficients of
the positive and negative free ions are and respectively, and that of the ion pairs
is f , one can write
IP

or, using the definition of the mean ionic-activity coefficient [Eq. (3.72)],

Some simplifications can now be introduced. The ion-pair activity coefficient
is assumed to be unity because deviations of activity coefficients from unity are
ascribed in the Debye–Hückel theory to electrostatic interactions. But ion pairs are not
involved in such interactions owing to their zero charge and hence they behave ideally
like uncharged particles, i.e.,
Furthermore, in very dilute solutions: (1) The ions rarely come close enough
together (i.e., to within a distance q) to form ion pairs, and one can consider or
(2) activity coefficients tend to unity, i.e., or
Hence, under these conditions of very dilute solutions, Eq. (3.154) becomes

and substituting for from Eq. (3.147), one has