AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/5/5-10)
Unit 5 · Topic 5.10
5.10 Multistep Reaction Energy Profile
The energy profile of a multistep reaction has one hump for each elementary step, with intermediates sitting in the valleys between them. The step with the largest activation energy is usually the slowest, rate-determining step.
Key terms
- multistep energy profile
- intermediate
- transition state
- rate-determining step
Building a multistep profile
Each elementary step has its own transition state, so each step adds a peak to the profile. A two-step mechanism has two peaks; a three-step mechanism has three.
Between the peaks are valleys. Each valley is an intermediate: a real species with a definite structure that is made in one step and used in the next. Unlike a transition state, an intermediate can sometimes be detected, because it lasts long enough to exist briefly in the mixture.
Reading a multistep profile
- Activation energy of each step: measured from the bottom of the valley (or the reactants) just before that peak, up to the peak.
- Rate-determining step: the step with the largest activation energy is usually the slowest.
- Energy change of each step: the energy after the step minus the energy before it. Individual steps can be endothermic even if the overall reaction is exothermic.
- Overall energy change: products minus reactants, ignoring everything in between.
Matching a profile to a mechanism
If a mechanism has a slow first step and a fast second step, its profile should have a taller first hump (larger Eₐ for step 1) and a smaller second hump, measured from the intermediate valley. If the second step is slow, the second climb should be the bigger one.
When the first step is a fast equilibrium and the second step is slow (topic 5.9), the first hump is small, and the climb from the intermediate valley up to the second peak is the largest.
Sketching a profile from a mechanism
- Count the elementary steps. Draw that many peaks.
- Put an intermediate in each valley between peaks, and label it.
- Make the climb into the slow step's peak the largest, measured from the valley (or reactants) just before it.
- Set the heights of the valleys and of the final products so each step's energy change and the overall energy change have the right signs.
- Label Eₐ for at least the rate-determining step and the overall ΔH, with arrows starting at the correct baseline.
Transition states versus intermediates
A catalyzed reaction often has more steps than the uncatalyzed one, so its profile has more humps. But each hump is lower, which is why the catalyzed path is faster (topic 5.11).
| Feature | Transition state | Intermediate |
|---|---|---|
| Position on profile | peak | valley between peaks |
| Lifetime | fleeting; can't be isolated | brief but real; can sometimes be detected |
| Appears in mechanism steps? | no | yes, as a product then a reactant |
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Reading a two-step profile
A two-step reaction's profile has: reactants at 0 kJ/mol, first peak at +90, a valley (intermediate) at +40, a second peak at +70 and products at −30 kJ/mol. Find each step's Eₐ, identify the rate-determining step and give the overall energy change.
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- Step 1: Step 1: Eₐ = 90 − 0 = 90 kJ/mol. Its energy change = 40 − 0 = +40 kJ/mol (endothermic).
- Step 2: Step 2: Eₐ = 70 − 40 = 30 kJ/mol (measured from the intermediate). Its energy change = −30 − 40 = −70 kJ/mol (exothermic).
- Step 3: Step 1 has the larger activation energy, so it's the rate-determining step.
- Step 4: Overall: −30 − 0 = −30 kJ/mol, exothermic. Check: +40 + (−70) = −30.
Answer: Eₐ(step 1) = 90 kJ/mol, Eₐ(step 2) = 30 kJ/mol; step 1 is rate determining; overall ΔE = −30 kJ/mol
- Example 2
Measuring from the right baseline (classic trap)
Using the same profile, a student says step 2 has an activation energy of 70 kJ/mol. What's wrong?
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- Step 1: The student measured from the reactants' energy (0) to the second peak (+70).
- Step 2: Step 2 starts from the intermediate, at +40, so its climb is only 70 − 40 = 30 kJ/mol.
- Step 3: Always measure each step's Eₐ from the valley directly before its peak.
Answer: Step 2's activation energy is 30 kJ/mol, measured from the intermediate at +40 kJ/mol, not from the reactants.
Common mistakes
- Calling a peak an intermediate. Intermediates are in valleys; peaks are transition states.
- Measuring every step's Eₐ from the reactants.
- Assuming each step must be exothermic because the overall reaction is.
- Drawing a profile with the wrong number of peaks for the number of steps.
On the exam
- Expect to sketch a profile consistent with a given mechanism: the right number of humps, intermediates in the valleys, the tallest climb for the slow step and the correct overall energy change.
- Or you may be given a profile and asked which step is rate determining and how many intermediates there are.
Connected topics
Videos
Check yourself
5 questions on 5.10 Multistep Reaction Energy Profile. Pick an answer to see if you got it, and why.
An energy profile for a two-step reaction is described below, from left to right along the reaction coordinate.
The reactants start at 0 kJ/mol. The energy rises to a first peak at 60 kJ/mol, then falls to a dip at 20 kJ/mol. It rises again to a second peak at 90 kJ/mol, then falls to the products at −40 kJ/mol.
Described energy profile
Which step is the rate-determining step, and why?
What does the dip at 20 kJ/mol represent?
| Point on the profile (left to right) | Energy (kJ/mol) |
|---|---|
| Reactants | 0 |
| Peak 1 | 50 |
| Dip 1 | 20 |
| Peak 2 | 95 |
| Dip 2 | −10 |
| Peak 3 | 25 |
| Products | −60 |
Energies of the points on a reaction energy profile for a three-step reaction
How many intermediates are formed in this reaction?
Which step is the rate-determining step?
What is ΔH for the overall reaction?
0 of 5 answered