A → B (first reaction); C → D (second reaction) Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double…

$$\begin{aligned} & \mathrm{A} \longrightarrow \mathrm{~B} \text { (first reaction) } \\ & \mathrm{C} \longrightarrow \mathrm{D} \text { (second reaction) } \end{aligned} $$Consider the above two first-order reactions. The rate constant for first reaction at $\displaystyle 500$ K is double of the same at $\displaystyle 300$ K . At $\displaystyle 500$ K, $\displaystyle 50$ % of the reaction becomes complete in $\displaystyle 2$ hour. The activation energy of the second reaction is half of that of first reaction. If the rate constant at $\displaystyle 500$ K of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at $\displaystyle 300$ K is $\displaystyle \_\_\_\_$ $\displaystyle \times 10^{-1}$ hour $\displaystyle ^{-1}$ (nearest integer).