UPSC Combined Geo-Scientist, Mains · 2020 · Mains Paper II

Q1(h). Catalytic rate enhancement

Question

Activation energy is 75.2 kJ mol⁻¹ without catalyst and 50.14 kJ mol⁻¹ with catalyst. How many times does the rate increase at 25° C?

Assuming equal Arrhenius prefactors, k_(cat)/k_(unc)=2.46×10⁴.

Arrhenius law gives k=Ae^(-Eₐ/(RT)). Therefore k_(cat)/k_(unc)=(A_(cat)/A_(unc))exp [(E_(a, unc)-E_(a, cat))/(RT)].
With equal A, the exponent is (75.2-50.14)×1000/(8.314×298.15)=10.110.
Exponentiation gives 2.458×10⁴. This assumes the compared rates have the same concentration dependence and are evaluated at the same concentrations.

The full model answer

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CoversCatalytic rate enhancementChemical kinetics