For a first order reaction, the time required for 93.75 % completion at 300 K is equal to the time required for 75 % completion at 320 K . The activation energy of the reaction is ________ kJ mol ⁻¹ . (Nearest integer) [Given: R = 8.314 J K ⁻¹ mol ⁻¹ , 2 = 0.693 ]

Step-by-step solution

For a first order reaction, the time required for a certain percentage completion is related to the half-life. 93.75 % completion means 100 - 93.75 = 6.25 % of the reactant remains, which is 1 16 or ( 1 2 )^4 of the initial amount. This requires 4 half-lives. 75 % completion means 25 % of the reactant remains, which is 1 4 or ( 1 2 )^2 of the initial amount. This requires 2 half-lives. Given that t_ 93.75 % at 300 K = t_ 75 % at 320 K : 4 t_ 1/2 (300 K ) = 2 t_ 1/2 (320 K ) 4 2 k₃₀₀ = 2 2 k₃₂₀ k₃₂₀ k₃₀₀ = 4 2 = 2 U