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Difficulty: Very hardActivation Energy and Energy Profile Diagrams

In an energy profile diagram for a reversible chemical reaction, the potential energy of the reactants is 140 kJ mol−1140\text{ kJ mol}^{-1} and the potential energy of the products is 60 kJ mol−160\text{ kJ mol}^{-1}. If the activation energy for the reverse uncatalyzed reaction is 210 kJ mol−1210\text{ kJ mol}^{-1}, what is the activation energy of the reverse reaction in the presence of a catalyst that reduces the forward activation energy by 35 kJ mol−135\text{ kJ mol}^{-1}?

  1. 175 kJ mol−1175\text{ kJ mol}^{-1}Answer
  2. B
    95 kJ mol−195\text{ kJ mol}^{-1}
  3. C
    245 kJ mol−1245\text{ kJ mol}^{-1}
  4. D
    290 kJ mol−1290\text{ kJ mol}^{-1}

Answer

The activation energy of the reverse reaction in the presence of the catalyst is 175 kJ mol−1175\text{ kJ mol}^{-1}.
A catalyst lowers the energy of the activated complex (peak of the curve) by a fixed amount without altering the ground state energies of reactants or products. Because the transition state is lowered by 35 kJ mol−135\text{ kJ mol}^{-1}, both the forward and reverse activation energies decrease by exactly 35 kJ mol−135\text{ kJ mol}^{-1}. Subtracting 35 kJ mol−135\text{ kJ mol}^{-1} from the uncatalyzed reverse activation energy (210 kJ mol−1210\text{ kJ mol}^{-1}) gives 175 kJ mol−1175\text{ kJ mol}^{-1}.

Step-by-Step Solution

1
Determine the effect of a catalyst on the energy barrier
A catalyst provides an alternative pathway with a lower transition state energy, reducing the activation energy of both the forward and reverse reactions by the exact same value.
The difference between reactant/product energy levels (ΔHΔ H) remains constant, so ΔEaΔ E_a is identical for forward and reverse directions.
2
Calculate the catalyzed reverse activation energy
Ea,reverse(cat)=Ea,reverse(uncat)−35 kJ mol−1=210 kJ mol−1−35 kJ mol−1=175 kJ mol−1E_{a,\text{reverse(cat)}} = E_{a,\text{reverse(uncat)}} - 35\text{ kJ mol}^{-1} = 210\text{ kJ mol}^{-1} - 35\text{ kJ mol}^{-1} = 175\text{ kJ mol}^{-1}.
Directly subtracting the energy reduction brought by the catalyst yields the new reverse activation energy barrier.

Key Concept

Equal lowering of forward and reverse activation energy barriers by catalysts
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Topics

Activation Energy and Energy Profile Diagrams