Automatic titration by stepwise addition of equal volumes of titrant. Part IV. General-purpose program for evaluating potentiometric acid-base titrations

Abstract

A computational procedure for evaluating titration results is described. It utilises non-linear regression techniques to solve the equations for titration graphs from acid-base titrations. The procedure is based on the fact that the titration of an n-protic acid can usually be treated as a titration of n monoprotic acids of the same molarity as the n-protic acid.

In principle, the composition of an unknown mixture of acids can be determined by non-linear regression if a sufficient number of measurements (millilitres of titrant versus pH) are available. However, this assumes that the measured values are known with adequate accuracy, an assumption that is not correct in practice. All measured values (especially the pH values) are imperfect, hence a conventional non-linear regression can give a large number of mathematically equivalent solutions. This approach may therefore, by chance, produce a result that is mathematically correct but chemically impossible. This problem is avoided by setting boundary conditions and carrying out calculations in an appropriate sequence. Dominating terms are dealt with first, then the effects of the remaining terms are included. A computer program TITRA, capable of handling such a calculation scheme, is presented. No preliminary estimates of the required concentrations or equivalence volumes are necessary in the program.

The general equation for the titration graph derived is applicable to samples that may contain monoprotic acids (strong or weak), polyprotic acids, mixtures of acids, ampholytes, salts of weak acids and “abnormal” acids (acids with an abnormal sequence of stability constant values). By exchanging hydrogen-ion concentrations for hydroxide-ion concentrations and vice versa the equation is applicable to the titration of bases.