Activation Energy — MCQ Practice

For a first-order reaction, the rate constant ($k$) at $298\,\text{K}$ is $2.0 \times 10^{-3},\text{s}^{-1}$ and at $308\,\text{K}$ is $4.0 \times 10^{-3},\text{s}^{-1}$. Calculate the activation energy ($E_a$) for the reaction. (Given $R = 8.314\,\text{J K}^{-1}\text{ mol}^{-1}$, $\ln 2 = 0.693$)

Which of the following statements is INCORRECT regarding activation energy?

An energy profile diagram for a reaction shows the energy of reactants at $50\,\text{kJ/mol}$, products at $20\,\text{kJ/mol}$, and the transition state at $100\,\text{kJ/mol}$. What is the activation energy for the forward reaction?

For a reaction, the activation energy is $60\,\text{kJ/mol}$. If a catalyst is added, the activation energy is lowered to $40\,\text{kJ/mol}$. By what factor will the rate constant increase at $300\,\text{K}$ due to the catalyst? (Given $R = 8.314\,\text{J K}^{-1}\text{ mol}^{-1}$)

Which of the following factors does NOT affect the activation energy of a reaction?

If the activation energy of a reaction is $0\,\text{kJ/mol}$, what can be inferred about the reaction rate?