GATE 2021 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

Decomposition in oxygen has rate constants $0.237\times10^{-4}$ L mol$^{-1}$ s$^{-1}$ at 0 °C and $2.64\times10^{-4}$ at 25 °C. Its activation energy is ______ kJ/mol (one decimal place). $R=8.314$ J mol$^{-1}$ K$^{-1}$.

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Correct answer: 65.0 to 66.0

Explanation

The two-temperature relation is ln(k2/k1)=(Ea/R)(1/T1−1/T2). Use T1=273.15 K, T2=298.15 K and k2/k1=2.64/0.237.

Thus Ea=8.314 ln(2.64/0.237)/(1/273.15−1/298.15)≈65284 J/mol. Rounded to one decimal, this is **65.3 kJ/mol**.