The Ion-Association Constant of Bjerrum

The quantity 0 yieids a definite idea of the fraction of ions that are associated in ion pairs in a particuiar eiectrolytic 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. 

It would, however, be advantageous if each electrolyte [e.g., NaCl, BaS04, and LafNOjIj] were assigned a particular number that would reveal, without going through the calculation of 6, the extent to which the ions of that electrolyte associate in ion pairs. The quantitative measure chosen to represent the tendency for ion-pair formation was guided by historical considerations. 

Arrhenius in 1887 had suggested that many properties of electrolytes could be explained by a dissociation hypothesis The neutral molecules AB of the electrolyte dissociate to form ions A and B , and this dissociation is governed by an equilibrium 

Applying the law of mass action to this equilibrium, one can define a dissociation constant 

By analogy, one can define an association constant ion-pair formation. Thus, one can consider an equilibrium between free ions (the positive M ions and the negative A ions) and the associated ion pairs (symbolized IP) 

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The momentary association of simple ions is a well-known phenomenon that has been treated in a number of ways. For example, the ion association constant of Bjerrum has received much experimental support. However, the association of simple electrolytes is considered to be shortlived and has been included in the Debye-Hiickel electrostatic theory as correction constants to the concentration. On the contrary, the hydration of the ions may be long-lived. This may be accounted for by considering additionally the ionic interaction ... 

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