Kinetics, activation energy; Arrhenius equation: Practice Questions

In the context of collision theory, which of the following best describes the activation energy (\(E_a\)) of a chemical reaction?

For two different chemical reactions, Reaction 1 and Reaction 2, the activation energy of Reaction 1 is much higher than that of Reaction 2 (\(E_{a,1} > E_{a,2}\)). Which of the following statements regarding the temperature sensitivity of their rate constants (\(k_1\) and \(k_2\)) is CORRECT?

Two reactions, A and B, have activation energies of \(40\text{ kJ mol}^{-1}\) and \(60\text{ kJ mol}^{-1}\) respectively. Assuming they have identical pre-exponential factors (\(A\)), what is the approximate ratio of their rate constants \(\frac{k_A}{k_B}\) at \(300\text{ K}\)?
(Given: \(R = 8.314\text{ J K}^{-1}\text{ mol}^{-1}\); \(e^{8.02} \approx 3040\))

In the Arrhenius equation, \(k = A e^{-E_a/RT}\), what does the term \(e^{-E_a/RT}\) represent?

Which of the following statements correctly describes the changes to the Maxwell-Boltzmann distribution of molecular kinetic energies when the temperature of a gas sample is increased?

Explain, in terms of collision frequency, why increasing the concentration of reactants typically increases the rate of a chemical reaction.

Considering the Arrhenius equation, \(k = A e^{-E_a/RT}\), explain why the rate constant (\(k\)) of a reaction is highly sensitive to changes in activation energy (\(E_a\)).

A zero-order reaction has a rate constant of \(0.050 \text{ mol dm}^{-3} \text{ s}^{-1}\) at \(300 \text{ K}\). When the temperature is increased to \(320 \text{ K}\), the rate constant increases to \(0.200 \text{ mol dm}^{-3} \text{ s}^{-1}\).

Assuming the pre-exponential factor \(A\) remains constant over this temperature range, calculate the activation energy (\(E_a\)) for this reaction in \(\text{kJ mol}^{-1}\).
(Given: \(R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}\))

A chemical reaction is often visualized using an energy profile diagram.

(a) With reference to a typical energy profile diagram, identify and define the activation energy ($$E_a$$) of a reaction.

(b) Describe the effect of adding a suitable catalyst on the energy profile diagram for this reaction.

(c) Explain, based on your answer in (b), why the presence of a catalyst increases the rate of a chemical reaction at a constant temperature.

A specific chemical reaction has an activation energy, \(E_a\), of \(65.0 \text{ kJ mol}^{-1}\). At a temperature of \(300 \text{ K}\), the rate constant, \(k\), for this reaction is \(2.0 \times 10^{-3} \text{ s}^{-1}\).

Calculate the rate constant for this reaction at \(320 \text{ K}\). Assume the activation energy remains constant over this temperature range.
(Given: Ideal gas constant \(R = 8.314 \text{ J mol}^{-1} \text{ K}^{-1}\)).