Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

3 CHEMICAL RELAXATION METHODS 131ture of the relaxation expression for a reaction proceeding via an intermediate, e.g.AB+C zA+B+C f A+ BC (3 1will depend on the nature of the intermediate, in this case B. If the concentrationof B is small relative to those of the other species (e.g., if B cannot be detected),then the steady state hypothesis may be applied to its formation and dissociationrates. The concentration of B will not appear in the expression for the relaxationtime, and this reaction will effectively be single-step, with only one relaxation time.If, on the other hand, the intermediate B is present in significant concentrations,then the system must be regarded as two-step, and will generally be associatedwith two relaxation times. In general, a multi-step reaction will be characterized by a“spectrum” of relaxation times whose order depends on the number of independentrelaxation steps (but not necessarily in a simple way). As the number of steps increases,the complexity of the relaxation expression also increases. Relaxation expressionshave been derived for several generalized systems3 3, 3s.@ HOx + Mg2+ MgOxH2+ @‘32’23Fig. 6. The formation of the magnesium-8-hydroxyquinoline 1 :1 complex (MgOx+) from protonated(HOx) and deprotonated (Ox-) 8-hydroxyquinolineThe system (3) can be mide a little more general. Suppose it is also possible forAB+C to go directly to A+BC. Then, if this is a “single-step” reaction (i.e., EBis relatively small), there will only be one relaxation time, but its expression willcontain the sum of all the rate coefficients of the component reactions, with theircorresponding concentration terms. It is sometimes a little difficult to differentiatebetween a single-step and a multiple-step reaction, but if more than one relaxationtime is observed then the reaction is necessarily a multiple-step one. The reverseis not necessarily true.A reaction which illustrates these principles quite well is the formation and dissociationof the 1 : 1 complex between magnesium and 8-hydroxyquinoline (oxine)in water 36. The postulated mechanism is shown in Fig. 6. MgOx’ may be regardedas being formed by two parallel paths: by the reaction of Mg2+ with the oxine anion(Ox-) or with the neutral molecule (HOx). Under the conditions used, the concentrationsof HOx and Ox- were comparable.t Consequently, the reaction via patht In this reaction scheme, H+ is the species present in smallest concentration, but, because it isbuffered, xH+ is effectively zero. It is therefore necessary to consider the species present in nextsmallest concentration, which may be any one of MgOx’, Ox- or HOx.References pp. 176-1 79