5.10 Multistep Profile

Multistep Reaction Energy Profile

Drag Eaᵢ and ΔHᵢ sliders for each step to reshape a 2- or 3-step profile. The rate-determining step highlights automatically and ΔH_rxn = ΣΔHᵢ updates live.

2 or 3 StepsRDS = Max EaᵢΣΔHᵢ = ΔH_rxnIntermediates
Topic 5.10

Multistep Reaction Energy Profile

Represent the activation energy and overall energy change in a multistep reaction with a reaction energy profile.

Knowing the energetics of each elementary reaction in a mechanism allows construction of an energy profile for the whole multistep reaction. The profile is simply the single-step profiles chained together.

How to read it:

  • Number of peaks = number of elementary steps. Two peaks means a two-step mechanism.
  • Each peak is a transition state.
  • Each valley between peaks is an intermediate — a real species at a local energy minimum, which is exactly why it can (sometimes) be detected.
  • The rate-determining step is the step with the highest transition state, measured from the species that precedes it.
  • Overall ΔH is still just the final level minus the initial level, regardless of how many steps intervene.

A subtlety worth getting right: the rate-determining step is not always the step with the tallest individual barrier drawn on the page. It is the step whose transition state is highest in absolute energy relative to the preceding stable species — because that is the largest energy hill the system must climb from where it is sitting.

Individual step enthalpies can be read the same way as ΔH for the whole reaction: the level of the intermediate minus the level of the reactants gives ΔH for step 1, and so on. They sum to the overall ΔH — Hess's law visible on a graph (see 6.9).

Key points

  • Peaks count steps; valleys are intermediates.
  • The tallest transition state marks the rate-determining step.
  • Individual step enthalpies sum to the overall ΔH.
  • An intermediate is at a local minimum, so it is a real species — unlike a transition state.

Common mistakes

  • Calling a valley a transition state. Valleys are intermediates.
  • Identifying the RDS by drawn barrier height alone instead of by the highest transition state.
  • Adding barrier heights to get overall ΔH. ΔH is a level difference, not a sum of barriers.

Worked example

A two-step mechanism has these energies (kJ/mol relative to reactants at 0): TS1 at +95, intermediate at +30, TS2 at +75, products at −50. Identify the rate-determining step, give Ea for each step, and give the overall ΔH.

Step 1: reactants (0) → TS1 (+95) → intermediate (+30)
Ea(step 1) = 95 − 0 = 95 kJ/mol
ΔH(step 1) = 30 − 0 = +30 kJ/mol (endothermic)

Step 2: intermediate (+30) → TS2 (+75) → products (−50)
Ea(step 2) = 75 − 30 = 45 kJ/mol
ΔH(step 2) = −50 − 30 = −80 kJ/mol (exothermic)

Rate-determining step: step 1. Its activation energy (95) is larger than step 2's (45), and its transition state is the highest point on the entire profile, so it is the bottleneck.

Overall ΔH = products − reactants = −50 − 0 = −50 kJ/mol (exothermic).
Check with Hess's law: +30 + (−80) = −50 ✓

Full notes for topic 5.10 →