Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2020
Hard
An exothermic, aqueous, irreversible first-order reaction Y→Z runs in an adiabatic ideal CSTR at steady state, −rY=10⁹e^(−6500/T)CY. Feed: 50°C, CY0=1.0 mol/L, 1.0 L/min. ΔHrxn=−42000 J/mol, Cp=4.2 J/g·K, ρ=1000 g/L. At 90% conversion, the CSTR volume (L) is (round off to 2 decimal places)
2.84 L(± 0.3 accepted)
Explanation
Adiabatic ΔTmax=(−ΔHrxn)CY0/(ρCp)=42000×1/(1000×4.2)=10K at XY=1. At XY=0.9, ΔT=9K, so T=323.15+9=332.15K. k=10⁹e^(−6500/332.15)=10⁹×3.17×10⁻⁹=3.17 min⁻¹. CY,exit=0.1 mol/L. −rY=3.17×0.1=0.317 mol/L/min. V=Q·CY0·XY/(−rY)=1×0.9/0.317=2.84 L.
Source: GATE CH 2020 (2020)
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