MATHEMATICAL TREATMENT FOR VERY RAPID 2ND-ORDER REVERSIBLE KINETICS AS MEASURED BY STOPPED-FLOW SPECTROPHOTOMETRY WITH CORRECTIONS FOR THE CELL CONCENTRATION GRADIENT

A mathematical approach is described for treating stopped-flow spectro photometric data for very rapid second-order reversible reactions. The treatment involves integration of the theoretical concentration gradi ent down the length of the observation cell, based on an experimentall y measured filling time. No restrictions are placed on the starting re agent concentrations, and allowance is made for the presence ed finite amounts of product at the selected ''zero'' time, that is, the treatm ent allows for reversible reactions with prior product formation. Care ful calibration of the stopped-flow instrument is required since absol ute, rather than relative, values of the absorbance must be utilized. Using a computer analysis based on the described mathematical treatmen t, it is anticipated that second-order rate constants as large as 10(8 ) M(-1) s(-1) may be determined with reasonable accuracy for reactions with sizeable absorbance changes (Delta epsilon > 10(4)) using instru ments with filling times on the order of 3 ms.