Half-Lives and Lifetimes

A rate constant is a quantitative measure of how fast reactions proceed and therefore is an indicator of how long a given set of reactants will survive in the atmosphere under a particular set of reactant concentrations. However, the rate constant per se is not a parameter that by itself is readily related to the average length of time a species will survive in the atmosphere before reacting. More intuitively meaningful parameters are the half-life (/l/2) or the natural lifetime (r), the latter usually referred to simply as lifetime, of a pollutant with respect to reaction with a labile species such as OH or NO-, radicals. 

The half-life (tl/2) is defined as the time required for the concentration of a reactant to fall to one-half of its initial value, whereas the lifetime is defined as the time it takes for the reactant concentration to fall to /e of its initial value (e is the base of natural logarithms, 2.718). Both tl/2 and r are directly related to the rate constant and to the concentrations of any other reactants involved in the reactions. These relationships are given in general form in Table 5.2 for first-, second-, and third-order reactions and are derived in Box 5.1. 

TABLE 5.2 Relationships between the Rate Constant, Half-Lives, and Lifetimes for First-, Second-, and Third-Order Reactions 

Reaction order Reaction Half-life of A Lifetime of A 

A relevant example is the use of lifetimes to characterize the reactivity of organics. Compressed natural gas (CNG), for example, is a widely used fuel whose major component is methane, CH4. The only known significant chemical loss process for CH4 is reaction with OH  

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The expressions for half-lives and lifetimes in Table 5.2 can be readily derived from the rate laws. For a first-order reaction of a pollutant species A, the rate law for the reaction... 

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