Calculating equilibrium constants from spectral data: Reliability of the Benesi-Hildebrand method and its modifications

Equations for statistical evaluation of complex formation in solution were revised and a simple modification of the correct least-squares procedure was advanced. The main difference against the previous treatment is in the uncertainty of the estimated parameters: the equilibrium constant K and extinction coefficient of the complex ε. This uncertainty is always greater, often by an order of magnitude, than that given in the literature using various methods and programs. On a couple of examples, the new method was compared with the previous ones, also with most commonly used procedure of BenesiHildebrand. According to the quality of data, particularly the concentration range and the number of measurements, one can distinguish cases when Benesi-Hildebrand method yields reasonable results and when it is unreliable: in no case it gives any idea about the uncertainty. Many K values determined in this way should be better removed from the literature.