Immobilized enzymes in plug flow reactors can show an effectiveness factor (η) greater than 1, which seems counterintuitive. This occurs under specific kinetic conditions with diffusion limitations.
Correct Answer
The correct option is (A) Substrate inhibited kinetics with internal pore diffusion limitation.
In substrate-inhibited kinetics, high substrate concentrations reduce reaction rates, creating a negative apparent reaction order inside the particle. Internal pore diffusion lowers substrate levels deeper within the support, shifting operation to a higher-rate region on the kinetic curve, making observed rates exceed surface rates without diffusion—thus η > 1.
Option Explanations
(A) Substrate Inhibited Kinetics with Internal Pore Diffusion Limitation
Substrate inhibition follows kinetics like r = VmS/(Km + S + S2/Ki), where rate peaks then drops at high S. Internal diffusion causes a substrate gradient: surface has high S (low rate), interior has lower S (higher rate). Actual reaction rate integrates to more than surface-only rate, yielding η > 1.
(B) External Pore Diffusion Limitation
External film diffusion limits substrate supply to the particle surface, reducing observed rate below intrinsic kinetics. This always gives η < 1, as the particle underperforms due to mass transfer resistance.
(C) Sigmoidal Kinetics
Sigmoidal (cooperative) kinetics, like allosteric enzymes or Hill equation r = VmSn/(Kn + Sn) (n > 1), show a lag then acceleration. Diffusion can enhance rates in rising phase, but literature confirms it does not typically cause η > 1; standard cases yield η ≤ 1.
(D) Instability of the Enzyme
Enzyme instability leads to deactivation, lowering active enzyme amount and thus observed rate. This reduces performance, resulting in η < 1, not enhancement.
| Option |
Cause η > 1? |
Key Mechanism |
| (A) Substrate inhibition + internal diffusion |
Yes |
Interior higher-rate zone |
| (B) External diffusion |
No |
Surface limitation |
| (C) Sigmoidal kinetics |
No |
Cooperative but not exceeding |
| (D) Enzyme instability |
No |
Deactivation loss |
