Rank deficiency in spectrophotometric study of acid dissociation equilibria in mixed solvent media

A methanol/water mixture, although considered a binary system, does not conform to solute distribution theory. Moreover, similar shortcomings are encountered in studies concerning acid-base reactions in mixtures of these two components. We demonstrate that in mixtures of methanol/water and an acid-base dye as indicator, three components exist for each of the protonated and deprotonated forms. In contrast, analysis of spectrophotometric data obtained from pH-metric titration of the dye in mixtures of methanol/water, shows no more than one component for each form of the dye. This can only be interpreted as a rank deficiency in the acquired data. We used matrix augmentation strategy for eliminating rank deficiency and constructing the corresponding full rank data matrices. In addition, concentration and spectral profiles of the components were obtained using multivariate curve resolution-alternating least squares.