Question

The Thiele modulus represents:

• A. Surface reaction rate to diffusion rate
• B. Overall reaction order
• C. Mass transfer rate
• D. Temperature profile

Hint:

Think of the Thiele modulus as a way to judge whether a reaction is limited by diffusion or by the chemical reaction itself inside a catalyst particle.

Answer 1

The Correct Option is A

The Thiele modulus is a dimensionless number used in chemical reaction engineering, particularly in the analysis of reactions within porous catalyst particles.
It provides a measure of the relative importance of the reaction rate to the diffusion rate inside the particle.
Mathematically, the Thiele modulus ($\phi$) is defined as:
\[ \phi = L \sqrt{\frac{k}{D}} \]
Where:
- $L$ is the characteristic length (e.g., particle radius)
- $k$ is the reaction rate constant
- $D$ is the effective diffusivity of the species
A high Thiele modulus ($\phi \gg 1$) implies that the reaction is much faster than diffusion, leading to diffusion limitation.
A low Thiele modulus ($\phi \ll 1$) implies that diffusion is fast compared to the reaction, and the reaction controls the process.
Let’s assess the other options:
- (2) Overall reaction order: This is a kinetic parameter, not related to Thiele modulus directly.
- (3) Mass transfer rate: Thiele modulus is a ratio of rates, not a direct measure of mass transfer.
- (4) Temperature profile: While temperature affects both reaction and diffusion, Thiele modulus does not directly represent temperature distribution.
Thus, the correct interpretation is: Ratio of surface reaction rate to diffusion rate.