The rate equation for a reaction, $A ⟶ B$ is $r = {k [A]}^{0}$ . If the initial concentration of the reactant is $a$ $m o l . {d m}^{- 3}$ , the half-life period of the reaction is:

\frac{a}{2 k}

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\frac{k}{a}

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\frac{a}{k}

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\frac{2 a}{k}

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Solution

The correct option is A $\frac{a}{2 k}$
Reaction is $A ⟶ B$
Rate is given as $r = k [A]^{0} = k$
Order of the reaction is 0.

Initial concentration of A is $A_{0} = a$
Order of the reaction is zero.

Half-life, $t_{1 / 2} = \frac{[A_{0}]}{2 k} = \frac{a}{2 k}$

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