The rate constant for a first order reaction is 0.58 ~s ⁻¹ at 300 K and 0.026 ~s ⁻¹ at 290 K . What is the energy of activation? ( R =8.314 ~J ~K ⁻¹ ~mol ⁻¹ )

Step-by-step solution

The activation energy E_a is determined using the Arrhenius equation for two temperatures and their corresponding rate constants: ( k₂ k₁ ) = E_a R ( 1 T₁ - 1 T₂ ) Given k₁ = 0.026~ s ⁻¹ at T₁ = 290~ K and k₂ = 0.58~ s ⁻¹ at T₂ = 300~ K , with R = 8.314~ J~K⁻¹~mol⁻¹ , the ratio k₂ k₁ 22.30769 and (22.30769) 3.1048 . The temperature term evaluates to 1 290 - 1 300 = 10 87000 0.0001149425~ K ⁻¹ . Substituting yields 3.1048 = E_a 8.314 0.0001149425 , giving E_a = 3.1048 8.314 0.0001149425 224627.9~ J~mol⁻¹ . Convertin