Project ForgeChemical Reaction Engineering
Reaction Kinetics
GATE 2011
Hard
For a first order catalytic reaction, the Thiele modulus (φ) of a spherical pellet is φ=(Rs/3)√(kρp/De). If φ>5, then the apparent activation energy (Ea) is related to the intrinsic (true) activation energy (E) as
- AEa=E^0.5
- Ea=0.5E
- CEa=2E
- DEa=E²
Explanation
For φ>5 (strong pore-diffusion resistance), the effectiveness factor η≈3/φ, so the observed rate constant kapp=k·η∝k/√k=√k. Since k=A·exp(−E/RT), kapp∝√A·exp(−E/(2RT)), meaning the apparent activation energy observed is exactly half the true value: Ea=0.5E.
Source: GATE CH 2011 (2011)
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