Q.48 Which of the following statements are CORRECT for an enzyme entrapped in a
spherical particle?
(A) Effectiveness factor is ratio of the reaction rate with diffusion-limitation to the
reaction rate without diffusion-limitation
(B) Internal diffusion is rate-limiting at low values of Thiele modulus
(C) Effectiveness factor increases with decrease in Thiele modulus
(D) Internal diffusion-limitation can be reduced by decreasing the size of the
particle
Understanding Enzyme Entrapment in Spherical Particles: Effectiveness Factor and Thiele Modulus Explained
Enzymes entrapped in spherical particles often face diffusion limitations that impact reaction rates, key concepts in biocatalysis and chemical engineering. The correct statements from the multiple-choice query are (A), (C), and (D), as they accurately describe the effectiveness factor, its relation to the Thiele modulus, and strategies to mitigate internal diffusion issues.
Effectiveness Factor Defined
The effectiveness factor (η) measures how diffusion limitations affect the actual reaction rate compared to an ideal scenario without such constraints. It is precisely the ratio of the observed reaction rate (with diffusion limitation) to the intrinsic reaction rate (without diffusion limitation) in enzyme-loaded spherical particles. This dimensionless parameter helps quantify performance loss due to substrate diffusion within the particle.
Thiele Modulus Role
The Thiele modulus (φ) is a dimensionless number that compares reaction rate to diffusion rate inside the particle; low φ values indicate minimal diffusion control. Statement (B) is incorrect because internal diffusion becomes rate-limiting at high Thiele modulus values, not low ones, where reaction kinetics dominate. Conversely, η increases as φ decreases, making statement (C) correct since smaller φ means better substrate access throughout the particle.
Reducing Diffusion Limitations
Decreasing particle size lowers the Thiele modulus by shortening diffusion paths, thereby reducing internal diffusion limitations and boosting η, which confirms statement (D). Smaller particles enhance overall enzyme efficiency in applications like immobilized biocatalysts.
| Statement | Correct? | Key Reason |
|---|---|---|
| (A) Effectiveness factor definition | Yes | Matches standard ratio of rates with/without diffusion |
| (B) Internal diffusion rate-limiting at low φ | No | Actually rate-limiting at high φ |
| (C) η increases with decreasing φ | Yes | Low φ minimizes diffusion impact |
| (D) Reduce limitation by smaller size | Yes | Shortens diffusion distance |
