Rate Law from Data—Two Examples

Many sources of error complicate the deduction of a rate law from kinetic data. In each experiment the time dependence of the concentration has a specific functional form which is usually not self-evident from the data unless isolation or relaxation methods are used. In addition no data ever precisely fit a trial function. However, if all errors in the experiment are random, probabilistic methods can be used to determine whether the trial function is reasonable and to estimate the parameters of the function. As long as only a single chemical process is significant, isolation and relaxation data are most readily treated using linear least-squares analysis, described in the Appendix. This procedure provides the most reliable estimate of the decay constant. Then, by varying experimental conditions the concentration dependence of the decay constant can be obtained. With such information probabilistic methods are again useful. A presumed rate 

Hammes, ed., Investigations of Rates and Mechanisms of Reactions, Part. II (New York Wiley-Interscience, 1974), p. 57. 

In general the kineticist is faced with the problem of deducing rate laws that describe consecutive reactions involving many steps. The corresponding rate equations are coupled, and, in most cases, the functions that are to be fit cannot be determined using linear least-squares analysis. A vast literature of nonlinear function-fitting methods exists to treat these problems. 

L A Concentration-Dependent Rate Constant The electron-transfer reaction 

While the fit is gratifying, it is hardly conclusive since many other functions are qualitatively similar, e.g.. 

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