Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2020
Hard
An elementary liquid-phase reversible reaction P⇌Q is run in an ideal CSTR at steady state, −rP=CP−0.5CQ. Pure P feed at 1 mol/L; exit conversion is 75% of the equilibrium conversion; no volume change. The space time (min) of the CSTR is (round off to 1 decimal place)
2 min(± 0.1 accepted)
Explanation
At equilibrium, −rP=0 ⟹ CP,eq=0.5CQ,eq, and CP,eq+CQ,eq=1, giving CP,eq=1/3, XP,eq=2/3. Exit conversion=0.75×2/3=0.5. CP=0.5, CQ=0.5, −rP=0.5−0.25=0.25. τ=CP0·XP/(−rP)=1×0.5/0.25=2.0 min.
Source: GATE CH 2020 (2020)
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