At a particular temperature, the magnitude of the rate constant of a reaction is $5 \times 10^{-5}$ and the unit of the pre-exponential factor of the Arrhenius equation for this reaction is $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~min}^{-1}$. Which of the following plots is correct for this reaction?

$\left[\right.$ Note: $[\mathrm{R}]_0$ is the initial concentration and $t_{1 / 2}$ is the half-life of the reaction $]$

For a reaction $R \rightarrow P$ with a rate constant of $3 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$, which one of the following plots is correct? (Given [R] $]_0$ is the initial concentration of $R$ and $[R]$ is the concentration of $R$ at time t)

A first-order reaction is found to have a half-life of one second (sec). What will be the time required for $99.9 \%$ completion of the reaction?