The half-life periods of a first order reaction at 300 ~K and 400 ~K are 50 ~s and 10 ~s respectively. The activation energy of the reaction in kJ mol ⁻¹ is ( 5=0.70)

Step-by-step solution

Given, For first order reaction, (i) half-life (t_ 1 / 2 ) at temperature 300 ~K =50 ~s (ii) half-life (t_ 1 / 2 ) at temperature 400 ~K =10 ~s aligned & K₁( at 300 ~K )= 0.693 50 =0.014 ~s ⁻¹ & and K₂( at 400 ~K )= 0.693 10 =0.07 ~s ⁻¹ & . K=0.693 / t_ (1 / 2) for lst order reaction ] aligned where, K₁ and K₂ are rate constant at 300 ~K and 400 ~K respectively. Also, according to Arrhenius theory K₂ K₁ = E_a 2.303 R [ T₂-T₁ T₁ T₂ ] where, E_a= activation energy aligned T₁ & = temperature (300 ~K ) T₂ & = temperatu