A first order reaction is 50%complete in 30 minutes at 300 K and in 10 minutes at 320 K. The activation energy of the reaction (E_a ) is: [R=8.314 J K ⁻¹ mol ⁻¹ ; log 2 = 0.3010; log 3=0.4771]

Step-by-step solution

For a first-order reaction, the rate constant is given by k = 0.693 t_ 1/2 . At T₁ = 300 K , k₁ = 0.693 30 min ⁻¹ At T₂ = 320 K , k₂ = 0.693 10 min ⁻¹ k₂ k₁ = 30 10 = 3 Using the Arrhenius equation: ( k₂ k₁ ) = E_a 2.303 R ( T₂ - T₁ T₁ T₂ ) 3 = E_a 2.303 8.314 ( 320 - 300 300 320 ) 0.4771 = E_a 19.147 ( 20 96000 ) E_a = 0.4771 19.147 96000 20 E_a = 43848 J mol ⁻¹ = 43.8 kJ mol ⁻¹ Answer: 43.8 kJ mol ⁻¹