Method of half-lives

The method of half-lives requires many experiments 

The haif-life of a reaction, is defined as the time it take.s for the conci tration of the reactant to fall to half of its initial value. By determining half-life of a reaction as a function of the initial concentration, the reacii order and specific reaction rate can be determined. If two reactants. involved in the chemical reaction, the experimenter will use the method excess in conjunction with the method of half-lives to arrange the rate law the form 

The concept of a a mole balance on species A in a constant-volume batch reaction system c half life. f i. is bined with the rate law results in the following expression very imponani in 

Integrating with the initial condition Q Cao when / = 0, we find that 

The half-life is defined as the time required for the concentration to drop half of its initial value that is. 

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B. Method of Half-lives. The time required to consume a given fraction, say one-half, of one of the starting materials will depend on the initial concentration of the reactants in a way which is fixed by the order of the reaction. If a number of experiments have been performed under conditions of very different initial concentrations of reactants, then it is possible from a comparison of the half-lives (or other fraction, whichever is more conveniently obtained from the data) in the different experiments bo decide the proper order of the reaction. 

The method of half-lives offers a simple, direct approach to the estimation of reaction order and one which involves the least amount of computation when only one species is involved in the rate equation. It becomes, however, fairly complicated when applied to systems in which there is more than one reactant (see Table II.2). 

For the method of half-lives, taking the natural log of both sides of Equation (5-18),... 

Method of Initial Rates 239 Method of Half-Lives 242 Differential Reactors 243... 

P5-9. Straight forward problem involving the method of half lives. 

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