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(1) and k(-1) and Gibbs activation energies are directly obtained from the chromatographic parameters (retention times t(R)(A) and t(R)(B) of the interconverting or reacting species A and B, the peak widths at half-height w(A) and w(B), and the relative plateau height h(p)), the initial amounts A(o) and Bo of the reacting species, and the equilibrium constant K-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.