Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]'[B]' 377The point is that, corresponding to the number of degrees of freedom used inestimating s(k;), we can look up in statistical tables the absolute value of t whichis exceeded with a given frequency. In this way, we can establish for a givenconfidence level the limits between which K; must lie. A numerical example takenfrom Appendix 2 will make this clearer.Example. Taking run 1 of the set of experiments, we find thatk; = 7.097 x sec-'s(k;) = 0.023 x sec-'n, = 22Our object in this example is to establish the 90% confidence limits for K;; thatis, the limits between which K; is likely to lie with 90% probability. From tables,90% of all values of t based on 20 degrees of freedom lie between f 1.72 and sothe 90 % confidence limits for the difference between k; and the population averagearef 1.72 x s(k;)= f0.w x sec"In other words, on the basis of the data of run 1, we expect with 90% confidencethat the 'true' value of the rate coefficient (the population average) will lie between(7.057 and 7.137) x sec- 'Returning to the general case, it should be obvious that, if we can establishconfidence limits for each value of k; , we can calculate confidence limits for eachvalue of the rate coefficient.(iii) Homogeneity of the rate coeficientsTo this point, our discussion has been confined to describing the methods ofprocessing the data of a single run and to offering some explanation of the significanceof the derived quantities. However, we have repeatedly stressed that validconclusions can only be reached if the data of several runs are compared. It is thepurpose of this section to demonstrate how this comparison is best carried out.We have r values of the rate coefficient together with a corresponding numberof estimates of standard error. This-set of values can be divided into u groupst These data are characterized by m, = 1 and so in this particular case ki can be identified withthe rate coefficient.References p. 407