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ION–ION INTERACTIONS 251
It was to obtain this potential that Debye and Hückel conceived their model of
an ionic solution. The analysis presented the picture of an ion being enveloped in an
ionic cloud. What is the origin of the ionic cloud? It is born of the interactions between
the central ion and the ions of the environment. If there were no interactions (e.g.,
Coulombic forces between ions), thermal forces would prevail, distribute the ions
randomly and wash out the ionic atmosphere. It appears therefore that the
simple ionic cloud picture has not only led to success in describing the distribution of
ions but also given the electrostatic potential at the surface of a reference ion
due to the interactions between this reference ion and the rest of the ions in the solution
(the quantity required for reasons explained in Section 3.3.1).
Thus, the expression (3.49) for can be substituted for in Eq. (3.3) with
the result that
The Debye–Hückel ionic-cloud model for the distribution of ions in an electro-
lytic solution has permitted the theoretical calculation of the chemical-potential change
arising from ion–ion interactions. How is this theoretical expression to be checked,
i.e., connected with a measured quantity? It is to this testing of the Debye–Hückel
theory that attention will now be turned.
3.4. ACTIVITY COEFFICIENTS AND ION–ION INTERACTIONS
3.4.1. Evolution of the Concept of an Activity Coefficient
The existence of ions in solution, of interactions between these ions, and of a
chemical-potential change arising from ion–ion interactions have all been taken
to be self-evident in the treatment hitherto presented here. This, however, is a modern
point of view. The thinking about electrolytic solutions actually developed along a
different path.
Ionic solutions were at first treated in the same way as nonelectrolytic solutions,
though the latter do not contain (interacting) charged species. The starting point was
the classical thermodynamic formula for the chemical potential of a nonelectrolyte
solute
