Modelling complex solution equilibria: III. Error-robust calculation of equilibrium constants from pH or potentiometric titration data

In calculating unknown equilibrium constants by the least-squares technique from pH (or potentiometric) titration data, errors in the chemical model (initial volume, reactant concentrations, carbonate or other impurities, pKw and other known equilibrium constants) and measurement errors (electrode calibration, drifts in ionic strength, non-ideal titrant mixing or temperature control) can strongly influence the results. Most of these errors will produce non-randomly distributed pH (or e.m.f.) residuals over some regions of data and thus violate the assumptions of the least-squares method. Simulations and deliberate errors in real data show that fitting the point-to-point changes in pH is less sensitive to such errors than is fitting the raw pH data, producing more trustworthy and reliable refinements of unknown equilibrium constants and more randomly distributed residuals. The refinement results are also insensitive to errors in calibration and more robust with regard to the range of pH spanned by the data. When applied to titrations of glycine-proton and Ni2+-glycine-proton mixtures from one laboratory, the results more closely matched the averages from several laboratories. Further, this approach will actually signal the presence of unsuspected errors.