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Difficulty: MediumActivation Energy and Energy Profile Diagrams

An uncatalyzed exothermic reaction has an activation energy for the forward reaction of 110 kJ mol−1110\text{ kJ mol}^{-1} and an overall enthalpy change (ΔH\Delta H) of −70 kJ mol−1-70\text{ kJ mol}^{-1}. If a catalyst is added that lowers the activation energy of the forward reaction by 35 kJ mol−135\text{ kJ mol}^{-1}, what is the activation energy of the reverse catalyzed reaction?

  1. 145 kJ mol−1145\text{ kJ mol}^{-1}Answer
  2. B
    75 kJ mol−175\text{ kJ mol}^{-1}
  3. C
    40 kJ mol−140\text{ kJ mol}^{-1}
  4. D
    215 kJ mol−1215\text{ kJ mol}^{-1}

Answer

145 kJ mol−1145\text{ kJ mol}^{-1}
For an exothermic reaction, the reverse activation energy is greater than the forward activation energy by ∣ΔH∣|\Delta H|. The uncatalyzed reverse activation energy is 110−(−70)=180 kJ mol−1110 - (-70) = 180\text{ kJ mol}^{-1}. Since a catalyst reduces both forward and reverse activation energy barriers by the exact same amount (35 kJ mol−135\text{ kJ mol}^{-1}), the reverse catalyzed activation energy is 180−35=145 kJ mol−1180 - 35 = 145\text{ kJ mol}^{-1}. Alternatively, using the catalyzed forward barrier of 75 kJ mol−175\text{ kJ mol}^{-1}, Ea,rev, cat=75−(−70)=145 kJ mol−1E_{a,\text{rev, cat}} = 75 - (-70) = 145\text{ kJ mol}^{-1}.

Step-by-Step Solution

1
Calculate the activation energy for the forward catalyzed reaction.
Ea,fwd, cat=110 kJ mol−1−35 kJ mol−1=75 kJ mol−1E_{a,\text{fwd, cat}} = 110\text{ kJ mol}^{-1} - 35\text{ kJ mol}^{-1} = 75\text{ kJ mol}^{-1}
A catalyst lowers the energy barrier for the forward reaction by the specified amount.
2
Relate the forward activation energy, reverse activation energy, and enthalpy change.
ΔH=Ea,fwd, cat−Ea,rev, cat\Delta H = E_{a,\text{fwd, cat}} - E_{a,\text{rev, cat}}
The difference between forward and reverse activation energy yields the reaction enthalpy change.
3
Solve for the reverse catalyzed activation energy.
Ea,rev, cat=75 kJ mol−1−(−70 kJ mol−1)=145 kJ mol−1E_{a,\text{rev, cat}} = 75\text{ kJ mol}^{-1} - (-70\text{ kJ mol}^{-1}) = 145\text{ kJ mol}^{-1}
Subtracting a negative enthalpy change adds its absolute value to the forward activation energy.

Key Concept

Effect of Catalysts on Forward and Reverse Activation Energies in Energy Profile Diagrams
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Topics

Activation Energy and Energy Profile Diagrams