Unified Equation for Access to Rate Constants of First-Order Reactions in Dynamic and On-Column Reaction Chromatography

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Abstract
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 k1 and k-1 and Gibbs activation energies are directly obtained from the chromatographic parameters (retention times and of the interconverting or reacting species A and B, the peak widths at half-height wA and wB, and the relative plateau height hp), the initial amounts A0 and B0 of the reacting species, and the equilibrium constant KA/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.

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