Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]"[BIb 373Combining eqns. (65), (66) and (67), we obtainwhich, irrespective of the values of a and b, shows thatorwi, 0 as ail 3 0 (c+ve)w,+O as a[,+ -c (c-ve)In other words, the experimental determinations made towards the end of areaction contribute very little to the least squares estimate of the rate coefficient.Eqn. (68) is of little use in computation, however, unless we can make some statementabout a(ai,). There are two clearcut situations which we can discuss. Thefirst of these situations is that the value of o(a,) does not depend onjand so withinany one run, o(ai,) is a constant. In other words, were it possible to determinea large number of values of each all, the width of the normal distribution would bethe same in each case. Since it is only relative weights which are important incomputation, we can omit such constant factors from the weights [as was done ineqn. (65)] and writewhen a(.[,) is independent ofj. The alternative situation which permits of discussionis that which arises when o(aij) is proportional to aij so that a(ai,)/ai, remainsconstant throughout the run; this situation is described by saying that the relativeerror in ai, is constant. In this caseThe choice between these two alternatives can only be made by considering theexperimental technique employed to determine the concentration of A.A simple example of common occurrence will illustrate the difference betweenthe two weighting procedures. Consider a simple first order disappearance ofA whose rate equation isordadt--Ika in differential form,-In a = k(t - to) in integral form.so that f(a) = In a.References p. 407