An algebraic approach to the study of the titration curves of weak acids and their mixtures

It is shown that the titration curves of weak acids and their mixtures which have rational mole-fractions of the components can be transformed into polynomials. These protonation polynomials are called normal or abnormal according to whether their coefficients do or do not satisfy certain inequalities derived from statistical considerations. The normality of a second-degree polynomial is shown to be a characteristic equivalent to the reality of its zeros. Protonation polynomials with real zeros are shown to be normal, but the converse of this statement is not necessarily true. The titration curve of a polyfunctional acid is identical with that of an equimolar mixture of monofunctional acids if and only if the protonation polynomial has real zeros. A method for determining the functionality of an acid from its titration curve by using protonation polynomials is outlined.