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GATE 2024 Chemical Engineering, Q19 · Kinetics

The correct answer is A, 2.818.

Question

The ratio of the activation energy of a chemical reaction to the universal gas constant is 1000 K. The temperature-dependence of the reaction rate constant follows collision theory (k ∝T1/2⋅e−Ea/RT).\propto T^{1/2}\cdot e^{−Ea/RT}). The ratio of the rate constant at 600 K to that at 400 K is

  • A. 2.818
  • B. 4.323
  • C. 1.502
  • D. 1.000

Official answer: 2.818

Why

GATE 2024 official key: (A). k600/k400=600/400×k₆₀₀/k₄₀₀ = \sqrt{600/400} \times exp(1000/400 −1000/600)=1.5×− 1000/600) = \sqrt{1.5} \times exp(0.833) ≈1.225×2.300≈2.818.\approx 1.225 \times 2.300 \approx 2.818.

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

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