The half-life of a first-order reaction is 20 min at 300 K and 2 min at 350 K . The activation energy of the reaction is: (Given: 2.303 R = 19.15 J K ⁻¹ mol ⁻¹ , R = 8.314 J K ⁻¹ mol ⁻¹ )

Step-by-step solution

For a first-order reaction, the rate constant k is inversely proportional to the half-life ( t_ 1/2 ): k = 0.693 t_ 1/2 Therefore, the ratio of rate constants at the two temperatures is: k₂ k₁ = (t_ 1/2 )₁ (t_ 1/2 )₂ = 20 min 2 min = 10 Using the Arrhenius equation: k₂ k₁ = E_a 2.303 R [ T₂ - T₁ T₁ T₂ ] (10) = E_a 19.15 [ 350 - 300 300 350 ] 1 = E_a 19.15 [ 50 105000 ] 1 = E_a 19.15 [ 1 2100 ] E_a = 19.15 2100 = 40215 J mol ⁻¹ Converting to kilojoules per mole: E_a = 40.215 kJ mol ⁻¹ Answer: 40.215 kJ mol ⁻¹