5.10 Multistep Reaction Energy Profile

A multistep reaction energy profile maps potential energy along the reaction coordinate as a reaction moves through more than one elementary step. Each peak represents a transition state, each valley between peaks represents an intermediate, and the tallest barrier usually marks the rate-determining step. For AP Chemistry, use the diagram to label activation energies, intermediates, and the overall energy change.

AP Chemistry expects you to represent the activation energy and overall energy change of a multistep reaction with an energy profile, which means turning a sequence of elementary steps into one diagram. You may also be asked to explain how that picture connects to the rate-determining step from Topics 5.8 and 5.9.

Each Step Adds a Peak and Its Own Barrier

• A multistep profile has one energy hump (transition state) for each elementary step, so two steps give two humps.
• Each hump has its own activation energy measured from the energy level just before it, not from the original reactants.
• Intermediates appear as the valleys (energy minima) between humps, since they form in one step and get used up in the next.
• The overall energy change is the difference between the final products and the starting reactants, no matter how many steps happen in between.
• The highest transition state usually corresponds to the rate-determining step, the slowest step in the mechanism.
• Comparing the energy level at the end of each step with the level at its start tells you whether that elementary step is endothermic or exothermic.

Reading a Multistep Energy Profile

A reaction energy profile plots potential energy on the y-axis against the reaction coordinate on the x-axis. The reaction coordinate represents the progress of the reaction from reactants to products, not time.

For a single elementary step, the profile goes from reactants up to one transition state (the peak) and down to products. The energy gap from reactants up to that peak is the activation energy for that step.

For a multistep reaction, you stack these single-step pictures end to end. Each elementary step contributes:

• A peak (transition state) representing the energy barrier for that step.
• A valley after the peak when the step produces an intermediate that the next step will use.

So a two-step mechanism shows two peaks with one valley between them. A three-step mechanism shows three peaks with two valleys, and so on.

Building the Profile from a Mechanism

Knowing the energetics of each elementary reaction in a mechanism lets you construct the whole profile. Work through it step by step:

1. Plot the reactants at their starting energy level on the left.
2. Draw the first peak (the first transition state). The height from reactants to this peak is the activation energy of step one.
3. Drop down to the first intermediate as a valley.
4. Draw the next peak for the second step. Measure its activation energy from the intermediate's energy level, not from the original reactants.
5. Continue adding peaks and valleys for each remaining step.
6. End at the final products on the right.

Label each activation energy (often written as Ea1, Ea2, and so on) and label the overall energy change between reactants and products. Use consistent energy units such as kJ.

Reactants, Intermediates, and Products

These three species each have a clear spot on the diagram.

• Reactants are the starting substances, shown at the far left.
• Intermediates form during the reaction and are used up in a later step. They appear as valleys between peaks and do not show up in the overall balanced equation.
• Products are the final substances, shown at the far right.

Because an intermediate is produced in one elementary step and consumed in another, it sits in a valley that is lower than the transition states on either side, though it may be above or below the products. That is why intermediates exist only while the reaction is running.

Connecting to Rate and Energy Change

Two pieces of information come straight out of a finished profile:

• Rate-determining step: The step with the highest peak (largest activation energy measured from its own starting point) is usually the slowest step and sets the overall rate. This links back to reaction mechanisms and rate laws.
• Overall energy change: Compare the energy of the final products to the energy of the starting reactants. If products are lower, the overall reaction is exothermic. If products are higher, it is endothermic. The number of peaks in between does not change this overall difference.

You can also describe each individual step. A step that ends lower than it started is exothermic for that step, and a step that ends higher is endothermic for that step.

Drawing and Reading Multistep Energy Profiles

Free Response: If you are asked to draw a profile from a mechanism, show one peak per elementary step and put intermediates in the valleys between peaks. Clearly label reactants, products, each activation energy, and the overall energy change. A common point comes from correctly measuring later activation energies from the intermediate level rather than from the reactants.

Diagram Interpretation: Given a finished profile, practice reading it: count the steps from the number of peaks, find intermediates in the valleys, identify the rate-determining step as the highest barrier, and decide if the overall reaction is exothermic or endothermic by comparing the start and end heights.

Common Trap: Watch the difference between an intermediate (a valley between peaks) and a transition state (a peak). Intermediates are real species that briefly exist; transition states are the unstable, highest-energy arrangements at the top of each peak.

Common Misconceptions

• Misconception: A multistep reaction has only one activation energy.
  Actually: Each elementary step has its own activation energy and its own transition state. The overall reaction does not collapse into a single barrier.
• Misconception: Later activation energies are measured from the reactants.
  Actually: Each step's activation energy is measured from the energy level right before that step, which is usually an intermediate, not the original reactants.
• Misconception: Intermediates and transition states are the same thing.
  Actually: Intermediates sit in valleys and are actual species. Transition states sit at the peaks and cannot be isolated.
• Misconception: The number of steps changes the overall energy change.
  Actually: The overall energy change depends only on the difference between reactants and products. Extra steps add peaks and valleys but do not change the start and end points.
• Misconception: The reaction coordinate is time.
  Actually: The x-axis tracks the progress of bond breaking and forming, not how many seconds have passed.
• Misconception: The tallest peak is always the first step.
  Actually: The rate-determining step is whichever step has the largest barrier from its own starting point, and that can be any step in the mechanism.

Related AP Chemistry Guides

• Unit 5 Review: Kinetics
• 5.1 Reaction Rates
• 5.2 Introduction to Rate Law
• 5.3 Concentration Changes Over Time
• 5.4 Elementary Reactions
• 5.5 Collision Model