ANALYSIS OF RELATIVE RATE MEASUREMENTS

Relative rate measurements using a reference compound with a well esta blished rate constant are widely used for determining rate constants f or gas-phase reactions. Linear least-squares regression is used to obt ain the rate constant ratio, k(A)/k(B),, from the slope of plots of In ([A](0)/[A](t)) vs. In ([B](0)/[B](t)) where [A](0) and [B](0) are th e initial concentrations of the reactant of interest, A, and of the re ference compound, B, respectively and the subscript ''t'' denotes the corresponding concentrations at time t. Linear least-squares analysis which does not take into account random errors in both [A] and [B] may lead to a small but systematic bias in the relative rate constant obt ained from the slope of such plots. The magnitude of this bias was exp lored using Monte Carlo simulations. It is shown that although the bia s is small for typical reaction conditions, of the order of a few perc ent, it can be of the same order of magnitude as the measured precisio n of most relative rate experiments. An algorithm for the analysis of such experiments which takes into account errors in both [A] and [B] a nd which avoids this systematic bias is discussed. (CV) 1997 John Wile y & Sons. Inc.