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GATE 2024 Chemical Engineering, Q20 · Reaction Engineering

The correct answer is A, 20.

Question

The rate of a reaction A → B is 0.2mol/(m3⋅s)0.2 mol/(m³\cdot s) at a particular concentration CA1.C_{A1}. The rate constant of the reaction at a given temperature is 0.1m3/(mol⋅s).0.1 m³/(mol\cdot s). If the reactant concentration is increased to 10⋅CA110\cdot C_{A1} at the same temperature, the reaction rate, in mol/(m3⋅s),mol/(m³\cdot s), is

  • A. 20
  • B. 10
  • C. 100
  • D. 50

Official answer: 20

Why

GATE 2024 official key: (A). Rate =k⋅CA2= k\cdot C_{A}² (second order). From initial: 0.2=0.1⋅CA12⇒CA1=2.0.2 = 0.1\cdot C_{A1}² \Rightarrow C_{A1} = \sqrt{2.} New rate =0.1⋅(102)2=0.1⋅200=20mol/(m3⋅s).= 0.1\cdot (10\sqrt{2})² = 0.1\cdot 200 = 20 mol/(m³\cdot s).

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

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