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

Explanation

Half life of a reaction is defined as the time required for the reactant concentration to reach one half of its initial value.
For a first order reaction, the half life is a constant i.e., it does not depend on the initial concentration.
The 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)`