Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2019
Hard
A reactor-separator-recycle process runs A+B→C in an ideal CSTR (holdup 10m³, r=10³xAxB kmol/h·m³), producing pure product C at 100 kmol/h with pure-A/B recycle (no impurities in product or recycle). The mole fraction of B (xB) in the reactor that minimizes the recycle rate is (rounded off to two decimal places)
0.1(± 0.01 accepted)
Explanation
Reaction rate requirement: r·V=1000xAxB×10=100 ⟹ xAxB=0.01 (fixed). Recycle rate=100(xA+xB)/(1−xA−xB), an increasing function of (xA+xB). By AM-GM, for fixed product xAxB=0.01, the sum xA+xB is minimized when xA=xB=√0.01=0.10.
Source: GATE CH 2019 (2019)
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