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GATE 2026 CH – Question 43

Chemical Reaction Engineering · Reaction rates and kinetics of homogeneous reactions · 2 marks · Multiple choice

The reaction rate constants of two reactions follow Arrhenius' law. The activation energies of Reaction 1 and Reaction 2 are $E_1$ and $E_2$, respectively and $E_1 < E_2$. Assuming same value for the frequency factor for both the reactions, which one of the following statements is CORRECT?

  1. Reaction 1 and Reaction 2 are less temperature sensitive at lower temperature than at higher temperature.
  2. Reaction 1 and Reaction 2 have the same temperature sensitivity at all temperatures.
  3. Reaction 1 is more temperature sensitive than Reaction 2 at all temperatures.
  4. Reaction 2 is more temperature sensitive than Reaction 1 at all temperatures.

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Correct answer: (D) Reaction 2 is more temperature sensitive than Reaction 1 at all temperatures.

Explanation

The temperature sensitivity of a rate constant is $\frac{d\ln k}{dT} = \frac{E}{RT^2}$. At any temperature it is larger for the reaction with the higher activation energy, so Reaction 2 is more sensitive at all temperatures. Statement A is also wrong, because the sensitivity of each reaction is higher at low temperature, as it falls with $T^2$.