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GATE 2024 CH – Question 19

Chemical Reaction Engineering · Reaction rates and kinetics of homogeneous reactions · 1 mark · Multiple choice

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 the collision theory. The ratio of the rate constant at 600 K to that at 400 K is

  1. 2.818
  2. 4.323
  3. 1.502
  4. 1.000

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Correct answer: (A) 2.818

Explanation

In collision theory $k \propto T^{1/2}e^{-E/RT}$. So $\frac{k_{600}}{k_{400}} = \sqrt{\frac{600}{400}}\exp\left[1000\left(\frac{1}{400} - \frac{1}{600}\right)\right] = 1.2247 \times e^{0.8333} = 1.2247 \times 2.301 = 2.818$.