Question

For a first order isothermal catalytic reaction A to B, occurring in an infinitely long cylindrical pore, the relationship between effectiveness factor \(\epsilon\) and thiele modulus \(\phi\), is

• A. \(\epsilon = \frac{1}{\phi^2}\)
• B. \(\epsilon = \phi\)
• C. \(\epsilon = 1\)
• D. \(\epsilon = \frac{1}{\phi}\)

Hint:

For reactions in porous media, understanding the relationship between the effectiveness factor and thiele modulus is crucial for determining catalyst efficiency.

Answer 1

The Correct Option is A

Step 1: Understanding the relation.
The effectiveness factor \(\epsilon\) and thiele modulus \(\phi\) are related in catalytic reactions occurring in porous media. The relationship for a first-order isothermal catalytic reaction in an infinitely long cylindrical pore is given by: \[ \epsilon = \frac{1}{\phi^2} \] This relationship reflects the behavior of the catalyst effectiveness depending on the diffusion and reaction rates.
Step 2: Analyzing the options.
(1) \(\epsilon = \frac{1}{\phi^2}\): This is the correct relationship for a first-order reaction occurring in an infinitely long cylindrical pore.
(2) \(\epsilon = \phi\): This is incorrect because it does not match the expected relationship.
(3) \(\epsilon = 1\): This is incorrect because it does not account for the influence of the thiele modulus.
(4) \(\epsilon = \frac{1}{\phi}\): This is incorrect as it does not reflect the correct relationship for the given scenario.
Step 3: Conclusion.
The correct answer is \(\epsilon = \frac{1}{\phi^2}\), as it matches the established relationship for this reaction type.