Question

Derive the relation between half-life period and rate constant for first order reaction

Answer 1

For a first order reaction differential rate law can be written as:

$-\frac{dA}{dt}=k\left[A\right]$ where $k$ is the rate constant of first order reaction

Integrating the above equation we can write the first order rate law expression as:

$[A{]}_t=[A{]}_o{e}^{-kt}$ or $kt=2.303log\frac{[A{]}_o}{[A{]}_t}$

For, half life period, $[A{]}_t=[A{]}_o/2$

Therefore, $t_{1/2}=\frac{2.303log2}{k}$ or $t_{1/2}=\frac{ln2}{k}$