Calculation of equilibrium constants from multiwavelength spectroscopic data-III Model-free analysis of spectrophotometric and ESR titrations.

Factor analysis of spectroscopic data is a well-known tool for the determination of the number of independent absorbing species in a series of mixtures. It has also been used for the reduction of the data-set in the calculation of equilibrium constants from multiwavelength data. The paper presents a new application of this powerful technique. In a completely model-free treatment, data from spectrophotometric or other spectroscopic titrations are subjected to repetitive abstract factor analysis. By starting with only the first two spectra, and introducing the additional measurements one by one, the number of significant eigenvalues is obtained as a function of the progressing titration. On repetition of the process from the opposite end and judicious combination of the results, the formation and dissociation of individual "species" can be obtained. After association of actual stoichiometries with these purely abstract "species" by chemical reasoning, it may be possible to arrive at a semiquantitative description and reasonable estimates for the equilibrium constants. This method is most successful for the detection of minor species which would go unnoticed in any visual inspection of spectrophotometric titration curves.