1. What is Effectiveness Factor at First Order?

Definition: The effectiveness factor is a measure of how much the reaction rate is reduced due to diffusion limitations within porous catalyst particles.

Purpose: It helps chemical engineers evaluate the efficiency of catalytic reactions in porous materials.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \xi \) — Effectiveness factor (dimensionless)
• \( MT \) — Thiele modulus (dimensionless)
• \( \tanh \) — Hyperbolic tangent function

Explanation: For a first-order reaction in a spherical catalyst particle, the effectiveness factor can be calculated from the Thiele modulus.

3. Importance of Effectiveness Factor

Details: The effectiveness factor indicates what fraction of the catalyst is being effectively used. A value of 1 means no diffusion limitations, while lower values indicate significant diffusion effects.

4. Using the Calculator

Tips: Enter the Thiele modulus (must be > 0). The calculator will compute the effectiveness factor using the standard formula for first-order reactions.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of the effectiveness factor?
A: The effectiveness factor ranges from 0 to 1, where 1 means no diffusion limitations and lower values indicate more severe diffusion limitations.

Q2: What does the Thiele modulus represent?
A: The Thiele modulus compares the reaction rate to the diffusion rate within the catalyst particle.

Q3: When is the effectiveness factor approximately 1?
A: When the Thiele modulus is small (typically < 0.3), indicating that diffusion is fast compared to reaction.

Q4: What happens at high Thiele modulus values?
A: The effectiveness factor decreases, approaching 1/MT for large MT values.

Q5: Does this formula work for all catalyst shapes?
A: This exact formula is for spherical particles. Other shapes require different formulas.