According to the collision theory of chemical reactions:

The rate law for the reaction $2NO + Cl_2 \rightarrow 2NOCl$ is given by $\text{rate} = k[NO]^2[Cl_2]$. Under what conditions will the value of the rate constant $k$ increase?

It is found that for every $10^{\circ}C$ rise in temperature,the rate of the reaction doubles itself. This is mainly because

For the reaction $A_2 + B_2 \rightleftarrows 2AB$,the activation energy for the forward and backward reactions are $180 \ kJ \ mol^{-1}$ and $200 \ kJ \ mol^{-1}$,respectively. If a catalyst lowers the activation energy of both forward and backward reactions by $100 \ kJ \ mol^{-1}$,what will be the enthalpy change $(\Delta H)$ for the reaction $A_2 + B_2 \rightarrow 2AB$ in the presence of the catalyst?

Thermodynamic feasibility of the reaction alone cannot decide the rate of the reaction. Explain with the help of one example.

If the rate constants of a reaction at $500 \ K$ and $700 \ K$ are $0.002 \ s^{-1}$ and $0.06 \ s^{-1}$,respectively,the value of activation energy is $(R=8.314 \ J \ mol^{-1} \ K^{-1}, \log 3=0.477)$.