Effect of Ion Association on Conductivity

In treating the thermodynamic consequences of ion-pair formation (Section 3.8.4), it was shown that the association constant for the equilibrium between free ions and ion pairs is given by 

A relation between 0 and the conductivity of the electrolyte will now be developed. The specific conductivity has been shown [c/. Eq. (4.161)] to be related to the concentration of mobile charge carriers (i.e., of free ions) in the following way  

Since is the fraction of ions that are nor associated (i.e., are free), it is equal 

Introducing these expressions for 0 and 1 -0 into Eq. (4.342), one finds that 

Though Eq. (4.351) relates the equivalent eonduetivity to the electrolyte concentration, it contains the unevaluated quantity Ag. By combining Eqs. (4.346) and (4.348), one gets 

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