Chemistry - Chemical Kinetics Question with Solution | TestHub

$\mathrm{A}\to \mathrm{B}$ (first reaction)

$\mathrm{C}\to \mathrm{D}$ (second reaction)

Consider the above two first-order reactions. The rate constant for the first reaction at $500\mathrm{K}$ is double that at $300\mathrm{K}$. At $500\mathrm{K}$, $50\%$ of the reaction becomes complete in $2$ hours. The activation energy of the second reaction is half that of the first reaction. If the rate constant at $500\mathrm{K}$ of the second reaction becomes double the rate constant of the first reaction at the same temperature, then the rate constant for the second reaction at $300\mathrm{K}$ is _______ $\times 10^{-1}$ hour^-1 (nearest integer).