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ION–ION INTERACTIONS 297

One sees at once that there is a possibility of a change in direction for the change
in log f with an increase in concentration in the solution. If the last term predominates,
±
RT log f may increase with concentration.
±
The situation here does have a fairly large shadow on it because of the use of the
expression (3.120) in It will be seen (Section 3.14) that, at concentrations as high
as 1 N, there are some fundamental difficulties for the ionic-cloud model on which this
expression of Eq. (3.120) was based (the ionic atmosphere can no longer be
considered a continuum of smoothed-out charge). It is clear that when the necessary
mathematics can be done, there will be an improvement on the expression, and one
will hope to get it more correct than it now is. Because of this shadow, a comparison
of Eq. (3.130) with experiment to test the validity of the model for removing solvent
molecules to the ions’ sheathes should be done a little with tongue in cheek.

3.6.3. The Water Removal Theory of Activity Coefficients and Its
Apparent Consistency with Experiment at High Electrolytic
Concentrations
If one examines the ion–solvent terms in Eq. (3.130), one sees that since
and in general (more than one hydration water per ion), both the terms are
positive. Hence, one can conclude that the Debye–Hückel treatment, which ignores
the withdrawal of solvent from solution, gives values of activity coefficients that are
smaller than those which take these effects into account. Furthermore, the difference
arises from the ion–solvent terms, i.e.,

As the electrolyte concentration increases, decreases and increases; hence both
ion–solvent terms increase the value of log f. Furthermore, the numerical evaluation
shows that the above ion-solvent term can equal and become larger than the Debye–
Hückel Coulombic term. This means that the versus curve can pass
through a minimum and then start rising, which is precisely what is observed (Fig.
3.39, where an activity coefficient is plotted against the corresponding molality).
On the other hand, with increasing dilution,
and and hence the terms vanish, which indicates that ion–solvent
interactions (which are of short range) are significant for the theory of activity