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Half Life of a First Order Reaction

Half life is defined as the time during which the concentration of the reactants is reduced to half of the initial concentration or it is the time required for the completion of half of the reaction. It is denoted by t ½

For first order reaction, we know that

It is quite clear from the above expression that the half life period or half change time for first order reaction does not depend upon initial concentration of the reactants. Similarly, the time required to reduce the concentration of the reactant to any fraction of the initial concentration for the first order reaction is also independent of the initial concentration.



A2 à products

For the above reaction the rate,

r = -d[A] / dt = k [A]2

r = – k [A]2 = y = mx2

A graph of rate, r versus [A]2 will given a curve as in Fig. 20.20.

Integrating the second-order rate equation:

If a graph of concentration, [A]-1  versus time, t, is drawn and a straight line is obtained. It indicates a second-order reaction. The gradient of such a curve is k, the rate constant. This is shown in Fig. 20.20. When evaluated, the half-life

t ½ = 1 / k [A]0

indicating that the half-life of a second-order reaction depends inversely on the initial concentration [A]0, and rate constant, k.

Fig. 20.20. Graph of [A],-1 versus time for a second-order reaction.