Activity Coefficients, Bjerrums Ion Pairs, and Debyes Free Ions

Activity Coefficients, Bjerrum s Ion Pairs, and Debye s Free Ions 

What direct role do the ion pairs have in the Dehye-Hiickel electrostatic theory of activity coefficients The answer is simply None. Since ion pairs carry no net charge,they are ineligible for membership in the ion cloud, where the essential qualification is charge. Hence, ion pairs are dismissed from a direct consideration in the Dehye-Hiickel theory. 

This does not mean that the Debye-Htickel theory gives the right answer when there is ion-pair formation. The extent of ion-pair formation decides the value of the concentration to be used in the ionic-cloud model. By removing a fraction 0 of the total number of ions, only a fraction 1 - 0 of the ions remain for the Debye-Hiickel treatment, which interests itself only in the free charges. Thus, the Debye-Htickel expression for the activity coefficient [Eq. (3.120)] is valid for the free ions, with two important modifications (1) Instead of there being a concentration c of ions, there is only (1 - 0)c the remainder Oc is not reckoned with owing to association. (2) The distance of closest approach of free ions is q and not a. These modifications yield 

This calculated mean activity coefficient is related to the measured mean activity coefficient of the electrolyte C4)obs by the relation (for the derivation, see Appendix 3.6) 

This equation indicates how the activity coefficient depends on the extent of ion association. In fact, this equation constitutes the bridge between the treatment of solutions of true electrolytes and that of solutions of potential electrolytes. 

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