For a reaction having three steps, the overall rate constant is $K = \frac{k_1 k_2}{k_3}$. The values of $E_{a1}$, $E_{a2}$ and $E_{a3}$ (activation energies for each step) are $40$, $50$ and $60 \text{ kJ mol}^{-1}$ respectively. The overall activation energy $E_a$ of the reaction is:

For a reversible reaction $A \rightleftharpoons B$,the $\Delta H_{\text{forward}} = 20 \ kJ \ mol^{-1}$. The activation energy of the uncatalysed forward reaction is $300 \ kJ \ mol^{-1}$. When the reaction is catalysed keeping the reactant concentration same,the rate of the catalysed forward reaction at $27^{\circ}C$ is found to be same as that of the uncatalysed reaction at $327^{\circ}C$. The activation energy of the catalysed backward reaction is $.... \ kJ \ mol^{-1}$.

$A$ reaction takes place in three steps with individual rate constant and activation energy as follows:

$Step$	$Rate \ constant$	$Activation \ energy$
$Step-1$	$k_1$	$E_{a1} = 180 \ kJ/mol$
$Step-2$	$k_2$	$E_{a2} = 80 \ kJ/mol$
$Step-3$	$k_3$	$E_{a3} = 50 \ kJ/mol$

If overall rate constant,$k = (\frac{k_1 k_2}{k_3})^{2/3}$,then overall activation energy of the reaction will be .......... $kJ/mol$.

The rate of a chemical reaction doubles for every $10\,^{\circ}C$ rise of temperature. If the temperature is raised by $50\,^{\circ}C,$ the rate of the reaction increases by about ......... times.

The following graph is obtained for a reaction $(A \rightarrow P)$. The activation energy ($E_{a}$ in $kJ \ mol^{-1}$) and heat of reaction ($|\Delta H|$ in $kJ \ mol^{-1}$) for this reaction are respectively ($x=$ reaction coordinate; $y=E$ in $kJ \ mol^{-1}$)

The rate of a reaction doubles when its temperature changes from $300 \, K$ to $310 \, K.$ Activation energy of such a reaction will be .......... $kJ \, mol^{-1}$. $(R= 8.314 \, J \, K^{-1} \, mol^{-1}$ and $\log 2=0.301)$