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ION–ION INTERACTIONS 249

Fig. 3.17. The superposition of the potential due to the ion
and the potential due to the cloud yields the total potential
at a distance r from the central ion.

The contribution can thus be easily found. One rearranges Eq. (3.45) to read

and substitutes for with Eq. (3.44) and for with the Debye–Hückel expression
[Eq. (3.33)]. Then,

The value of [cf. Eq. (3.20)] is proportional to In sufficiently dilute solutions,
can be taken as sufficiently small to make

and based on this approximation,

By introducing the expressions (3.44) and (3.49) into the expression (3.45) for the total
potential at a distance r from the central ion, it follows that