Resolution of stopped-flow kinetic data for second-order reactions with rate constants up to 10(8) M(-1) s(-1) involving large concentration gradients. Experimental comparison using three independent approaches

A program has been developed for the implementation of a mathematical treatment which corrects for a concentration gradient within the stopped-flow observation cell for reversible second-order reaction kinetics studied by longitudinal absorbance measurements. This program has been tested using experimental kinetic data for three selected electron-transfer cross reactions with predicted rate constants of 1.1 x 10(6), 5.8 x 10(7), and 1.2 x 10(8) M(-1) s(-1), respectively. A second gradient-corrected approach has also been applied based on the steady-state absorbance which exists after the flow tube has been filled with the new reaction mixture just prior to the stopping of the flow (a permutation of the continuous-flow method). As a third comparison, the same data were also analyzed using a standard reversible second-order kinetic treatment, without corrections for the concentration gradient, by applying an appropriate time base correction. The experimental kinetic data were obtained using an unmodified commercial stopped-flow instrument with a 2.0 cm observation cell, a measured filling time of 3.8 ms, and a total dead time of 4.6 ms. For reactions with Delta epsilon greater than or equal to 10(4) M(-1) cm(-1) all three methods have been shown to be capable of resolving second-order rate constants up to and exceeding 10(8) M(-1) s(-1) under conditions where the initial half-life is as small as 600 mu s (i.e., about one-eighth the dead time). When the absorbance change becomes extremely small, the steady-state approach appears to generate the most reliable rate constant values. The most surprising observation is that the standard second-order treatment-which ignores the existence of a concentration gradient-yields rate constant values which are virtually identical to those obtained when the gradient correction is taken into account. The implications of this discovery are discussed. The demonstrated ability of a standard commercial stopped-flow instrument to yield accurate second-order rate constants up to 10(8) M(-1) s(-1) represents at least a 10-fold extension in the previously presumed limits for this method.