Question

What is the half-life period of reaction? Justify from the rate equation for first-order reactions that the half-life period for such reaction is independent of the initial concentrations of the reactants.

Answer 1

The half-life period of reaction is the time needed for the reactant concentration to fall to one half of its initial value.
The rate equation for first order reaction is $k=\frac{2.303}{t}log\frac{[A{]}_0}{[A{]}_t}$
When time $t=t_{1/2}=$ half life period, the initial concentration decreases from $[A{]}_0$ to $\frac{[A{]}_0}{2}$
$k=\frac{2.303}{t_{1/2}}log\frac{[A{]}_0}{\frac{[A{]}_0}{2}}$
$k=\frac{2.303}{t_{1/2}}log2$
$k=\frac{0.693}{k}$
Hence, the half-life period for such reaction is independent of the initial concentrations of the reactants.