Question

The activation energy at high temperatures is lower than at lower temperatures, which represents

• A. Diffusion regime
• B. Reaction regime
• C. Kinetic regime
• D. Intermediate regime

Hint:

In catalytic reactions, a lower activation energy at high temperatures indicates a diffusion-limited regime, while a higher activation energy at low temperatures indicates a reaction-limited (kinetic) regime.

Answer 1

The Correct Option is A

Step 1: Understand activation energy and temperature regimes.
Activation energy (\( E_a \)) is the energy barrier that reactants must overcome for a reaction to occur. In catalytic reactions, the observed (apparent) activation energy depends on the rate-limiting step, which can be influenced by temperature:
At low temperatures, the reaction rate is often limited by the chemical reaction itself (reaction or kinetic regime), where the intrinsic activation energy of the reaction dominates.
At high temperatures, the reaction rate may become limited by diffusion (mass transfer of reactants to the catalyst surface or within pores), where the activation energy is lower because diffusion processes have a smaller temperature dependence.
The statement indicates that the activation energy decreases as temperature increases, which suggests a transition in the rate-limiting step. Step 2: Analyze the regimes in catalytic reactions.
Kinetic (reaction) regime: At low temperatures, the reaction rate is controlled by the surface reaction (chemical kinetics). The observed activation energy is the intrinsic activation energy of the reaction, which is typically higher (e.g., 50–100 kJ/mol).
Diffusion regime: At high temperatures, the reaction rate becomes limited by the diffusion of reactants to the catalyst surface (external diffusion) or within the catalyst pores (internal diffusion). The activation energy for diffusion processes is much lower (e.g., 5–20 kJ/mol) because diffusion has a weaker temperature dependence (often following a \( T^{1/2} \) or linear dependence, compared to the exponential dependence of reaction rates via the Arrhenius equation).
Intermediate regime: At intermediate temperatures, the rate may be influenced by both reaction and diffusion, with an apparent activation energy between the kinetic and diffusion limits.
The Arrhenius equation for reaction rate is: \[ k = A e^{-\frac{E_a}{RT}}, \] where \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is temperature. In the kinetic regime, \( E_a \) is high. In the diffusion regime, the rate is controlled by mass transfer, and the apparent \( E_a \) is lower because diffusion processes are less temperature-sensitive. Step 3: Interpret the statement.
The statement “activation energy at high temperatures is lower than at lower temperatures” indicates:
At low temperatures, the system is in the kinetic regime with a higher \( E_a \).
At high temperatures, the system transitions to the diffusion regime, where the apparent \( E_a \) is lower due to diffusion limitations dominating the rate. This behavior is characteristic of the diffusion regime, where the observed activation energy decreases as temperature increases because diffusion becomes the rate-limiting step. Step 4: Evaluate the options.
(1) Diffusion regime: Correct, as the lower activation energy at high temperatures indicates diffusion limitations dominate, typical of the diffusion regime. Correct.
(2) Reaction regime: Incorrect, as the reaction (kinetic) regime has a higher activation energy, observed at lower temperatures. Incorrect.
(3) Kinetic regime: Incorrect, as the kinetic regime is the same as the reaction regime, with higher activation energy at lower temperatures. Incorrect.
(4) Intermediate regime: Incorrect, as the intermediate regime would show a gradual transition, not a clear shift to a lower activation energy at high temperatures. Incorrect.
Step 5: Select the correct answer.
The activation energy being lower at high temperatures than at lower temperatures represents the diffusion regime, matching option (1).