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ION–SOLVENT INTERACTIONS 99

2.14.2. A General Approach to Individual Ionic Properties:
Extrapolation to Make the Effects of One Ion Negligible

Let it be assumed that the value of the interaction energy of an ion with a solvent
is an inverse function of the ion–first water shell distance, r. Then, if one has a series
of salts where R is, say, a tetraalkylammonium ion, and the anion is
constant, the electrolyte property (e.g., the heat of hydration) can be plotted for the
series of RAs, against (where r represents the cation radius), and the extrapolated
value for is then the individual heat of hydration for the common anion,
If an accepted value of the property for this one anion can be derived, then, of
course, it can be coupled with data for various electrolytes containing this anion. If the
data pertain to dilute solutions, avoiding the interfering effects of ion-ion interactions,
it is possible to derive the individual value for the heat of hydration of the cations.
This method sounds simple at first. However, there are certain difficulties. One
has to decide on a value of n in the plot of and this may not always be unity or
simple. Various terms that affect the calculation of the heat of hydration of ions depend
on and Against which one should one plot?
Because the appropriate n is uncertain, it may be a better tactic to make a different
extrapolation and plot the property of the electrolyte against the molecular weight of
the cation and then extrapolate to zero, as with partial molar volumes, which was
illustrated in Fig. 2.15.
Conway and his associates have been foremost in studying individual ionic
properties and have published a weighted analysis of many suggested methods for
obtaining individual ionic properties (see the reading lists). Among the methods
chosen by Conway et al. as excellent, two have been discussed in this chapter so far,
namely, extrapolation against cation molecular weight and combining partial molar
volume with data on ionic vibration potential to determine individual solvation
numbers. Another method with good reliability involves measurements of the heat
produced in reversible electrolytic cells, which can be used to deduce individual, ionic
entropies, as will be explained in Section 2.15.8. First, though, it is desirable to describe
one particular method used for the individual heat of hydration of the proton, clearly
a most fundamental quantity.

2.15. INDIVIDUAL HEAT OF HYDRATION OF THE PROTON

2.15.1. Introduction

A particular method of obtaining this fundamental quantity was given by Halli-
well and Nyburg in 1963 and although there have been several reexaminations of the
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process, changes of only about 1 % in a value first calculated in 1963 have been made.
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These include information on the dynamics of proton hydration.