The energy profile diagram for a multi-step reaction,$A$ $\xrightarrow{1} B$ $\xrightarrow{2} C$ $\xrightarrow{3} D,$ is given below. The rate-determining step of the reaction is:

For a reaction taking place in three steps at the same temperature,the overall rate constant is $K = \frac{K_1 K_2}{K_3}$. If $E_{a1}$,$E_{a2}$,and $E_{a3}$ are $40 \ kJ/mol$,$50 \ kJ/mol$,and $60 \ kJ/mol$ respectively,the overall activation energy $E_a$ is . . . . . . $kJ/mol$.

What is the activation energy for the reverse of this reaction?
$N_2O_{4(g)} \to 2NO_{2(g)}$
Data for the given reaction is:
$\Delta H = +54 \ kJ$ and $E_a = +57.2 \ kJ$
Answer in $kJ$.

$A$ catalyst

For a first-order reaction,the time taken to complete $10\%$ at $298\, K$ is equal to the time taken to complete $25\%$ at $308\, K$. The activation energy of the reaction is ................ $kJ/mol$.

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