The temperature coefficient of the saponification reaction of an ester by $NaOH$ is $1.75$. The activation energy of the reaction is .......... $kcal \ mol^{-1}$. (in $.21$)

The energies of activation for forward and reverse reactions for $A_2 + B_2 \rightleftharpoons 2AB$ are $180 \, kJ \, mol^{-1}$ and $200 \, kJ \, mol^{-1}$ respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by $100 \, kJ \, mol^{-1}.$ The enthalpy change of the reaction $(A_2 + B_2 \rightarrow 2AB)$ in the presence of a catalyst will be (in $kJ \, mol^{-1}$)

$A$ 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 .......... $kJ/mol$.

Activation energy of any reaction depends on

The rate constant of a reaction increases by five times on increase in temperature from $27^{\circ} C$ to $52^{\circ} C$. The value of activation energy in $kJ \, mol^{-1}$ is $....$ . (Rounded-off to the nearest integer) $[R = 8.314 \, J \, K^{-1} \, mol^{-1}]$

In the Arrhenius equation,the fraction of molecules having energy equal to or greater than the activation energy at a given temperature is represented by .....