The temperature dependence of the rate constant for the decomposition of a gaseous hydrocarbon is given by the following equation: k = 12.5 - 4200 T What is the activation energy ( E_a ) for this reaction in kJ mol ⁻¹ ? (Given: R = 8.314 J K ⁻¹ mol ⁻¹ , 2.303 8.314 = 19.15 )

Step-by-step solution

The Arrhenius equation is given by: k = A - E_a 2.303 RT The given equation is: k = 12.5 - 4200 T Comparing the two equations, we get: E_a 2.303 R = 4200 E_a = 4200 2.303 R Substituting R = 8.314 J K ⁻¹ mol ⁻¹ : E_a = 4200 2.303 8.314 Given 2.303 8.314 = 19.15 : E_a = 4200 19.15 = 80430 J mol ⁻¹ E_a = 80.43 kJ mol ⁻¹ Answer: 80.43