Two chemical reactions of the same order have equal Frequency factor value. Their Activation energies differ by 26.8 ~kJ / mol . At 300 K if k₂=x k₁ find the value of x .

Step-by-step solution

The Arrhenius equation is given by k = A e^ -E_a / (RT) . Given that the frequency factors are equal, A₁ = A₂ = A . The rate constants for the two reactions are k₁ = A e^ -E_ a1 / (RT) and k₂ = A e^ -E_ a2 / (RT) . Taking the ratio k₂ / k₁ = e^ (E_ a1 - E_ a2 ) / (RT) . Given E_ a1 - E_ a2 = 26.8 kJ/mol = 26800 J/mol , T = 300 K , and R = 8.314 J K ⁻¹ mol ⁻¹ . Substituting the values: x = k₂ / k₁ = e^ 26800 / (8.314 300) . x = e^ 26800 / 2494.2 = e^ 10.7449 . x 46397 . Answer: 4.639 10^4