GATE 2020 CH – Question 60

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

Two parallel irreversible liquid reactions P → Q and P → R have first-order constants k₁,k₂. An isothermal steady CSTR has space time 1 min, conversion 60%, and selectivity of Q with respect to R of 50%. Find k₁ in min⁻¹, to one decimal place.

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Correct answer: 0.49 to 0.51

Explanation

For parallel first-order consumption in a CSTR, $X=\tau(k_1+k_2)/[1+\tau(k_1+k_2)]$. With X = 0.6 and τ = 1, $k_1+k_2=0.6/0.4=1.5$ min⁻¹. Product selectivity is $r_Q/r_R=k_1/k_2=0.5$, so k₂ = 2k₁. Therefore 3k₁ = 1.5 and k₁ = 0.5 min⁻¹.

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