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Analysis of relative rate measurements
Author(s) -
Brauers Theo,
FinlaysonPitts Barbara J.
Publication year - 1997
Publication title -
international journal of chemical kinetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.341
H-Index - 68
eISSN - 1097-4601
pISSN - 0538-8066
DOI - 10.1002/(sici)1097-4601(1997)29:9<665::aid-kin3>3.0.co;2-s
Subject(s) - chemistry , reaction rate constant , linear regression , constant (computer programming) , analytical chemistry (journal) , monte carlo method , statistics , systematic error , random error , least squares function approximation , thermodynamics , mathematics , chromatography , physics , kinetics , quantum mechanics , estimator , computer science , programming language
Relative rate measurements using a reference compound with a well established rate constant are widely used for determining rate constants for gas‐phase reactions. Linear least‐squares regression is used to obtain the rate constant ratio, k A / k B , from the slope of plots of ln ([ A ] 0 /[ A ] t ) vs. ln ([ B ] 0 /[ B ] t ) where [ A ] 0 and [ B ] 0 are the initial concentrations of the reactant of interest, A , and of the reference 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 obtained from the slope of such plots. The magnitude of this bias was explored using Monte Carlo simulations. It is shown that although the bias is small for typical reaction conditions, of the order of a few percent, it can be of the same order of magnitude as the measured precision of most relative rate experiments. An algorithm for the analysis of such experiments which takes into account errors in both [ A ] and [ B ] and which avoids this systematic bias is discussed. © 1997 John Wiley & Sons, Inc.