Multistep Reaction Energy Profile多步反应能量图

Big Idea · Transformations (TRA)AP Science Practice 3 · Representing Data and PhenomenaAP link · Unit 5~40 min

Learning goals

  • Read the number of steps, the intermediates, the transition states, and each step's activation energy from the energy profile of a multistep reaction
  • Identify the rate-determining step (the step with the largest activation energy and highest transition state), and match an energy profile to a mechanism and rate law
  • Compare catalyzed and uncatalyzed energy profiles, which follow different pathways with lower activation energy but share the same start, end, and ΔH

Before you start

  • Reaction energy profile (U5.6)
  • Introduction to reaction mechanisms (U5.7)
  • Reaction mechanism and rate law (U5.8)

Energy profiles of multistep reactions

A one-step energy profile from U5.6 has a single peak. In a multistep reaction each step has its own transition state, so the profile has several peaks:

  • The number of peaks (transition states) equals the number of steps. Each peak is the transition state of one step; it lasts an extremely short time and can’t be isolated.
  • A valley between two peaks is an intermediate. An intermediate sits at a local energy minimum, so it is more stable than a transition state and can in principle be detected, though it is usually higher in energy and lower in concentration than the reactants and products.
  • Each step’s activation energy is measured from the start of that step. Step 1 is measured from the reactants to the first peak; step 2 from the intermediate to the second peak; and so on.
  • ΔH for the whole reaction is still the energy difference between products and reactants, however many steps there are. Each individual step can be endothermic or exothermic.

The rate-determining step on a profile

The step with the largest activation energy is slowest, so it is the rate-determining step. On AP questions, it is also the step with the highest transition state: the tallest peak on the graph.

  • When the first step is slow (U5.8), the first peak is the highest.
  • When the first step is a fast equilibrium and the second is slow (U5.9), the first peak is fairly low (the forward and reverse reactions both happen easily), and the second peak is the highest.

On the profiles below, decide which step is rate-determining, then look at the labels for transition states, intermediates, and each step’s activation energy:

Try it: read multistep energy profiles
Reaction coordinateEnergy (kJ/mol)ReactantsProducts‡190Intermediate‡230

How many steps does this reaction have? Which is the rate-determining (slowest) step?

Energies are schematic. Each step’s activation energy is measured from the start of that step (the reactants or the previous intermediate) to its transition state.

Catalyzed and uncatalyzed profiles

OpenStax uses energy profiles to show what a catalyst does: the catalyzed and uncatalyzed curves start at the same energy and end at the same energy (the same overall reaction, so the same ΔH), but they follow different pathways. Without a catalyst the reaction might happen in one step; with a catalyst it might take two steps with an intermediate. What matters is that the rate-determining step of the catalyzed pathway has a lower activation energy.

For example, Cl atoms catalyze O₃ + O → 2O₂. With Cl present there are two steps (Cl + O₃ → ClO + O₂; ClO + O → Cl + O₂), so the profile has two peaks, and the valley between them is the intermediate ClO.

Example 1: Reading a two-step profile

On the energy profile of a two-step reaction, the reactants are at 0 kJ/mol, the first transition state at 60, the intermediate at 25, the second transition state at 95, and the products at −15. Find each step’s activation energy, identify the rate-determining step, and state whether the overall reaction and step 1 are endothermic or exothermic.

Step-by-step solution

  1. Identify the five points. Reactants 0 → transition state 1 (60) → intermediate (25) → transition state 2 (95) → products (−15), all in kJ/mol. Each step’s activation energy is measured from that step’s starting point to its peak.

  2. Step 1 activation energy. It starts from the reactants:

    Ea1=60−0=60 kJ/molE_{a1} = 60 - 0 = \boxed{60\ \text{kJ/mol}}

  3. Step 2 activation energy. It starts from the intermediate, not the reactants:

    Ea2=95−25=70 kJ/molE_{a2} = 95 - 25 = \boxed{70\ \text{kJ/mol}}

  4. Rate-determining step. Step 2 has the larger activation energy (70 > 60), and the second peak is also higher: step 2 is rate-determining.

  5. Endothermic or exothermic? End minus start:

    ΔHoverall=−15−0=−15ΔH1=25−0=+25ΔH2=−15−25=−40\begin{aligned} \Delta H_\text{overall} &= -15 - 0 = -15 \\ \Delta H_1 &= 25 - 0 = +25 \\ \Delta H_2 &= -15 - 25 = -40 \end{aligned}

    The overall reaction is exothermic; step 1 is endothermic (step 2 is exothermic).

  6. Check. The two steps’ ΔH values should add up to the overall ΔH: (+25) + (−40) = −15. It agrees.

Example 2: Matching a profile to a mechanism

Below 225 °C, the mechanism for NO₂ + CO is NO₂ + NO₂ → NO₃ + NO (slow); NO₃ + CO → NO₂ + CO₂ (fast). Describe the features its energy profile should have.

Step-by-step solution

  1. Identify: how many steps. Two elementary steps, each with its own transition state, so the profile has two peaks.

  2. The valley between the peaks. It corresponds to the product of step 1 and reactant of step 2: the intermediate NOX3\ce{NO3} (together with the NO formed alongside it).

  3. Compare the peak heights. Step 1 is slow, with the larger activation energy; step 2 is fast, with the smaller one. So the first peak is higher than the second (each measured from its own starting point).

  4. The two ends. Whether the end is lower or higher than the start depends on the ΔH of the overall reaction NOX2+CO→NO+COX2\ce{NO2 + CO -> NO + CO2}, not on the number of steps; this reaction is exothermic, so the end is lower.

  5. Summary of the features.

    • Two peaks, the first higher
    • One valley between them (NO₃ + NO)
    • The end lower than the start (exothermic)
Practice: on a multistep energy profile, what does each description refer to?
  1. A valley between two peaks (not at either end of the curve)
  2. The top of a peak
  3. Lasts an extremely short time and can’t be isolated
  4. Can in principle be detected; formed in one step and used up in the next
  5. Old bonds partly broken and new bonds partly formed
  6. The start of the curve
  7. ClO, at a valley on the profile for Cl-catalyzed ozone decomposition
  8. The number of these equals the number of steps
  9. The end of the curve, whose energy difference from the start is ΔH
  10. A local energy minimum that isn’t at either end of the curve

Common mistakes

Mistake 1: “Valleys are transition states and peaks are intermediates.” It’s the other way around: a peak is a transition state (can’t be isolated), and a valley between peaks is an intermediate (can be detected).

Mistake 2: “The rate-determining step is always the first step.” The rate-determining step is the one with the largest activation energy, which can be any step. When the first step is a fast equilibrium, the rate-determining step comes later.

Mistake 3: “A catalyst changes where the profile starts or ends.” A catalyst changes only the pathway in between: the start, the end, and ΔH stay the same, and the highest peak gets lower.

Quick check

A reaction’s energy profile has 3 peaks. How many steps and how many intermediates does it have?

A three-step reaction has activation energies of 45, 90, and 30 kJ/mol (the second transition state is also the highest). Which step is rate-determining?

Mechanism: A ⇌ I (fast equilibrium); I + B → C (slow). Which energy profile is most likely?

On a two-step energy profile, the intermediate is 30 kJ/mol above the reactants. Which statement is correct?

Without a catalyst, a reaction happens in one step (Ea = 120 kJ/mol); with a catalyst, it takes two steps (Ea = 50 and 70 kJ/mol). Which statement is correct?

On a two-step profile, the reactants are at 10, the first transition state at 70, the intermediate at 40, the second transition state at 85, and the products at −20 kJ/mol. What is the activation energy of step 2?

AP-style free response

AP-style free response

On the energy profile for X + Y → Z (kJ/mol), the reactants are at 0, the first transition state at 85, the intermediate I at 30, the second transition state at 60, and the products at −40. The proposed mechanism is step 1: X + Y → I; step 2: I → Z.

(a) How many steps does the reaction have? Where is the intermediate on the profile?

(b) Calculate the activation energy of each step, and identify the rate-determining step.

(c) Calculate ΔH for the overall reaction and for each step, and state whether each is endothermic or exothermic.

(d) Write a rate law consistent with this energy profile.

(e) Adding a catalyst speeds up the reaction. Describe how the catalyzed energy profile compares with the original: what stays the same and what changes?

Model answer and scoring

(a) Two peaks, so two steps. The intermediate I is in the valley between the peaks, at 30 kJ/mol.

(b) Step 1: 85 − 0 = 85 kJ/mol; step 2: 60 − 30 = 30 kJ/mol. Step 1 has the larger activation energy, so it is rate-determining.

(c) Overall: −40 kJ/mol, exothermic. Step 1: +30 kJ/mol, endothermic; step 2: −40 − 30 = −70 kJ/mol, exothermic.

(d) The rate-determining step is step 1 (bimolecular): rate = k[X][Y].

(e) The same: the energies of the reactants and products (the start and the end), and ΔH = −40 kJ/mol. Different: the pathway, with a lower activation energy (lower highest peak) for the rate-determining step; there may be different intermediates and a different number of steps.

Scoring: (a) number of steps and the intermediate’s position; (b) both activation energies (step 2 measured from the intermediate) and the rate-determining step; (c) the three ΔH values with endothermic or exothermic; (d) rate law from the slow step; (e) identifies what stays the same and what changes.

Summary

  • On a multistep energy profile, the number of peaks equals the number of steps; peaks are transition states, and valleys between peaks are intermediates.
  • Each step’s activation energy is measured from the start of that step (the reactants or the previous intermediate) to its transition state; the step with the largest activation energy (highest transition state) is rate-determining.
  • The overall ΔH depends only on the start and end; each individual step can be endothermic or exothermic.
  • Catalyzed and uncatalyzed profiles start and end at the same energies; the catalyzed pathway’s rate-determining step has a lower activation energy.

AP tip: To write a mechanism or rate law from a profile, count the peaks to get the number of steps, then find the highest peak to get the rate-determining step. When finding a step’s activation energy, always measure from the start of that step, not from the reactants.

Practice this chapter: Unit 5 · Kinetics · 12 questionsPractice this topic: U5.10 · Multistep Reaction Energy Profile · 5 questions

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