Second-order reactions, complication half-life

Even for more complicated reactions, the linear half-life expression is a good approximation for short times. Second-order reactions have a characteristic time of 1/kC, and a general time constant for higher-order reactions can be defined l/kC" . The concepts of rate and characteristic time are used interchangeably throughout the chapter. 

It is not uncommon to find the persistence of a spin adduct quantified in terms of half-life . This is a dangerous practice unless the experimental conditions are precisely defined, or it is known that the nitroxide decays by a unimolecular process. Decay may depend on reaction with a reducing agent present in the system, in which case the concentration of this species will influence the half-life. More commonly, decay will be second order (p. 5), in which case the time for disappearance of 50% of the spin adduct will show a profound dependence on its absolute concentration. The possibility of bimolecular association of nitroxides has been recognized for many years, but only very recently has it been suggested that this may be a complication under experimental conditions employed for spin trapping. Whilst the problem, which was encountered with the important [DMPO-HO ] system (Bullock et al., 1980), seems unlikely to be widespread, it is one which should always be borne in mind in quantitative studies. 

For first-order reactions in closed vessels, the half-life is independent of the initial reactant concentration. Defining characteristic times for second- and third-order reactions is somewhat complicated in that concentration units appear in the reaction rate constant k. Integrated expressions are available in standard references (e.g., Capellos and Bielski, 1980 Laidler, 1987 Moore and Pearson, 1981). 

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