Discussion
Match each controlling resistance in the shrinking core model with its conversion time relation.
List I
A. Gas film control
B. Ash layer diffusion control
C. Chemical reaction control
D. Mixed control
List II
1. one minus the cube root of unreacted fraction
2. time proportional to conversion
3. no simple closed form
4. a cube root expression in conversion
Answer: D
Correct answer: A-2, B-4, C-1, D-3
Each controlling resistance leaves its own signature in the conversion-time curve. Under gas film control the time is directly proportional to conversion. Under ash layer diffusion it follows \( 1-3(1-X)^{2/3}+2(1-X) \), a cube root expression. Under chemical reaction control it is \( 1-(1-X)^{1/3} \). And when two resistances are comparable there is no simple closed form. Fitting data to the three forms is how the controlling step is identified.
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