Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

386 TREATMENT OF EXPERIMENTAL DATAThis procedure is all very well, but a problem arises if the F-test suggests thatthe scatter of the ratecoe5cients is not consistent with the scatter of the pointsabout the lines. If no replicate experiments have been performed, there are insufficientdata to test the reproducibility of the procedure. In this case, failure ofthe data to pass the F-test is as likely to arise from inadequate control of theexperimental conditions as from incorrect assumptions about the form of the rateequation. It follows, therefore, that a certain amount of replication is desirable.The essential feature of the procedures described above is that the test employedto decide whether or not a given rate equation represents the kinetics of a particularreaction is based on the values of the rate coefficients obtained at a number ofdifferent values of [A], and [B],. If the rate coefficients show no systematicvariation with one or other of the initial concentrations, the assumed rate equationis applicable and the orders a and b postulated from the preliminary examination ofthe data are confirmed. Linearity of the graph of a particular form of f(a) against(r - to) at one pair of values of [A], and [B], is not conclusive proof of the applicabilityof the chosen rate equation since it is a matter of fairly common experiencethat kinetic data may fit a particular equation quite well at one set of initialconcentrations only to show significant deviations when the initial concentrationsare changed.(c) A re-examination of the functions f(a) of Table IWe have already suggested that eacn equation of Table 1 can be written in thegeneral formf(uo)-f(a) = k'(t-to)With the exception of eqns. (34) to (38), this formulation is inexact since eachintegrated expression contains the parameter c; a better generalization of theequations of Table 1 isf(uo, c)-f(u, c) = kyt-to) (78)For certain values of c, some of the equations given are inappropriate. Moresuitable forms are described in this section.It will be recalled thatc = (I/r) - 1where Z stands for the ratio oE the initial concentrations, [B],/[A],, and r representsthe ratio of the stoichiometric coefficients, vB/vA. Thus c can range fromvery large values (I >> r) to values close to - 1 (Z