For a reaction having three steps, the overall rate constant is k = k₁ k₂ k₃ . The values of E_ a₁ , E_ a₂ and E_ a₃ (activation energies stepwise) are 40 , 50 and 60 kJ mol ⁻¹ respectively. Then the overall E_a (activation energy) of the reaction is ____

Step-by-step solution

The overall rate constant is given by k = k₁ k₂ k₃ . Taking the natural logarithm on both sides: k = k₁ + k₂ - k₃ Differentiating with respect to temperature T : d k dT = d k₁ dT + d k₂ dT - d k₃ dT Using the Arrhenius equation d k dT = E_a RT^2 : E_a RT^2 = E_ a₁ RT^2 + E_ a₂ RT^2 - E_ a₃ RT^2 E_a = E_ a₁ + E_ a₂ - E_ a₃ Substituting the given values E_ a₁ = 40 kJ mol ⁻¹ , E_ a₂ = 50 kJ mol ⁻¹ , and E_ a₃ = 60 kJ mol ⁻¹ : E_a = 40 + 50 - 60 = 30 kJ mol ⁻¹ Answer: 30 kJ mol ⁻¹