Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2019
Hard
Elementary liquid reactions A→B (k1=0.4/min)→C (k2=0.1/min) occur in an isothermal ideal CSTR. Pure A is fed at 2 mol/L. For the residence time that maximizes exit CB, the percentage yield of B (net formation rate of B/consumption rate of A × 100) is (rounded off to nearest integer)
67 %(± 2 accepted)
Explanation
Maximizing CB=k1CA0τ/[(1+k1τ)(1+k2τ)] over τ gives τopt=1/√(k1k2)=1/√0.04=5min. At τ=5: CA=2/(1+2)=0.667, CB=0.4×2×5/(3×1.5)=0.889. Yield=(k1CA−k2CB)/(k1CA)=(0.2667−0.0889)/0.2667=0.667=67%.
Source: GATE CH 2019 (2019)
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