Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

3 CONSISTENCY WITH COMPLICATED RATE EXPRESSIONS 397chemistry of the process under investigation, there is a good case for comparingthe fit of the data to an expression of the type (84) or (85) with the fit obtainedwhen it is represented by an equation of the type (86).Let us return to the criteria that we used to recognize a complex reaction. Westated that a reaction is necessarily characterized by a complicated rate expressionif, on a preliminary examination of the concentration-time data, we observe anyone of the following three features:(1) stoichiometric coefficients which vary with the extent of the reaction or withtemperature;(2) an initial rate which is affected by the presence of product;(3) an initial rate which is less than a rate observed at a later stage in the reaction.To these criteria, we might now add a fourth, namely, that a complicated rateexpression is required if(4) the concentration-time data cannot be adequately represented by the simplerate expression k[A]"[BIb.The variation of the stoichiometric coefficients is not in itself of great utilityin deciding upon one particular form of eqns. (84) or (85) for investigation. Itsimply means that the reactants are involved in more than one reaction in such away that their rate of disappearance is the sum or difference of the rates of theseparate reactions. For example, consider the simple mechanismA + P rate coefficient kiA+B + Q+R rate coefficient k2where the stoichiometric coefficients in the elementary reactions are unity. Anticipatingthe discussion of Chapter 1, Vol. 2, we have- a = k,[A]+k2[A][B]dt--= dCB1dtk2[A][B]and so the instantaneous ratio of the stoichiometric coefficients, ( v~/v~)~, is givenbyClearly this ratio varies with the extent of the reaction (or time) as theconcentrationof B alters. This example illustrates one very important point: although the variationof the stoichiometric coefficients in itself is no guide to the form taken by therate equation, a close examination of the timedependence of a particular stoichiometricratio may reveal that the reaction is divided into two stages:Reference; p. 407