For a first order reaction, the half - life period is independent of

The rate depends upon the concentration of one reactant only is known as first Order reaction.

$\frac{-\mathrm{dx}}{\mathrm{dt}}=K\left[A\right]$

The integrated rate law for first order reaction is

$\mathrm{K}=\frac{2.303}{\mathrm{t}}{\log }_{10}\frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}\to \mathrm{eqn}\left(1\right)$

The time taken for completion of one-half from the initial concentration is called half life of a reaction.

When $\mathrm{x}=\frac{\mathrm{a}}{2} \& \mathrm{t}={\mathrm{t}}_{\frac{1}{2}},\mathrm{then} \mathrm{the} \mathrm{eqn},\left(1\right) \mathrm{becomes}$

$\mathrm{K}=\frac{2.303}{{\mathrm{t}}_{{\displaystyle \frac{1}{2}}}}{\log }_{10}\frac{\mathrm{a}}{\mathrm{a}-{\displaystyle \frac{\mathrm{a}}{2}}}$

$\Rightarrow \mathrm{K}=\frac{2.303}{{\mathrm{t}}_{{\displaystyle \frac{1}{2}}}}{\log }_{10}2$

$\therefore {\mathrm{t}}_{\frac{1}{2}}=\frac{0.693}{\mathrm{k}}$

Thus, 1/2 t is independent of initial concentration.