Question

There is strong pore resistance, when the Thiele Modulus is ______

• A. less than 0.4
• B. equal to one
• C. greater than two
• D. greater than one

Hint:

For a first-order reaction in a flat plate catalyst, the transition boundaries are:
\( \phi \lt 0.4 \rightarrow \) Reaction-rate controlled regime (\( \eta \approx 1 \)).
\( \phi \gt 2.0 \rightarrow \) Diffusion-rate controlled regime (\( \eta \approx 1/\phi \)).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the condition under which a catalytic reaction experiences strong pore diffusion resistance, expressed in terms of the dimensionless Thiele modulus (\( \phi \)).
This is a key concept in heterogeneous catalysis.

Step 2: Key Formula or Approach:
The Thiele modulus (\( \phi \)) is a dimensionless number that compares the rate of reaction to the rate of diffusion within a catalyst pore:
\[ \phi = L \cdot \sqrt{\frac{k}{D_{\text{eff}}}} \]
The effectiveness factor (\( \eta \)) measures the reduction in reaction rate caused by diffusion resistance:
\[ \eta = \frac{\tanh \phi}{\phi} \]

Step 3: Detailed Explanation:

• Small Thiele Modulus (\( \phi \lt 0.4 \)): When the Thiele modulus is small, the rate of diffusion is much faster than the rate of chemical reaction.
The reactant concentration remains nearly uniform throughout the catalyst pore.
Under this condition, pore diffusion resistance is negligible, and the effectiveness factor approaches 1:
\[ \eta \approx 1 \]

• Large Thiele Modulus (\( \phi \gt 2 \)): When the Thiele modulus is large, the chemical reaction occurs much faster than the rate at which reactants can diffuse into the pore.
The reactants are consumed near the outer surface of the catalyst, leaving the inner pore volume unused.
This is the regime of strong pore diffusion resistance, where the effectiveness factor is inversely proportional to the Thiele modulus:
\[ \eta \approx \frac{1}{\phi} \]


Step 4: Final Answer:
Strong pore resistance occurs when the Thiele modulus is greater than two.