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GATE 2020 CH – Question 61

Chemical Reaction Engineering · Single and multiple reactions in ideal reactors · 2 marks · Numerical answer

A second-order catalytic gas reaction P → Q occurs isothermally and isobarically in a steady packed-bed reactor with ideal plug flow. Pure-P feed is 1 L/min at 2 mol/L, and concentration is 0.4 mol/L at catalyst mass 4 g. Reactant and product are ideal gases and total gas volume does not change with reaction. Find k in L²/(g-catalyst mol min), to one decimal place.

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Correct answer: 0.49 to 0.51

Explanation

Feed molar rate is Fₚ₀ = 1(2) = 2 mol/min and conversion is $X=1-0.4/2=0.8$. Constant volume flow gives $C_P=C_{P0}(1-X)$. The packed-bed equation integrates to $W=F_{P0}X/[kC_{P0}^2(1-X)]$. Thus $4=2(0.8)/[k(4)(0.2)]=2/k$, giving k = 0.5 L²/(g mol min).

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