Given below is an expression for the rate constant of a first order reaction occurring at a certain temperature, T (K). k = 14.34 - 1.25 10⁴ T The energy of activation in kcal mol ⁻¹ for the reaction is : (Given : k in s ⁻¹ , R = 1.987 cal mol ⁻¹ K ⁻¹ )

Step-by-step solution

The Arrhenius equation is given by: k = A - E_a RT The given equation is: k = 14.34 - 1.25 10⁴ T Comparing the two equations: E_a R = 1.25 10⁴ E_a = 1.25 10⁴ R Substituting R = 1.987 cal mol ⁻¹ K ⁻¹ : E_a = 1.25 10⁴ 1.987 E_a = 24837.5 cal mol ⁻¹ E_a = 24.8375 kcal mol ⁻¹ 24.84 kcal mol ⁻¹ Answer: 24.84