Q.Write the mathematical relation between half life of zero order reaction and its rate constant.

Half-life of a zero order reaction is directly proportional to the initial concentration.

For a zero order reaction, the integrated rate law is $[A] = [A]_0 - kt$. At $t = t_{1/2}$, $[A] = [A]_0/2$:

$\frac{[A]_0}{2} = [A]_0 - kt_{1/2} \implies kt_{1/2} = \frac{[A]_0}{2} \implies t_{1/2} = \frac{[A]_0}{2k}$ …

Substituting $[A]=[A]_0/2$ at $t=t_{1/2}$ into the zero-order integrated rate law gives $t_{1/2}=[A]_0/2k$.

The integrated rate law for a zero order reaction is $[A]_t = [A]_0 - kt$. At the half-life, $t=t_{1/2}$ and $[A]_t = [A]_0/2$:

$\dfrac{[A]_0}{2} = [A]_0 - k\,t_{1/2} \Rightarrow k\,t_{1/2} = [A]_0 - \dfrac{[A]_0}{2} = \dfrac{[A]_0}{2}$

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