The decomposition of $N_2O$ into $N_2$ and $O_2$ in the presence of argon follows first-order kinetics. If the rate constant is given by $K = 5.0 \times 10^{11} \, e^{-2000/T}$,what is the activation energy of the reaction?

Explain the collision theory of chemical reactions.

An increase in temperature by $10\,^{\circ}C$,generally increases the rate of a reaction by .......... times.

The activation energy is ..........

The energy profile diagram for a multi-step reaction,$A$ $\xrightarrow{1} B$ $\xrightarrow{2} C$ $\xrightarrow{3} D,$ is given below. The rate-determining step of the reaction is:

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 $R = 8.31 \ J \ K^{-1} \ mol^{-1}$]