Multistep Reaction Energy Profile

AP Chemistry· AP Chemistry CED — Kinetics· 14 min read

1. Core Definition and Structural Features★★☆☆☆⏱ 3 min

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.

📘 Definition

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 $, t h er e a c t i o ni se x o t h er mi c (p r o d u c t s ha v e l o w er e n er g y t han r e a c t an t s); i f$ 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.

2. Identifying the Rate-Determining Step★★★☆☆⏱ 4 min

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: $E_{a 2} > E_{a 1}$ , 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.

3. Connecting Profiles to Mechanisms and Catalysis★★★☆☆⏱ 4 min

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): $\ce A + B - > A B$ Step 2 (slow): $\ce A B + C - > A B C$ Step 3 (fast): $\ce A B C - > A D + E$ 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} $an d$ \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} $an d$ \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.

4. AP-Style Worked Practice Problems★★★★☆⏱ 3 min

📐 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.

5. Common Pitfalls

Wrong move:

Counting the starting reactant or final product as a reaction intermediate.

Why:

Students confuse any energy minimum on the graph with an intermediate, forgetting intermediates are formed and consumed during the reaction.

Correct move:

Only count energy minima between the initial reactant and final product as intermediates, ignore the starting and end points.

Wrong move:

Identifying the RDS by comparing peak height relative to initial reactant energy, not step-specific activation energy.

Why:

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 move:

For every step, calculate $E_{a} = E_{TS of step} - E_{starting species of step}$ , then select the step with the largest $E_{a}$ as RDS.

Wrong move:

Claiming a transition state is the same as a reaction intermediate because both are high-energy species.

Why:

Students mix up the definitions of unstable transition states and short-lived but detectable intermediates.

Correct move:

Memorize the rule: peaks = transition states, valleys = intermediates; transition states cannot be isolated, intermediates can be detected.

Wrong move:

Calculating $Δ H_{rxn}$ as the difference between the highest transition state energy and initial reactant energy.

Why:

Students confuse activation energy of the RDS with overall enthalpy change of the reaction.

Correct move:

Always calculate $Δ H_{rxn}$ as the energy of final products minus energy of initial reactants, regardless of the number of peaks in between.

Wrong move:

Stating that a catalyst changes the overall enthalpy of reaction because it lowers activation energy.

Why:

Students associate lower energy barriers with lower product energy, forgetting catalysts work by changing the mechanism, not the starting or ending energy.

Correct move:

Remember: catalysts only change activation energies of elementary steps, they do not change $Δ H_{rxn}$ , so products and reactants have the same energy in catalyzed and uncatalyzed profiles.

Wrong move:

Stating that a 3-step reaction has 3 intermediates.

Why:

Students match the number of intermediates to the number of steps, instead of steps minus one.

Correct move:

Recall that every step after the first consumes the intermediate from the previous step, so number of intermediates = number of elementary steps - 1.

6. Quick Reference 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	$E_{a} = E_{transition state of step} - E_{starting species of step}$	Calculate relative to the step's starting point, not the initial reactant
Overall enthalpy of reaction	$Δ H_{rxn} = E_{products} - E_{reactants}$	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 $Δ H_{rxn}$	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

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · MCQ
Identify RDS from energy profile
2022 · FRQ
Analyze catalyzed energy profile

Going deeper

official syllabusAP Chemistry Course and Exam DescriptionOfficial Kinetics unit reference

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.