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GATE 2025 Chemical Engineering, Q58 · Reaction Engineering

The correct answer is 0.22 to 0.27.

Question

The reaction A → products, with reaction rate (−rA)=k(CA)3,(−r_{A}) = k(C_{A})³, occurs in an isothermal PFR operating at steady state. As shown in the figure, the conversion reaches X1=0.3X₁ = 0.3 at axial position 1 (length l1l₁ from the inlet) and X2=0.6X₂ = 0.6 at axial position 2 (a further length l2l₂ downstream). The value of l1/l2l₁/l₂ is ____ (rounded off to 2 decimal places).

Figure for Q58 (Reaction Engineering, PFR Design): The reaction A → products, with reaction rate (−r_A) = k(C_A)³, occurs in an isothermal PFR operatin…

Official answer: 0.22 to 0.27

Why

GATE 2025 official key: 0.22 to 0.27. For third-order kinetics, l ∝∫dX/(1−X)3=½[1/(1−X)2−\propto \int dX/(1−X)³ = ½[1/(1−X)² − 1]. l1l₁ (0→0.3) ∝½[1/0.72−1]=\propto ½[1/0.7²−1] = 0.520; l2l₂ (0.3→0.6) ∝½[1/0.42−1/0.72]=2.105.l1/l2≈0.520/2.105≈0.25.\propto ½[1/0.4²−1/0.7²] = 2.105. l₁/l₂ \approx 0.520/2.105 \approx 0.25.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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