Page 376 - MODERN ELECTROCHEMISTRY

312 CHAPTER 3

But

and therefore,

The value of the association constant provides an indication of whether ion-pair
formation is significant. The higher the value of the more extensive is the ion-pair
formation (Table 3.18).
What are the factors that increase K A andthereforeincrease thedegree of ion-pair
formation? From Eq. (3.158), it can be seen that the factors that increase are (1)
low dielectric constant (2) small ionic radii, which lead to a small value of a and
hence [Eq. (3.148)] to a large value of the upper limit b of the integral in Eq. (3.158);
and (3) large and
These ideas based on Bjerrum’s picture of ion-pair formation have received
considerable experimental support. Thus, in Fig. 3.46, the association constant is seen
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to increase markedly with decrease of dielectric constant. The dependence of ion-pair
formation on the distance of closest approach is seen in Fig. 3.47.
When numerical calculations are carried out with these equations, the essential
conclusion that emerges is that in aqueous media, ion association in pairs scarcely
occurs for l:l-valent electrolytes but can be important for 2:2-valent electrolytes.
(However, see the results of post-Bjerrum calculations in 3.13.) The reason is that
depends on through Eq. (3.156). In nonaqueous solutions, most of which have
dielectric constants much less than that of water ion association is extremely
important.

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The critical dielectric constant above which there is no more ion-pair formation (as indicated by Fig. 3.46)
is really a result of the arbitrary cutting off of ion-pair formation at the distance q.