Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by 20 ~kJ ~mol ⁻¹ . If k ₁ and k ₂ are the rate constants of first and

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Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by 20 ~kJ ~mol ⁻¹ . If k ₁ and k ₂ are the rate constants of first and second reaction respectively at 300 K, then k ₂ k ₁ will be _ _ _ _ . (nearest integer) [ R =8.3 ~J ~K ⁻¹ ~mol ⁻¹ ]

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Given: A₁ = A₂ , E_ a1 = E_ a2 + 20 kJ/mol, T = 300 K, R = 8.3 J K⁻¹ mol⁻¹ Using Arrhenius equation: k = Ae^ -E_a/RT k₂ k₁ = e^ -E_ a2 /RT e^ -E_ a1 /RT = e^ (E_ a1 - E_ a2 )/RT E_ a1 - E_ a2 = 20 kJ/mol = 20000 J/mol k₂ k₁ = e^ 20000 8.3 300 = e^ 20000 2490 k₂ k₁ = 20000 2490 = 8.03 8

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