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ION–ION INTERACTIONS 309
For mathematical convenience, a new variable y is defined as
Hence, in terms of the new variable y, Eq. (3.145) becomes (Appendix 3.5)
where
Bjerrum has tabulated the integral for various values of b (Table 3.16). This
means that, by reading off the value of the corresponding integral and substituting for
the various other terms in Eq. (3.147), the degree of association of an electrolyte may
be computed if the ion sizes, the dielectric constant, and the concentrations are known
(Table 3.17).
3.8.4. The Ion-Association Constant of Bjerrum
The quantity yields a definite idea of the fraction of ions that are associated in
ion pairs in a particular electrolytic solution at a given concentration. The ions that get
associated are those that get sufficiently close to an ion of opposite sign so that the
energy of Coulombic attraction is greater than the thermal energy of the pair.
