$k=\frac{2.303}{t} \log \frac{a}{a-x}$

Where, $k=$ Rate constant

$a=$ initial concentration

$a-x=$ concentration after time ${ }^{\prime} t^{\prime}$

For half-life, $t=t_{1 / 2}, x=\frac{a}{2}$

On substituting the values, we get

$k=\frac{2.303}{t_{1 / 2}} \log \frac{a}{a-\frac{a}{2}}=\frac{2.303}{t_{1 / 2}} \log 2$

$=\frac{0.693}{t_{1 / 2}}$

$k=\frac{0.693}{t_{1 / 2}}$

Thus, $t_{1/2}$ of a first order reaction does not depend upon the concentration.