Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2020
Hard
Liquid-phase irreversible reactions P→Q (k1) and P→R (k2), both first order in P, run in an ideal CSTR at steady state, space time 1 minute. Exit conversion of P is 60%, and selectivity of Q with respect to R is 50%. The value of k1 (min⁻¹) is (correct to 1 decimal place)
0.5 min^-1(± 0.02 accepted)
Explanation
In a CSTR, the exit ratio CQ/CR=k1/k2=0.5 (uniform composition throughout). Overall: τ=X/[(1−X)(k1+k2)]. At X=0.6: 1=0.6/(0.4×(k1+k2)) ⟹ k1+k2=1.5. With k1=0.5k2: 1.5k2=1.5 ⟹ k2=1.0, k1=0.5 min⁻¹.
Source: GATE CH 2020 (2020)
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