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250 CHAPTER 3

The second term, which arises from the cloud, reduces the value of the potential
to a value less than that if there were no cloud. This is consistent with the model; the
cloud has a charge opposite to that on the central ion and must therefore alter the
potential in a sense opposite to that due to the central ion.
The expression

leads to another, and helpful, way of looking at the quantity It is seen that
is independent of r, and therefore the contribution of the cloud to the potential at the
site of the point-charge central ion can be considered to be given by Eq. (3.49). But,
if the entire charge of the ionic atmosphere [which is as required by electroneu-
trality—Eq. (3.39)] were placed at a distance from the central ion, then the potential
produced at the reference ion would be It is seen therefore from Eq. (3.49)
that the effect of the ion cloud, namely, is equivalent to that of a single charge,
equal in magnitude but opposite in sign to that of the central ion, placed at a distance
from the reference ion (Fig. 3.18). This is an added and more important reason that
the quantity is termed the effective thickness or radius of the ion atmosphere
surrounding a central ion (see Section 3.3.8).

3.3.10. The ionic Cloud and the Chemical-Potential Change Arising
from Ion–Ion Interactions

It will be recalled (see Section 3.3.1) that it was the potential at the surface of the
reference ion which needed to be known in order to calculate the chemical-potential
change arising from the interactions between a particular ionic species i and the
rest of the ions of the solution, i.e., one needed to know in Eq. (3.3),

Fig. 3.18. The contribution of the ionic
cloud to the potential at the central ion is
equivalent to the potential due to a single
charge, equal in magnitude and opposite sign
to that of the central ion, placed at a distance
from the central ion.