The Arrhenius equation is represented as $k = A e^{-E_a/RT}$. The activation energy $E_a$ of the reaction can be calculated by plotting:

In an exothermic reaction $A \to B$,the evolved heat is $280 \ kJ \ mol^{-1}$ and the activation energy is $200 \ kJ \ mol^{-1}$. The activation energy of the reverse reaction $B \to A$ is $.......... \ kJ \ mol^{-1}$.

In the reaction of decomposition of reactant $A$ into product,the rate constant is $4.5 \times 10^{-3} \ s^{-1}$ at $283 \ K$ temperature and energy of activation is $60 \ kJ \ mol^{-1}$. At which temperature will the value of rate constant $K$ be $3 \times 10^{10} \ s^{-1}$ (in $K$)?

Consider the following reversible reaction,
$A_{(g)} + B_{(g)} \rightleftharpoons AB_{(g)}.$
The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in $J \ mol^{-1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction,the absolute value of $\Delta G^{\ominus}$ (in $J \ mol^{-1}$) for the reaction at $300 \ K$ is. . . . . (Given; $\ln(2)=0.7, RT=2500 \ J \ mol^{-1}$ at $300 \ K$ and $G$ is the Gibbs energy)

Catalyst $A$ reduces the activation energy for a reaction by $10 \ kJ \ mol^{-1}$ at $300 \ K$. The ratio of rate $\frac{k_{T, \text{Catalysed}}}{k_{T, \text{Uncatalysed}}}$ is $e^{x}$. Find the value of $x$ [nearest integer].
[Assume that the pre-exponential factor is same in both the cases.
Given $R = 8.31 \ J \ K^{-1} \ mol^{-1}$]

For a certain reaction,a large fraction of molecules has energy more than the threshold energy,yet the rate of reaction is very slow. Why?