The table lists potential-energy data (relative to the reactants) for a gas-phase reaction both in the absence and presence of a homogeneous catalyst.
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State E (kJmol−1)
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Reactants 0
TS (uncatalyzed) +210
Products −60
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Catalyzed Step 1 TS +105
Intermediate +10
Catalyzed Step 2 TS +115
Products −60
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Answer the following.
(a) Compute the activation energy for each elementary step in the catalyzed mechanism and compare each value with the activation energy of the uncatalyzed reaction.
(b) Draw a single energy-profile diagram that overlays the catalyzed pathway on the uncatalyzed pathway using the numerical values in the table. Clearly label all transition states and the reaction intermediate.
(c) Using the diagram, explain why the catalyst increases the reaction rate even though it introduces an additional elementary step.
(d) Suppose experimental data show that, at a given temperature, the catalyzed reaction is 4.0×103 times faster than the uncatalyzed reaction. Assuming that the pre-exponential factors are similar, estimate (to the nearest kJmol−1) the difference in activation energy between the two pathways that is consistent with this rate enhancement.