[Olympiad] The rate constant for a reaction is 2.5 × 10⁻² s⁻¹ at 300 K and 5.0 × 10⁻² s⁻¹ at 310 K. Calculate the activation energy (Ea) in kJ/mol. (R = 8.314 J/mol·K)
- 26.5 kJ/mol
- 53.6 kJ/mol
- 107.2 kJ/mol
- 12.4 kJ/mol
📝 Detailed explanation
Using ln(k₂/k₁) = (Ea/R) * (1/T₁ - 1/T₂):ln(2) = (Ea / 8.314) * (1/300 - 1/310).
0.693 = (Ea / 8.314) * (0.0001075).
Ea = (0.693 * 8.314) / 0.0001075 = 53598 J/mol ≈ 53.6 kJ/mol.