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68 CHAPTER 2

where A depends on the electrolyte.
Bockris and Saluja applied these equations derived by Debye to a number of
electrolytes and, using data that included information provided by Conway and by
Zana and Yeager, calculated the difference of the solvation numbers of the ions of
salts. The relevant parameters are given in Table 2.6.
Now, since the ultrasound method gives the difference of the hydration numbers,
while the compressibility method gave the sum, individual values can be calculated
(Table 2.7).

2.9. SOLVATION NUMBERS AT HIGH CONCENTRATIONS

2.9.1. Hydration Numbers from Activity Coefficients

A nonspectroscopic method that has been used to obtain hydration numbers at
high concentrations will be described here only in qualitative outline. Understanding
it quantitatively requires a knowledge of ion–ion interactions, which will be developed
in Chapter 3. Here, therefore, are just a few words of introduction.
The basic point is that the mass action laws of chemistry ([A][B]/[AB] = constant)
do not work for ions in solution. The reason they do not work puzzled chemists for 40
years before an acceptable theory was found. The answer is based on the effects of
electrostatic interaction forces between the ions. The mass action laws (in terms of
concentrations) work when there are no charges on the particles and hence no
long-range attraction between them. When the particles are charged, Coulomb’s law
applies and attractive and repulsive forces (dependent on where r is the distance
between the ions) come in. Now the particles are no longer independent but “pull” on
each other and this impairs the mass action law, the silent assumption of which is that
ions are free to act alone.
There are several ways of taking the interionic attraction into account. One can
work definitionally and deal in a quantity called “activity,” substituting it for concen-
tration, whereupon (by definition) the mass action law works. Clearly, this approach
does not help us understand why charges on the particles make the concentration form
of the mass action law break down.
From a very dilute solution to about mol the ratio of
the activity to the concentration ( or the activity coefficient, ) keeps on getting
smaller (the deviations from the “independent” state increase with increasing concen-
tration). Then, somewhere between and M solutions of electrolytes such as
NaCl, the activity coefficient (the arbiter of the deviations) starts to hesitate as to which
direction to change with increasing concentration; above 1 mol it turns around and
increases with increasing concentration. This can be seen schematically in Fig. 2.18.