Half Life Period of a Reaction

Half life period of a reaction is defined as the time during which the concentration of a reactant is reduced to half of its initial concentration.

or

The time in which half of a reaction is completed. It is generally denoted as t_½

The half life period of a first order reaction may be calculated as given below:

The first order rate equation for the reaction

A ———–> Products

Now, half life period corresponds to time during which the initial concentration, [A]₀ is reduced to half i.e.

[A] = [A]₀ /2   at t= t_½

Then half life period, t_½ becomes

Thus, half life period of a first order reaction is independent of the initial concentration of the reactant. Half life period for the first order reaction is inversely proportional to the rate constant.

For example,

 

(i) time required to complete 1/3 of the reaction will be given as:

[A]_o = a ,  [A] = a – a/3=2/3a

(ii) time required to complete 3/4 of the reaction will be

[A]_o =  a , [A] = a – 3/4 a = 1/4 a

Half Life period of zero order and second order reactions

The integrated rate equation is ,

kt = [A]_o -[A]

For half life period, t_½ , [A] = [A]₀/2

t_½ = [A]_o /2k

Similarly for second order reaction,