In the presence of a catalyst at a given temperature of 27^ C , the Activation energy of a specific reaction is reduced by 100 ~J / mol . What is the ratio between the rate constants for the catalysed ( k ₂) and uncatalysed ( k ₁) reactions?

Step-by-step solution

The Arrhenius equation for the rate constant is given by k = A e^ -E_a / RT . For the uncatalysed reaction, k₁ = A e^ -E_ a1 / RT . For the catalysed reaction, k₂ = A e^ -E_ a2 / RT . The ratio of the rate constants is k₂ k₁ = A e^ -E_ a2 / RT A e^ -E_ a1 / RT = e^ (E_ a1 - E_ a2 ) / RT . Given that the activation energy is reduced by 100 J/mol , we have E_ a1 - E_ a2 = 100 J/mol . The temperature T = 27^ C = 27 + 273 = 300 K . The gas constant R = 8.314 J K ⁻¹ mol ⁻¹ . Substituting these values, k₂ k₁ = e^ 100 / (