The rate constant of a first order reaction was doubled when the temperature was increased from 300 to 310 K . What is its approximate activation energy (in kJ mol ⁻¹ )? ( R =8.3 ~J ~mol ⁻¹ ~K ⁻¹ ; 2=0.3 )

Step-by-step solution

According to Arrhenius theory. aligned & K = A e ^ - E _ a / RT & ~K ₂ ~K ₁ = E _ a 2.303 R [ 1 ~T ₁ - 1 ~T ₂ ] aligned Given, array ll K ₁= x , & ~T ₁=300 ~K ₂=2 x & ~T ₂=310 2 x x = E _ a 2.303 8.3 [ 1 300 - 1 310 ] E _ a = 2 2.303 8.3 300 310 10 E _ a =53.49 ~kJ ~mol ⁻¹ array