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ION–ION INTERACTIONS 253

It was argued that, in nonideal solutions, it was not just the analytical concentration
of species i, but its effective concentration which determined the chemical-po-
tential change This effective concentration was also known as the activity
of the species i, i.e.,

and the correction factor as the activity coefficient. For ideal solutions, the activity
coefficient is unity, and the activity becomes identical to the concentration i.e.,

when

Thus, the chemical-potential change in going from the standard state to the final
state can be written as

Equation (3.57) summarizes the empirical or formal treatment of the behavior of
electrolytic solutions. Such a treatment cannot furnish a theoretical expression for the
activity coefficient It merely recognizes that expressions such as (3.52) must be
modified if significant interaction forces exist between solute particles.

3.4.2. The Physical Significance of Activity Coefficients
For a hypothetical system of ideal (noninteracting) particles, the chemical poten-
tial has been stated to be given by

For a real system of interacting particles, the chemical potential has been expressed in
the form

Hence, to analyze the physical significance of the activity coefficient term in Eq.
(3.57), it is necessary to compare this equation with Eq. (3.52). It is obvious that when
Eq. (3 52) is subtracted from Eq. (3.57), the difference [i.e., (real) – (ideal)] is
the chemical-potential change arising from interactions between the solute
particles (ions in the case of electrolyte solutions). That is,

and therefore,