GATE 2020 CH – Question 59
An exothermic first-order aqueous reaction Y → Z takes place adiabatically in a steady ideal CSTR. Rate is $-r_Y=10^9e^{-6500/T}C_Y$ mol/(L min), with T in K and C in mol/L. Feed is 1 mol/L Y at 50°C and 1 L/min. Reaction heat is −42000 J/mol, specific heat 4.2 J/(g K), density 1000 g/L, all constant; neglect shaft work. For 90% conversion, find reactor volume in litres, to two decimal places.
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Correct answer: 2.40 to 3.00
Explanation
Adiabatic heat release raises temperature by $\Delta T=(-\Delta H)C_{Y0}X/(\rho c_p)=42000(1)(0.9)/(1000\times4.2)=9$ K, so exit T = 332.15 K. Exit concentration is 0.1 mol/L. The CSTR balance gives $V=F_{Y0}X/[10^9e^{-6500/T}C_Y]$, with Fᵧ₀ = 1 mol/min. Substitution gives approximately 2.84 L, within the official 2.40–3.00 L interval. The rate must be evaluated at the hotter reactor exit, not feed temperature.