Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2013
Hard
A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____
52 %(± 2 accepted)
Explanation
Single CSTR: τ1=(X/(1−X))/k=(0.9/0.1)/k=9/k, so V1=9Q/k. For n equal CSTRs in series (first order): (1−X)=1/(1+kτ)ⁿ. For n=2: 0.1=1/(1+kτ)² ⟹ (1+kτ)=√10=3.162 ⟹ kτ=2.162, τ=2.162/k per reactor. Total V=2×2.162Q/k=4.325Q/k. % reduction=(9−4.325)/9×100≈52%.
Source: GATE CH 2013 (2013)
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