The decomposition of hydrogen peroxide follows the equation: k = ≤ft(…

The correct answer is Option (3) → 174.594 kJ/mol

The given equation has the form of the Arrhenius equation, k = A e^−E_a/RT. Comparing the exponents:

    \( \displaystyle \frac{E_a}{RT} = \frac{21000\ \mathrm{K}}{T} \;\Rightarrow\; \frac{E_a}{R} = 21000\ \mathrm{K} \)

    \( \displaystyle E_a = 21000\ \mathrm{K} \times 8.314\ \mathrm{J\,K^{-1}\,mol^{-1}} = 174594\ \mathrm{J\,mol^{-1}} \)

So E_a = 174.594 kJ mol⁻¹. The pre-exponential factor A = 2.9 × 10¹⁴ s⁻¹ is not needed for E_a.

Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.

NCERT (2026-27 edition):
Exercises – “… The decomposition of hydrocarbon follows the equation

    \( \displaystyle k = (4.5 \times 10^{11}\,\mathrm{s^{-1}})\,e^{-28000\,\mathrm{K}/T} \)

Calculate E_a.”