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The decomposition of dinitrogen pentoxide follows first-order kinetics: 2 N2O5(g) -> 4 NO2(g) + O2(g) Initially 0.2 mol of N2O5 was taken in a 1 L vessel. A plot of ln[N2O5] vs time (figure-1) yields the rate constant k. A separate plot of ln(k) vs (1/T) (figure-2) is linear with a slope of -1.2 * 10⁴ K. What is the activation energy of the reaction in kJ/mol? (Use R = 8.31 J/mol-K)
- 49.86 kJ/mol
- 99.72 kJ/mol
- 24.93 kJ/mol
- 199.44 kJ/mol
Correct answer: 99.72 kJ/mol
Solution
From the Arrhenius equation, ln k = ln A - Ea/(R*T), so the slope of ln k vs 1/T equals -Ea/R. Given slope = -1.2 * 10⁴ K, we get Ea = 1.2 * 10⁴ * 8.31 = 99720 J/mol = 99.72 kJ/mol.
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