The time taken for half of the initial amount of $N_2O_5$ to decompose is $12 \ min$ at $310 \ K$ and $2 \ hrs$ at $300 \ K$. The activation energy of the reaction in $kJ \ mol^{-1}$ is $\left(R=8.3 \ J \ K^{-1} \ mol^{-1}\right)$

An exothermic reaction $X \rightarrow Y$ has an activation energy of $30 \ kJ \ mol^{-1}$. If the energy change $\Delta E$ during the reaction is $-20 \ kJ \ mol^{-1}$,then the activation energy for the reverse reaction in $kJ \ mol^{-1}$ is $...$.

For a first-order reaction,if the rate constant is $k_1$ at temperature $T_1$ and $k_2$ at temperature $T_2$,which of the following relations is correct? ($E_a$ = activation energy)

How are the values of $E_a$ and $A$ obtained from the Arrhenius equation?

Correct statements regarding Arrhenius equation among the following are:
$(A)$ Factor $e^{-Ea/RT}$ corresponds to fraction of molecules having kinetic energy less than $Ea$.
$(B)$ At a given temperature, lower the $Ea$, faster is the reaction.
$(C)$ Increase in temperature by about $10^{\circ}C$ doubles the rate of reaction.
$(D)$ Plot of $\log k$ vs $\frac{1}{T}$ gives a straight line with $slope = -\frac{Ea}{2.303R}$.
Choose the correct answer from the options given below:

The minimum energy required for molecules to participate in a chemical reaction is called $.......$.