Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]”[B]’ 383andc W(k;)jk; - E‘)’i=rvi= 11= 1i=r.r,-1i=r.c Elc (ni-2)i= 1each provide an estimate of 0’. The first quantity estimates 0’ from the scatterof the individual values of k; about their weighted mean while the second quantitypredicts 0’ from the weighted sum of the squares of the residuals over all the lines[see eqns. (61) and (62)]. If we write the ratio Faswe can decide the maximum value of F which is consistent with the hypothesisthat the replicate experiments constitute an homogeneous group for a chosenconfidence level and given values of (r,, - 1) and xi:‘;. (4-2). If F < 1, the groupis homogeneous since the scatter of the gradients of the lines about their mean canbe accommodated within the scatter of the individual points about the lines.Similarly, if F > 1 but is less than the critical value, the situation needs no discussion.The real problem arises when the replicate experiments are found to constitutea non-homogeneous group for then the straight lines are so well-defined that thedifferences between the gradients are significant. In this case, it is probable thatthe reaction rate is influenced by some factor which, although remaining constantwithin any one run, varies from experiment to experiment within the group. Forexample, suppose the group of replicate experiments were carried out in a thermostaton separate days and suppose that,for some reason, thethermostat temperatureshifted slightly from day to day though remaining constant over the time scaleof any one experiment. Such a day-to-day temperature variation could give rise toa non-homogeneous group of k; values if the points on the graphs of f(crij) against(fir - ti,,) happened to fall on particularly well-defined straight lines. Anotherexample is afforded by the three experiments, 1,2 and 3, of Table 3; the reason fortheir non-homogeneity is disccssed in Appendix 2. If the data of a group of replicateexperiments do not survive the test for homogeneity, the experimental techniquesemployed must be critically considered. It may be possible to redesign theprocedures so that the uncontrolled factors are eliminated and satisfactory replica-References p. 407