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Half-Life of first Order Reaction

April 8th, 2008

A general formula of the half life of the first order reaction can be derived from the integrated rate law for the general reaction:

aA -> products

If the reaction is fisrt order in [A] we can write that:

ln([A]o/[A]) = kt

when t=t_1/2 the equation above become:

[A] = [Ao]/2

thus for t=t_1/2 the integrated rate law becomes:

ln { [A]o/([A]/2) } = kt_1/2
ln(2) = kt_1/2

by substituting ln(2) = 0.693 and solving for the t_1/2 we have:

t_1/2 = 0.693/k

The last equation above is the general equation for the half-life of the first order reaction. Note that for the first order reaction, the half life does not depend on the concentration.

Entry Filed under: Chemical Kinetics