# Multistep Reaction Energy Profile

> AP Chemistry · Unit 5: Kinetics
> Source: https://www.owlsprep.com/study/ap-chemistry-u5-multistep-reaction-energy-profile/

This guide covers core analysis of multistep reaction energy profiles for AP Chemistry, including identification of key features, calculation of enthalpy and activation energy, and connections to reaction mechanisms and catalysis.

**Prerequisites:** [Elementary reactions in reaction mechanisms](https://www.owlsprep.com/study/ap-chemistry-u5-elementary-reactions/); [Relationship between activation energy and reaction rate](https://www.owlsprep.com/study/ap-chemistry-u5-collision-theory/); [Enthalpy change of chemical reactions](https://www.owlsprep.com/study/ap-chemistry-u6-enthalpy-change/)

## Learning objectives

- Identify transition states, intermediates, and rate-determining steps from multistep energy profiles
- Calculate overall reaction enthalpy and activation energy for each elementary step
- Connect energy profiles to multistep reaction mechanisms
- Predict the effect of a catalyst on a multistep energy profile

## Core Definition and Structural Features

A multistep reaction energy profile (or reaction coordinate diagram) plots the potential energy of all species along a reaction pathway against the reaction coordinate, a qualitative measure of reaction progress from initial reactants to final products. Unlike single-step reactions (which have only one energy peak), multistep profiles have one energy peak per elementary step, with valleys between peaks corresponding to reaction intermediates.

**Key Structural Rules** — For a reaction with $n$ elementary steps: (1) $n$ peaks = $n$ transition states (activated complexes): unstable, high-energy species that exist only fleetingly and cannot be isolated. (2) $n-1$ valleys = $n-1$ reaction intermediates: species formed in one step and consumed in a later step that are detectable experimentally.

*Example:* A 2-step reaction will always have 2 transition states and 1 reaction intermediate.

The overall enthalpy change of the reaction is independent of the number of steps in the mechanism, calculated as:

$$Delta H_{\text{rxn}} = E_{\text{products}} - E_{\text{reactants}}$$

If $
Delta H_{\text{rxn}} < 0$, the reaction is exothermic (products have lower energy than reactants); if $
Delta H_{\text{rxn}} > 0$, it is endothermic.

**Worked example:** A two-step reaction has the following potential energies (all in kJ/mol): reactants = 12, first transition state = 52, intermediate = 18, second transition state = 70, products = 28. (a) How many transition states and intermediates are present? (b) Calculate $
Delta H_{\text{rxn}}$ and classify the reaction as endothermic or exothermic.

1. Apply the core structural rule relating steps to transition states/intermediates:
2. $$\text{Transition states} = 2, \quad \text{Intermediates} = 2 - 1 = 1$$
3. Substitute values into the overall enthalpy formula:
4. $$\Delta H_{\text{rxn}} = 28 - 12 = +16\ \text{kJ/mol}$$
5. A positive $
Delta H_{\text{rxn}}$ indicates the reaction is endothermic.

> **Exam tip:** Never count the initial reactant or final product as an intermediate. Only energy minima between the start and end points count as intermediates, regardless of their energy value.

## Identifying the Rate-Determining Step

The rate-determining step (RDS, or rate-limiting step) is the slowest elementary step in a multistep mechanism, and it dictates the overall rate of the entire reaction, analogous to a bottleneck controlling traffic flow on a highway.

To find the RDS on an energy profile, calculate the activation energy $E_a$ for each individual step. Activation energy for a step is the difference between the energy of the step's transition state (peak) and the energy of the starting species for that step:

$$E_{a,\text{step } i} = E_{\text{TS}_i} - E_{\text{start}_i}$$

The step with the highest activation energy is always the rate-determining step, because a higher $E_a$ means fewer molecules have enough kinetic energy to overcome the barrier, so the step proceeds slower.

**Worked example:** Use the energy values from the previous example: reactants (12 kJ/mol), TS1 (52 kJ/mol), intermediate (18 kJ/mol), TS2 (70 kJ/mol), products (28 kJ/mol). Identify the rate-determining step and calculate its activation energy.

1. Calculate activation energy for the first step:
2. $$E_{a1} = 52 - 12 = 40\ \text{kJ/mol}$$
3. Calculate activation energy for the second step:
4. $$E_{a2} = 70 - 18 = 52\ \text{kJ/mol}$$
5. Compare activation energies: $E_{a2} > E_{a1}$, so the second step is the rate-determining step.

> **Exam tip:** Do not just pick the peak highest relative to the initial reactant y-axis as the RDS. Always calculate $E_a$ relative to the starting point of the individual step, because intermediates can be higher in energy than the original reactants.

## Connecting Profiles to Mechanisms and Catalysis

A core AP Chemistry skill is matching an energy profile to a proposed mechanism, and vice versa. Every elementary step in a mechanism corresponds to exactly one energy peak (transition state) on the profile, so the number of peaks directly tells you the number of steps in the mechanism. Intermediates, which are formed in one step and consumed in another, are never part of the overall balanced reaction.

Catalysts modify multistep energy profiles by providing an alternate reaction mechanism with a lower activation energy for the rate-determining step. Catalysts do not change the overall energy of reactants or products, so $
Delta H_{\text{rxn}}$ remains identical for catalyzed and uncatalyzed reactions.

**Worked example:** A reaction follows the three-step mechanism below:
Step 1 (fast): $\ce{A + B -> AB}$
Step 2 (slow): $\ce{AB + C -> ABC}$
Step 3 (fast): $\ce{ABC -> AD + E}$
What key features would you expect to see on the energy profile for this mechanism? Identify the reaction intermediate(s) and the location of the highest energy peak.

1. Count the number of elementary steps: 3 steps, so the profile will have 3 peaks (transition states).
2. Number of intermediates = 3 - 1 = 2 intermediates: $
\ce{AB}$ and $
\ce{ABC}$, which correspond to the two valleys between the three peaks.
3. Step 2 is given as the slow step, so it is the rate-determining step, meaning it will have the highest activation energy, so its peak will be the highest energy peak on the profile.
4. Confirmation: Intermediates $
\ce{AB}$ and $
\ce{ABC}$ cancel out when adding the steps, so they do not appear in the overall reaction, matching their definition.

> **Exam tip:** If you are asked to draw an energy profile from a mechanism, always draw the RDS peak as the highest peak, regardless of where it falls in the reaction sequence. AP exam graders look for this key feature.

## AP-Style Worked Practice Problems

**Worked example:** The energy profile for a three-step reaction has the following energy values (all in kJ/mol): Reactants: 0, TS1: 50, Int1: 20, TS2: 80, Int2: 30, TS3: 65, Products: 10. Which of the following statements is correct?
A) The overall reaction is endothermic, and the third step is the rate-determining step.
B) The overall reaction is endothermic, and the second step is the rate-determining step.
C) The overall reaction is exothermic, and the second step is the rate-determining step.
D) The overall reaction is exothermic, and the third step is the rate-determining step.

1. First calculate the overall enthalpy change:
2. $$\Delta H_{\text{rxn}} = 10 - 0 = +10\ \text{kJ/mol}$$
3. A positive $
\Delta H_{\text{rxn}}$ means the reaction is endothermic, eliminating options C and D. Next calculate activation energy for each step:
4. $$E_{a1} = 50 - 0 = 50\ \text{kJ/mol}, \quad E_{a2} = 80 - 20 = 60\ \text{kJ/mol}, \quad E_{a3} = 65 - 30 = 35\ \text{kJ/mol}$$
5. The highest activation energy is for the second step, so the correct answer is B.

## Common pitfalls

- **Wrong:** Counting the starting reactant or final product as a reaction intermediate.
  - Why it fails: Students confuse any energy minimum on the graph with an intermediate, forgetting intermediates are formed and consumed during the reaction.
  - Correct: Only count energy minima between the initial reactant and final product as intermediates, ignore the starting and end points.
- **Wrong:** Identifying the RDS by comparing peak height relative to initial reactant energy, not step-specific activation energy.
  - Why it fails: Students see the tallest peak relative to the y-axis origin and automatically pick it, forgetting intermediates can be higher in energy than reactants.
  - Correct: For every step, calculate $E_a = E_{\text{TS of step}} - E_{\text{starting species of step}}$, then select the step with the largest $E_a$ as RDS.
- **Wrong:** Claiming a transition state is the same as a reaction intermediate because both are high-energy species.
  - Why it fails: Students mix up the definitions of unstable transition states and short-lived but detectable intermediates.
  - Correct: Memorize the rule: peaks = transition states, valleys = intermediates; transition states cannot be isolated, intermediates can be detected.
- **Wrong:** Calculating $\Delta H_{\text{rxn}}$ as the difference between the highest transition state energy and initial reactant energy.
  - Why it fails: Students confuse activation energy of the RDS with overall enthalpy change of the reaction.
  - Correct: Always calculate $\Delta H_{\text{rxn}}$ as the energy of final products minus energy of initial reactants, regardless of the number of peaks in between.
- **Wrong:** Stating that a catalyst changes the overall enthalpy of reaction because it lowers activation energy.
  - Why it fails: Students associate lower energy barriers with lower product energy, forgetting catalysts work by changing the mechanism, not the starting or ending energy.
  - Correct: Remember: catalysts only change activation energies of elementary steps, they do not change $\Delta H_{\text{rxn}}$, so products and reactants have the same energy in catalyzed and uncatalyzed profiles.
- **Wrong:** Stating that a 3-step reaction has 3 intermediates.
  - Why it fails: Students match the number of intermediates to the number of steps, instead of steps minus one.
  - Correct: Recall that every step after the first consumes the intermediate from the previous step, so number of intermediates = number of elementary steps - 1.

## Cheatsheet

| Category | Formula/Rule | Notes |
| --- | --- | --- |
| Number of transition states | = number of elementary steps | One peak per elementary step; all transition states are at profile peaks |
| Number of reaction intermediates | = number of elementary steps - 1 | Intermediates are at valleys between starting reactant and final product |
| Activation energy of a step | $E_a = E_{\text{transition state of step}} - E_{\text{starting species of step}}$ | Calculate relative to the step's starting point, not the initial reactant |
| Overall enthalpy of reaction | $\Delta H_{\text{rxn}} = E_{\text{products}} - E_{\text{reactants}}$ | Independent of number of steps or activation energy barriers |
| Rate-determining step identification | Step with the highest $E_a$ | Highest $E_a$ = slowest step, determines overall reaction rate |
| Effect of a catalyst | Lowers $E_a$ for at least one step, no change to $\Delta H_{\text{rxn}}$ | Catalyst provides an alternate mechanism, does not change start/end energy |
| Transition state vs intermediate | Transition state = peak (unstable), Intermediate = valley (detectable) | Neither appears in the overall balanced reaction |

## What's next

This topic is the foundational link between reaction mechanisms and reaction kinetics, the core of AP Chemistry Unit 5. Next, you will connect the rate-determining step you identify from energy profiles to writing rate laws for multistep reactions, a skill heavily tested on AP free-response questions. Without being able to correctly identify the RDS and intermediates from an energy profile, you will not be able to write a consistent rate law that matches a proposed mechanism, a common AP exam prompt. This topic also connects to thermodynamics in Unit 6, where you will use Hess's law to confirm that overall enthalpy is independent of reaction pathway.

- [Elementary reactions](https://www.owlsprep.com/study/ap-chemistry-u5-elementary-reactions/)
- [Catalysis and reaction rates](https://www.owlsprep.com/study/ap-chemistry-u5-catalysis/)
- [Thermodynamics Overview](https://www.owlsprep.com/study/ap-chemistry-u6-overview/)

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