Define half life of a reaction, Show that for a first order reaction half life is independent of initial concentration.

Explanation

(i) The half life of a reaction is defined as the time required for the reactant concentration to one half its initial value.
(ii) For a first order reaction, the half life is a constant i.e., it does not depend on the initial concentration. Then rate constant for a first order reaction is given by
`k=(2.303)/(t)"log"([A_(0)])/([A])`
at `t=t_(1//2),[A]=[A_(0)]_(//2)`
`k=(2.303)/(t_(1//2))"log"([A_(0)])/([A_(0)]_(//2))`
`k=(2.303)/(t_(1//2))log 2`
`k=(2.303xx0.3010)/(t_(1//2))=(0.6932)/(t_(1//2))`
`t_(1//2)=(0.6932)/(k)`