Exact equations for the equilibrium constants of single intermolecular complexes in terms of spectrophotometric data

Abstract

Exact algebraic equations were established to calculate without iteration the equilibrium constants of single intermolecular complexes from spectrophotometric data. Each spectrophotometric measurement produces three numbers: the two initial concentrations of the donor and acceptor and the absorbance at equilibrium. Without experimental errors, all perfect data would satisfy a quadratic polynomial equilibrium equation specific to the complex under consideration. With experimental errors, however, imperfect data need not satisfy any common equilibrium equation. Nevertheless, exact equations produce without iteration the equilibrium constant that minimizes any weighted sum of squares of the quadratic polynomial corresponding to the complex at hand.