The rate constant of a decomposition reaction becomes ten times its initial value when the temperature is increased from 200 K to 250 K . Calculate the activation energy of the reaction. (Given: R = 8.314 J K ⁻¹ mol ⁻¹ and 2.303 8.314 = 19.15 )

Step-by-step solution

Using the Arrhenius equation: ( k₂ k₁ ) = E_a 2.303 R ( 1 T₁ - 1 T₂ ) Given k₂ = 10 k₁ , T₁ = 200 K , T₂ = 250 K , and 2.303 R = 19.15 J K ⁻¹ mol ⁻¹ . Substituting the values: (10) = E_a 19.15 ( 1 200 - 1 250 ) 1 = E_a 19.15 ( 250 - 200 200 250 ) 1 = E_a 19.15 ( 50 50000 ) 1 = E_a 19.15 ( 1 1000 ) E_a = 19.15 1000 J mol ⁻¹ E_a = 19.15 kJ mol ⁻¹ Answer: 19.15 kJ mol ⁻¹