Integrated rate laws consecutive

A special problem arises with consecutive reactions, A —> B — C (Scheme 3.1, centre), that have similar rate constants.199 The integrated rate law for the time-dependent... 

The first serious challenge to the single-step mechanism for the reaction for the nitroalkanes in water appeared in 2001 for the reaction of 1-(4-nitrophenyl)-ethane (NNPEh) with sodium hydroxide in water/acetonitrile (50 50 vol. %). The kinetics of the reaction (Scheme 1.16) were studied under pseudo-first-order conditions using stopped-flow spectrophotometry and the data were analyzed as IRC-time profiles. Rate constants and KIE were obtained by fitting experimental to calculated data for the reversible consecutive mechanism (Scheme 1.17) which is the simplest bimolecular mechanism. The theoretical data were obtained using the integrated rate law for that mechanism ignoring B as appropriate for pseudo-first-order conditions. 

Rate laws derived for reaction schemes consisting of any number and combination of consecutive, parallel and independent first-order reaction steps can be integrated in closed form to give a sum of exponential terms, so that the total absorbance A of a solution in which these reactions proceed can also be expressed as a sum of exponential terms (Equation 3.9), but see last paragraph of this Section. 

Two consecutive reactions constitute a simple mechanism for a chemical reaction, and the rate law can be integrated for a simple case. 

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