Rate constants of a reaction at 500 K and 700 K are 0.04 ~s ⁻¹ and 0.14 ~s ⁻¹ , respectively; then, activation energy of the reaction is : (Given: 3.5=0.5441, R =8.31 ~J ~K ⁻¹ ~mol ⁻¹

Step-by-step solution

K =A e^ -E_a / R T After taking In both side K= A- E_a R T In K ₁= A - E _ a RT ₁ at temp. T ₁ ...(i) In K ₂= A - E _ a RT ₂ at temp. T ₂ ,,(ii) (ii) - (i) In K₂- InK K₁= E_a R [ 1 T₁ - 1 T₂ ] K ₂ ~K ₁ = E _ a R [ 1 500 - 1 700 ] 0.14 0.04 = E_a R [ 700-500 500 700 ] 14 4 = E_a R [ 200 500 700 ] 3.5= E_a 2.303 R [ 1 250 7 ]0.5441= E_a 2.303 8.31 [ 1 250 7 ]E_a=0.5441 8.31 250 7 2.303=0.5441 83.1 25 7 2.303=18222.65 18219 ~J