What is the activation energy for a reaction if its rate doubles when the temperature is raised from 20^ C to 35^ C ? (R=8.314 ~J ~mol ⁻¹ ~K ⁻¹ )

Step-by-step solution

Given, initial temperature, T₁=20+273=293 ~K Final temperature aligned T₂ & =35+273 & =308 ~K R & =8.314 ~J ~mol ⁻¹ ~K ⁻¹ aligned Since, rate becomes double on raising temperature, r₂=2 r₁ or r₂ r₁ =2 As rate constant, k r k₂ k₁ =2 From Arrnhenius equation, we know that aligned & k₂ k₁ =- E₂ 2.303 R [ T₁-T₂ T₁ T₂ ] & 2=- E₂ 2.303 8.314 [ 293-308 293 308 ] & 0.3010=- E₂ 2.303 8.314 [ -15 293 308 ] aligned aligned E₂ & = 0.3010 2.303 8.314 293 308 15 & =34673.48 ~J ~mol ⁻¹=34.7 ~kJ ~mol ⁻¹ aligned