Question

Show that the half-life period of a first order reaction is independent of the initial concentration of the reactant.

Answer 1

Half life period $t_{1/2}$ of a reaction is defined as the time required to reduced the concentration of a reactant to one half of its initial value.

$k_1=\frac{2.303}{t}log\left(\frac{a}{a-x}\right)$

if amount reacted $x=\frac{a}{2}$then $t=t_{1/1}$

$\therefore t_{1/2}=\frac{2.303}{t}log\left(\frac{a}{a-a/2}\right)$

$t_{1/2}=\frac{2.303log\left(2.0\right)}{k_1}\Rightarrow t_{1/2}=\frac{0.693}{k_1}secs$

Thus half life period of a first order reaction is independent of the initial concentration of the reactant.