Project ForgeElementary irreversible gas-phase A→B+C runs adiabatically in an ideal CSTR at 10 atm. Pure A enters at 10 mol/s, 450K. CpA=30, CpB=10, CpC=20 J/mol·K. H°A=−90, H°B=−54, H°C=−45 kJ/mol (ref 273K). k(per s)=0.133exp[(E/R)(1/450−1/T)], E=31.4 kJ/mol, R=8.314 J/mol·K=0.082 L·atm/mol·K. The reactor volume (L) for 75% conversion is (rounded off to nearest integer)
Explanation
Adiabatic enthalpy balance (from 450K feed to exit T, X=0.75) gives exit T=675K. k(675K)=0.133×exp[3777.2×(1/450−1/675)]=0.133×exp(2.798)=2.18/s. CA0=P/(RT0)=10/(0.082×450)=0.271mol/L. εA=1. CA,exit=0.271×0.25/1.75×(450/675)=0.0258 mol/L. −rA=k·CA=2.18×0.0258=0.0564. V=FA0X/(−rA)=10×0.75/0.0564=133 L.
Source: GATE CH 2019 (2019)
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