Critique of Bjerrums theory

Bjerrum s theory has been criticised because it involves the arbitrary cut-off at a critical distance q between ion pairs and free ions. It is felt that a more realistic situation would be one which would allow more of a fall-off between paired and free ions as the distance between them alters. 

For a symmetrical electrolyte, the ion pair is taken to behave as though it were a neutral species. It is, however, a dipole and as such will interact with the other ions. Consideration of this would lead to an activity coefficient for the ion pair which is not unity. There is also the question as to whether the ions of the ion pair are in contact, or are separated by one or more water molecules. Bjerrum himself recognised these limitations to his treatment the distinction between free and associated ions is not a chemical one, but only a mathematical device . 

There have been attempts to modify Bjerrum s treatment to remove this arbitrariness, but none has been used universally to any great extent in the interpretation of experimental data. Nevertheless, despite this artificiality, the Bjerrum theory coupled with the Debye-Hiickel theory has proved a very useful and relatively successfiil tool in discussing electrolyte solutions. This success is especially noteworthy when the Bjerrum-Debye-Huckel theory is compared with the alternative approach of Guggenheim s numerical integration which gives similar results (see Section 10.13.1). Table 10.2 gives values of K ssoc for various charge types and for various values of a and q. 

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