Equivalent Conductivity of Weakly Dissociated Electrolytes

Many dissolved acids or bases but also some salts are only weakly dissociated. Equation 1.33 gives an example for an acid HA with the related dissociation constant K of Equation 1.34. 

The dissociation grade a describes the fraction of dissolved molecules that are dissociated, leading to the concentrations c(H+) and c(A ) for the cations and anions. For a solution of pure HA with c(H+) = c(A ) = ac, one obtains the relation between K. and a presented in Equation 1.34. In the case of acetic acid, the dissolved molecules HA are not charged and ions form by dissociation only. This opens the possibility to determine a and K. by conductivity measurements. For the very small value of K= 1.8 x 10 for acetic acid, is mainly determined by the concentration of ions ac and thus by the value of the dissociation grade a and its changes with concentration. The ionic interaction described by the Debye-Hiickel theory is of minor influence. This may be seen easily in Equation 1.35, which contains both effects, dissociation, and ionic interaction. 

The expression in brackets is multiplied by Jm with small values for a and thus with a negligibly small value subtracted from Aq leading to a = A Aq as a good approximation. Insertion of this expression for a in Equation 1.34 yields Ostwald s law (Equation 1.36) for the dissociation constant as a function of the equivalent conductivity A.  

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