Determination of equilibrium constants by chemometric analysis of spectroscopic data

We describe a chemometric method to determine equilibrium constants with high accuracy from spectroscopic titrations. Knowledge of component spectra is not required for the analysis, and titrations can be analyzed even when the titration end points are not reached. In fact, the component spectra are determined in the analysis. The analysis is based on a decomposition of the recorded spectra into a product of target and projection matrices using NIPALS. The matrices are then rotated to give the correct concentrations and spectral profiles of the components utilizing the functional form of the equilibrium expression. The output of the analysis is the equilibrium constant and the component spectral profiles. The analysis is highly accurate and can be performed on a standard personal computer. As examples, we determine the protolytic constant for the equilibrium between the anionic and dianionic forms of fluorescein in aqueous solution and the dimerization constant of benzoic acid in n-heptane.