Discussion
A catalyst particle has a Thiele modulus of 10. Roughly what is its effectiveness factor for a first order reaction in a slab?
Answer: B
Correct answer: about 0.1
For a first order reaction in a slab, \[ \eta = \frac{\tanh\phi}{\phi}, \] and at \( \phi=10 \) the hyperbolic tangent is essentially 1, so \( \eta \approx 1/10 = 0.1 \). The useful rule is that for any large modulus the effectiveness factor is close to \( 1/\phi \) whatever the pellet shape, so only about a tenth of this catalyst is being used.
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