Consider a complex reaction taking place in three steps with rate constants k₁, k₂ and k₃ respectively. The overall rate constant k is given by the expression k= k₁ k₃ k₂ . If the activation energies of the three steps are 60,30 and 10 ~kJ ~mol ⁻¹ respectively, then the overall energy of activation in kJ mol ⁻¹ is . (Nearest integer)

Step-by-step solution

k ₁, k ₂ and k ₃ are given as rate constants of three steps of a complex reaction. Rate constant (k) of the overall reaction is given as k= k₁ k₃ k₂ Activation energies of the three steps are given as aligned & E _ a ₁ =60 ~kJ ~mol ⁻¹, E _ a ₂ =30 ~kJ ~mol ⁻¹, & E _ a ₃ =10 ~kJ ~mol ⁻¹ aligned From Arrhenius equation, we know that k = Ae ^ - Ea / RT T If E_a is the activation energy of the overall reaction, then aligned & E_a= 1 2 [E_ a₁ +E_ a₃ -E_ a₂ ] & = 1 2 [60+10-30]=20 ~kJ ~mol ⁻¹ aligned