When the temperature changes from $293 \ K$ to $313 \ K$,the rate of a certain reaction becomes four times. Find the activation energy of the reaction in $kJ \ mol^{-1}$. $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

When a biochemical reaction is carried out in a laboratory without the presence of enzymes,the rate of reaction is $10^{-6}$ times slower. What will be the activation energy $(E_a)$ in the presence of enzymes?

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 $.... \ kJ \ mol^{-1}$.

In a reversible reaction,the catalyst

$A$ reaction takes place in three steps with individual rate constant and activation energy,

Step	Rate constant and Activation energy
$Step \ 1$	$k_1, E_{a_1} = 180 \ kJ \ mol^{-1}$
$Step \ 2$	$k_2, E_{a_2} = 80 \ kJ \ mol^{-1}$
$Step \ 3$	$k_3, E_{a_3} = 50 \ kJ \ mol^{-1}$

Overall rate constant,$k = (k_1 k_2 / k_3)^{2/3}$. The overall activation energy of the reaction will be ........ $kJ \ mol^{-1}$.

The rate constant for the first order decomposition of a certain reaction is described by the equation $\ln k (s^{-1}) = 14.34 - \frac{1.25 \times 10^{4} \ K}{T}$. The energy of activation for this reaction is