Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

4 DEPENDENCE OF RATE COEFFICIENTS ON VARIOUS FACTORS 403and--- d[A1 - k[A] + k’[A]’dt(Fig. 4)The numerical data for the construction of these curves are given in Appendix 4.The use of these and analogous curves to estimate the quantities Q, , u2, and Kshould be obvious; furthermore, the dependence of K and the displacement of thelog,, 6, log,, (t-to) scales on [B], enables estimates of b, and bz to be made.It is not necessary to give full details, for this procedure merely exemplifies thepoint that, by studying the reaction under experimental conditions where thekinetic equations assume comparatively simple forms, it is possible to obtainestimates of the rate coefficients and exponents. As an alternative to the reactionbeing studied in the presence of a large excess of A or B, these special conditionsmay correspond to the position at which a particular product reaches its maximumconcentration or to the position at which the reaction comes to equilibrium.Once some idea has been obtained of the type of expression that is required,it is then possible to integrate the rate equations numerically. An iterative methodis often convenient; the iteration would normally take the exponents in the variousconcentration terms as fixed and would proceed by substituting trial values ofthe rate coefficients (estimates of these having been obtained from prior experiments)in the differential equations and integrating: in this way, it is possible tofind values which give a satisfactory match of calculated and observed data.The question of the criterion of fit is outside the scope of this chapter.Some examples of the procedures employed when dealing with particular typesof reaction mechanism are given in Chapter 1, Vol. 2.4. Elucidating the dependence of the rate coefficient(s) on temperature, concentrationof catalyst, and ionic strengthIn general, the rate coefficient is a function of all factors which influence thereaction rate other than the concentrations of the reactants and products. We shallonly consider three factors here, namely temperature, concentration of catalystand ionic strength. The general experimental procedure is obvious. For example,suppose we wish to elucidate the effect of temperature on a particular rate coefficient.For this purpose, we perform a set of kinetic experiments at a particulartemperature T, keeping all other factors which are liable to influence the ratecoefficient constant. Following the procedures given earlier, we calculate therate coefficient and its standard error (if possible). We then repeat the experimentsat other temperatures Tz, T,, . : . etc., keeping the values of the other factorsconstant throughout the series. In this way, we obtain a set of values for k at thevarious temperatures T, , T2 , etc. Clearly, we can study the influence of the otherfactors on the rate coefficient in an analogous fashion.References p. 407