The rate constant of a reaction at $500 \ K$ and $700 \ K$ are $0.02 \ s^{-1}$ and $0.2 \ s^{-1}$ respectively. The activation energy of the reaction (in $kJ \ mol^{-1}$) is $(R=8.3 \ J \ K^{-1} \ mol^{-1})$

Collision theory is applicable to

Assertion $(A)$ : $A$ catalyst increases the rate of a reaction.
Reason $(R)$ : In presence of a catalyst,the activation energy of the reaction increases.
The correct answer is

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 the reaction $2NO + Cl_2 \rightarrow 2NOCl$,the rate is given by $Rate = K[NO]^2[Cl_2]$. How can the rate constant $(K)$ of the reaction be increased?

The rate constant of a reaction at $25\,^oC$ is $1 \times 10^{-3}\,s^{-1}$. If the rate of the reaction doubles when the temperature is increased to $35\,^oC$,the activation energy of the reaction is .......... $kJ\, mol^{-1}$.