Chemegate

GATE 2025 Chemical Engineering, Q59 · Reaction Engineering

The correct answer is 0.17 to 0.21.

Question

The catalytic gas phase reaction A → products is carried out in an isothermal batch reactor of 10 L volume using 0.1 kg of a solid catalyst. The reaction is first-order with (−rA)=k′⋅a(t)⋅CA,(−r_{A}) = k′\cdot a(t)\cdot C_{A}, where k′ = 1 L/(kg catalyst·h) and CAC_{A} is the concentration of A in mol/L. The catalyst activity a(t) undergoes first-order decay with rate constant kd=0.01k_{d} = 0.01 per hour and a(0) = 1. The reactant conversion after 1 day of operation is ____ (rounded off to 2 decimal places).

Official answer: 0.17 to 0.21

Why

GATE 2025 official key: 0.17 to 0.21.ln(CA/CA0)=−(k′w/V)∫024e(−kd0.21. ln(C_{A}/C_{A0}) = −(k′w/V)\int ₀²⁴e^(−k_{d} t)dt =−0.01×100×(1−e−0.24)≈−0.213,= −0.01 \times 100 \times (1−e^{−0.24}) \approx −0.213, giving X =1−e−0.213≈0.19.= 1−e^{−0.213} \approx 0.19.

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