Unified equation for access to rate constants of first-order reactions in dynamic and on-column reaction chromatography

A unified equation to evaluate elution profiles of reversible as well as irreversible (pseudo-) first-order reactions in dynamic chromatography and on-column reaction chromatography has been derived. Rate constants [k.sub.-1] and [k.sub.-1] and Gibbs activation energies are directly obtained from the chromatographic parameters (retention times [t.sup.A.sub.R] and [t.sup.B.sub.R] of the interconverting or reacting species A and B, the peak widths at half-height [w.sub.A] and [w.sub.B], and the relative plateau height [h.sub.p]), the initial amounts [A.sub.0] and [B.sub.0] of the reacting species, and the equilibrium constant [K.sub.A/B]. The calculation of rate constants requires only a few iterative steps without the need of performing a computationally extensive simulation of elution profiles. The unified equation was validated by comparison with a data set of 125 000 simulated elution profiles to confirm the quality of this equation by statistical means and to predict the minimal experimental requirements. Surprisingly, the recovery rate from a defined data set is on average 35% higher using the unified equation compared to the evaluation by iterative computer simulation.