Ionic Equilibria of Conjugate Acids and Bases

Once formed, the conjugate base of an acidic substance (i.e., the anion of that acid) is also capable of reacting with water:

Since aqueous solutions of anions are commonly prepared by the dissolution of a salt containing that anion, reactions of the type described by equation (28) are often termed hydrolysis reactions. Equation (28) is necessarily characterized by its base ionization constant expression:

and a corresponding pKB defined in the usual manner. But since:

it follows that:

Equation (31) contains the right-hand side expression of equation (22), so one deduces that:

The same relation between ionization constants of a conjugate acid-base pair can be developed if one were to begin with the conjugate acid of a basic substance, so equation (33) is recognized as a general property of conjugate acid-base pairs.

Knowledge of K\ for a weak acid (or KB for a weak base) facilitates estimation of the concentrations of the various species after equilibrium is established. When accurate solutions for equilibrium concentrations of a weak acid, for example, are required, the exact approach requires solving four simultaneous equations. Two of these have already been discussed, one being the acid ion-ization expression of equation (22), and the other being the water dissociation expression of equation (15). The third necessary equation is the charge balance equation:

and the fourth equation is the mass balance equation:

where CA is the initial concentration ofweak acid in the system. It is beyond the scope of this chapter to detail the exact solutions to these equilibria calculations, but interested readers can consult chapters 5 and 6 of the text by Frieser and Fernando (1963), which contains solutions to effectively all problems ofstandard interest.

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