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Difficulty: MediumActivation Energy and Energy Profile Diagrams

For a reversible gaseous reaction A+B⇌C+DA + B \rightleftharpoons C + D, the potential energy of the reactants is 120 kJ mol−1120\text{ kJ mol}^{-1} and the potential energy of the products is 45 kJ mol−145\text{ kJ mol}^{-1}. If the activation energy for the reverse reaction is 140 kJ mol−1140\text{ kJ mol}^{-1}, calculate the activation energy for the forward reaction in kJ mol−1\text{kJ mol}^{-1}.

Answer: 65 kJ mol^{-1}

Answer

The activation energy for the forward reaction is 65 kJ mol−165\text{ kJ mol}^{-1}.
The forward activation energy (Ea,forwardE_{a,\text{forward}}) is the energy barrier measured from the energy level of the reactants (120 kJ mol−1120\text{ kJ mol}^{-1}) to the peak of the activated complex. Since the products lie at 45 kJ mol−145\text{ kJ mol}^{-1} and require 140 kJ mol−1140\text{ kJ mol}^{-1} to reach the activated complex, the peak energy is 45+140=185 kJ mol−145 + 140 = 185\text{ kJ mol}^{-1}. Subtracting the reactant energy gives 185−120=65 kJ mol−1185 - 120 = 65\text{ kJ mol}^{-1}. Alternatively, using ΔH=Ea,forward−Ea,reverse\Delta H = E_{a,\text{forward}} - E_{a,\text{reverse}}, where ΔH=45−120=−75 kJ mol−1\Delta H = 45 - 120 = -75\text{ kJ mol}^{-1}, gives −75=Ea,forward−140  ⟹  Ea,forward=65 kJ mol−1-75 = E_{a,\text{forward}} - 140 \implies E_{a,\text{forward}} = 65\text{ kJ mol}^{-1}.

Step-by-Step Solution

1
Determine the potential energy of the activated complex (transition state).
Transition state energy Epeak=Hproducts+Ea,reverse=45+140=185 kJ mol−1E_{\text{peak}} = H_{\text{products}} + E_{a,\text{reverse}} = 45 + 140 = 185\text{ kJ mol}^{-1}.
The reverse activation energy is the energy required to overcome the barrier going from products up to the peak.
2
Calculate the forward activation energy.
Ea,forward=Epeak−Hreactants=185−120=65 kJ mol−1E_{a,\text{forward}} = E_{\text{peak}} - H_{\text{reactants}} = 185 - 120 = 65\text{ kJ mol}^{-1}.
The forward activation energy is the energy difference between the peak (activated complex) and the energy level of the reactants.

Key Concept

Activation energy and potential energy relationships in energy profile diagrams
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Activation Energy and Energy Profile Diagrams