Collision Theory of Chemical Reactions — Prelims Questions

According to collision theory, for a reaction to occur, which of the following conditions must be met?

For a reaction, the activation energy is $50 \text{ kJ/mol}$ at $300 \text{ K}$. If the temperature is increased to $310 \text{ K}$, what will be the approximate change in the fraction of molecules having energy equal to or greater than the activation energy? (Given: $R = 8.314 \text{ J/mol\cdot K}$, $e^{-20} \approx 2.06 \times 10^{-9}$, $e^{-19.35} \approx 3.58 \times 10^{-9}$)

Which of the following statements is a limitation of the collision theory?

If the steric factor (P) for a reaction is very small ($P \ll 1$), what does this imply about the reaction?

For a reaction, the rate constant $k$ is given by $k = 1.0 \times 10^{13} \text{ L mol}^{-1}\text{s}^{-1} \times e^{-10000/T}$. What is the activation energy ($E_a$) of the reaction in kJ/mol? (Given: $R = 8.314 \text{ J/mol\cdot K}$)

How does a catalyst affect the rate of a reaction according to collision theory?