For a first-order reaction, the time required for 75 % completion at 300 K is equal to the time required for 93.75 % completion at 320 K . The value of E_a R 2 is _________ K (nearest integer), where E_a is the activation energy and R is the universal gas constant.

Step-by-step solution

For a first-order reaction, the time required for a certain fractional completion is given by t = 1 k ( 100 100 - x ) . For 75 % completion: t_ 75 % = 1 k₃₀₀ ( 100 100 - 75 ) = 1 k₃₀₀ (4) = 2 2 k₃₀₀ For 93.75 % completion: t_ 93.75 % = 1 k₃₂₀ ( 100 100 - 93.75 ) = 1 k₃₂₀ ( 100 6.25 ) = 1 k₃₂₀ (16) = 4 2 k₃₂₀ Given that t_ 75 % at 300 K = t_ 93.75 % at 320 K : 2 2 k₃₀₀ = 4 2 k₃₂₀ k₃₂₀ k₃₀₀ = 2 Using the Arrhenius equation for two temperatures: ( k₃₂₀ k₃₀₀ ) = E_a R ( 1 T₁ - 1 T₂ ) (2) = E_a R ( 1 300 - 1 320 ) (2) =