Determining an Acid Dissociation Constant from a Titration

Another application of acid–base titrimetry is the determination of equilibrium constants. Consider, for example, a solution of acetic acid, CH₃COOH, for which the dissociation constant is

K_a = [H₃O⁺][CH₃COO^–]/[CH₃COOH]

When the concentrations of CH₃COOH and CH₃COO^– are equal, the K_a expression reduces to K_a = [H₃O⁺], or pH = pK_a. If we titrate a solution of acetic acid with NaOH, the pH equals the pK_a when the volume of NaOH is approximately ½V_eq. As shown in the following illustration, a potentiometric titration curve provides a reasonable estimate of acetic acid’s pK_a.

This method provides a reasonable estimate of a weak acid’s pK_a if the acid is neither too strong nor too weak. These limitations are easily to appreciate if we consider two limiting cases. For the first case let’s assume that the weak acid, HA, is more than 50% dissociated before the titration begins (that is, HA has a relatively large K_a). In this case the concentration of HA before the equivalence point is always less than the concentration of A^–, and there is no point on the titration curve where [HA] = [A^–]. At the other extreme, if the acid is too weak, less than 50% of the weak acid reacts with the titrant at the equivalence point. In this case the concentration of HA before the equivalence point is always greater than that of A^–. Determining the pK_a by the half-equivalence point method overestimates its value if the acid is too strong and underestimates its value if the acid is too weak.

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David Harvey

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