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(A) For a first-order reaction,the half-life period is given by $t_{1/2} = \frac{0.693}{k}$. This shows that $t_{1/2}$ is independent of the initial c

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$(i), (iii)$

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(A) For a first-order reaction,the half-life period is given by $t_{1/2} = \frac{0.693}{k}$. This shows that $t_{1/2}$ is independent of the initial concentration $[A_0]$,which corresponds to graph $(i)$.The integrated rate equation for a first-order reaction is $\log \frac{[A_0]}{[A]} = \frac{kt}{2.303}$. Plotting $\log \frac{[A_0]}{[A]}$ versus time $t$ gives a straight line passing through the origin with a slope of $\frac{k}{2.303}$,which corresponds to graph $(iii)$.Graph $(ii)$ represents a zero-order reaction where $t_{1/2} \propto [A_0]$.Therefore,graphs $(i)$ and $(iii)$ belong to a first-order reaction.

In the following graphs,which graph$(s)$ belong to a first-order reaction?

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