A-Level Reaction rates, rate laws and catalysis: worked solution

Question

In a further study, dinitrogen pentoxide (N₂O₅) decomposes when heated, giving nitrogen dioxide: N₂O₅ (g) → 2NO₂ (g) + ½O₂ (g) The following table lists how the rate constant for this decomposition changes with temperature. | Temperature, T / K | Rate constant, k / s⁻¹ | | 303 | 2.05 × 10⁻⁵ | | 333 | 8.90 × 10⁻⁴ | Using sections 1 and 2 of the data booklet, work out the activation energy of this decomposition reaction.

Use the two-point Arrhenius equation: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2). k2/k1 = 8.90x10⁻⁴ / 2.05x10⁻⁵ = 43.4, so ln(k2/k1) = 3.77. 1/T1 - 1/T2 = 1/303 - 1/333 = 2.97x10⁻⁴ K⁻¹. Ea = R x ln(k2/k1) / (1/T1 - 1/T2) = 8.31 x 3.77 / 2.97x10⁻⁴ = 1.05x10⁵ J mol⁻¹. Ea = 105 kJ mol⁻¹.