Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]”[BIb 375case, weighting in accordance with the reciprocals of either the squares of the errorbars or the error bars themselves is precisely equivalent to the two proceduresgiven.To summarize this matter of weighting, we can say that there are three differentsystems of assigning values to wij. These are:(1) wij = 1In most cases where non-linear functions of c1 are being considered, the firstmethod is unsatisfactory and so the choice lies between methods (2) and (3).Of these two procedures, method (2) is the more soundly based. It must be said,however, that weighting is, to a considerable extent, a matter of personal judgementand so the use of method (2) is not automatic in every case. The one certainrule that can be given is that every worker should state exactly which method ofweighting has been used and briefly indicate his reasons for his choice. Withoutthis information, it is very difficult to assess the reliability of the quoted ratecoefficient.(ii) The quantities ki and s(k;)Assuming that the previous calculations have been carried out, we now have a setof r values of k; and s(k;). Since some of the runs correspond to different initialconcentration conditions, the value of k; [and s(k;)] are not comparable directly.We therefore calculate the rate coefficient, kl, and an estimate of its standard error,s(k,), for each run using the simple expressionsNaturally, it is highly unlikely that all the calculated values of ki will be identicaland so the question arises ax to whether the differences between them are thosewhich result from the random error of measurement or whether they indicate thatthe rate equation under investigation does not represent the data adequately.Before discussing this important question, let us consider briefly the significanceof the basic quantities k; and s(k;); it is then not difficult to understand the significanceof the related quantities ki and s(ki).References p. 407