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GATE 2022 CY – Question 63

Physical Chemistry · Kinetics and Reaction Dynamics: Elementary, parallel, opposing, and consecutive reactions. Steady state approximation. Mechanism of complex reactions. Unimolecular reactions. Potential energy surface and classical trajectories, Concept of saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of unimolecular and bimolecular photophysical processes, Quantum yield calculation, static and dynamic quenching. · 2 marks · Numerical answer

The elementary gas-phase reaction $O_3+NO\to NO_2+O_2$ has activation energy 10.5 kJ/mol. Its standard enthalpy of activation at 25 °C is ______ kJ/mol (two decimal places). $R=8.314$ J mol$^{-1}$ K$^{-1}$.

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Correct answer: 5.50 to 5.60

Explanation

For a bimolecular gas reaction with standard-pressure transition-state convention, k has an explicit T² prefactor. Differentiating ln k with respect to 1/T gives Ea=ΔH‡+2RT.

Thus ΔH‡=10.5−2(8.314)(298.15)/1000=**5.54kJ/mol**, within 5.50–5.60. The 1RT correction applies to different molecularity/standard-state conventions.