Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2020
Hard
A catalytic gas-phase reaction P→Q (second order in P, no volume change, ideal plug flow) runs in an isothermal packed bed. Feed: pure P, 1.0 L/min, 2.0 mol/L. With 4g catalyst, exit CP=0.4 mol/L. The second-order rate constant (L²/g_cat/mol/min) is (correct to 1 decimal place)
0.5 L^2/g/mol/min(± 0.02 accepted)
Explanation
For a second-order PFR/PBR with no volume change: X/(1−X)=(k''CP0/Q)W. XP=1−0.4/2.0=0.8, X/(1−X)=4.0. 4.0=k''×(2.0/1.0)×4=8k'' ⟹ k''=0.5.
Source: GATE CH 2020 (2020)
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