For a reaction taking place in three steps at same temperature, overall rate constant K=(K₁ K₂)/K₃. If Ea₁, Ea₂ and Ea₃ are 40, 50 and 60 kJ / mol respectively, the overall Ea is ________ kJ / mol.

Solution

Chemistry ma’am · 4 steps

Write each k in Arrhenius form: multiplying k values adds their Ea, and dividing subtracts it.

1. Arrhenius for each step. Each step follows kᵢ = Aᵢ e^(-E_(a,i)/RT), and all three steps run at the same temperature T.
2. Combine the exponentials. Put the three forms into k = (k₁ k₂)/k₃. The exponents add for the two factors on top and subtract for the one on the bottom.

   k = (A₁ A₂)/A₃ e^(-(Eₐ₁ + Eₐ₂ - Eₐ₃)/RT)

3. Read off Ea. This has the form A e^(-Eₐ/RT), so the overall activation energy is Eₐ = Eₐ₁ + Eₐ₂ - Eₐ₃ = 40 + 50 - 60.
4. So. The overall activation energy is 30 kJ mol⁻¹.

The common slip: 150. Adding all three activation energies gives 150. The k₃ in the denominator means its Eₐ must be subtracted.

The idea to keep. Activation energy sits in an exponent. So it copies the rate constant's pattern as a sum: a k in the numerator adds its Ea, a k in the denominator subtracts it, and a power multiplies it.

Answer from the NTA final answer key. Solution by PrepWiser.