Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

3 CONSISTENCY WITH COMPLICATED RATE EXPRESSIONS 399is based upon the value of the initial rate. In the case of parallel reactions, theinitial rate is the maximum rate observed as can be seen from eqn. (87); on theother hand, a chain reaction would normally exhibit an induction period in whichthe rate of the reaction increases from a small initial value to a maximum value.If the reaction is thought to be a chain reaction, no guidance can be given as to thelikely form of the rate expression since, in these reactions, a wide range of kineticbehaviour is observed-probably the most practicable procedure is to postulate amechanism, deduceits kineticconsequences and test the data against these. Ofcourse,there are many chain reactions whose induction periods are so short that they areundetectable in the usual type of experimmtal procedure. However, those of thisgroup which are unaffected by the addition of product would be unlikely to be confusedwith parallel reactions since their variable stoichiometry would be confined to theinduction period; with apparently invariant stoichiometry and an initial rate themaximum observed and independent of the product concentration, this groupof chain reactions would automatically be examined on the basis of eqn. (1) andwould, therefore, not be considered as possible parallel reactions.If the products affect the initial reaction rate, the reaction is either reversibleor it involves a sequence of consecutive reactions in which the product enters as areactant at one stage-this sequence of consecutive reactions could well be achain reaction. If the reaction were a simple reversible reaction, e.g.A+B --t P+QP+Q 3 A+Bwe should observe that the initial rate is the maximum rate observed, that theinitial rate is reduced by the addition of the products and that the stoichiometryof the reaction is independent of time. In this case, the data should be examinedon the basis of an expression of the type generalized by eqn. (85); a common formis--- d[A1 - k,[A]"[Blb- kz[P]"[Q]QdtOn the other hand, in the usual type of consecutive reaction involvingproduct as areactant, the initial rate is not the maximum observed since the rate increases asproduct is formed; for this reason, the initial rate is increased by the addition of theproduct at the beginning of the reaction and the stoichiometry alters as the reactionproceeds. For this type of reaction, we require an equation of the type set outin eqn. (84), namely- dE1 = k,[A]"1[B]b1+kz[A~[P]P2+ ...dtSuch expressions are always extremely difficult to deal with.References p. 407