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(D) For a zero-order reaction,the rate law is given by $r = K[A]^0 = K$. Integrating the rate equation,we get $[A]_t = [A]_0 - Kt$. At half-life $(t =

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$\frac{a}{2k}$

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(D) For a zero-order reaction,the rate law is given by $r = K[A]^0 = K$. Integrating the rate equation,we get $[A]_t = [A]_0 - Kt$. At half-life $(t = t_{1/2})$,the concentration of the reactant $[A]_t = \frac{[A]_0}{2} = \frac{a}{2}$. Substituting these values into the integrated rate equation: $\frac{a}{2} = a - K t_{1/2}$. Rearranging for $t_{1/2}$: $K t_{1/2} = a - \frac{a}{2} = \frac{a}{2}$. Therefore,$t_{1/2} = \frac{a}{2K}$.

For a reaction,$A \rightarrow B$,the rate equation is $r = K[A]^0$. If the initial concentration of the reactant is $a \ mol \ dm^{-3}$,find the half-life time of the reaction.

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