Buffer capacity of a polyprotic acid:: First derivative of the buffer capacity and pKa values of single and overlapping equilibria

Buffer capacity appears in a variety of fields, and its approximate calculation is of practical importance for the design of new buffer solutions, being also a quantity related to titrations. The aims of this paper are (i) to devise simple expressions for the buffer capacity and its first derivative for a polyprotic acid, which maybe easily extended to a mixture of acids, e. g., universal buffer solutions; (ii) to evaluate overlapping acidity constants (pK'(a)s) for diprotic acids, from the knowledge of the singular points in the buffer capacity curve; and (iii) at the same time to provide a critical overview of the topic, with some twist of novelty. Hyperbolic functions in analytical chemistry have been surveyed. Conditions for the appearance of singular points in the buffer capacity curve for monoprotic acids and diprotic acids with overlapping pKa values have been established. Methods to evaluate strong and moderate overlapping pK'(a)s are suggested and applied to literature data. To check the computed values, the acidity constants were also determined by the graphical method of Irving and Rossotti, taken as reference. Results obtained agree well for moderate overlapping pK'(a) s values, whereas in the case of strong overlapping a s values the agreement is excellent. Limiting K-a1/K-a2 ratio as well as the relation between the acidity constants ratio and the half-values of the formation function, and the problem of distinguishing polyprotic acids from monofunctional ones have been envisaged. An attempt has also been made to derive compact expressions suitable for computer usage for the V = f (pH) derivative curves and buffer capacity curves, taken into account the dilution effects.