Unit 5 · Topic 5.10 Beta

Multistep Reaction Energy Profile

A multistep energy profile has one peak, a transition state, for each elementary step, with intermediates in the valleys between them.

Practice 3: Representing Data and PhenomenaPractice 4: Model Analysis

Question set for this topic

Part 1 · Hook

Why this matters

A hiking trail with two mountain passes has a rest hut in the valley between them. How long the hike takes depends mostly on the harder of the two climbs, and you only count each climb from where it starts: from the trailhead for the first pass, and from the hut for the second.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. On a one-step energy profile, the activation energy is:

  1. the climb from the reactants to the peak
  2. the energy of the products
  3. products minus reactants
  4. the energy of the peak alone
Show the answer

Ea = E(transition state) − E(reactants).

  • Correct: the climb from the reactants to the peak:
  • the energy of the products:
  • products minus reactants:
  • the energy of the peak alone:

2. Which step of a mechanism sets the overall rate?

  1. The slowest step
  2. The first step
  3. The last step
  4. The fastest step
Show the answer

The overall reaction cannot be faster than its slowest step.

  • Correct: The slowest step:
  • The first step:
  • The last step:
  • The fastest step:

Part 4 · See it

See it first

Potential energy against reaction progress for a reaction in two elementary steps. The curve rises from the reactants over a tall first peak, the first transition state, drops into a valley where the intermediate sits, rises over a smaller second peak, the second transition state, and falls to products lower than the reactants. A double arrow from the reactants to the first peak is the activation energy of step 1; a shorter double arrow from the valley to the second peak is the activation energy of step 2. Step 1 has the larger activation energy, so it is the slow step.
Two peaks for two steps, an intermediate in the valley, and the larger barrier on the slow step. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Each elementary step has its own transition statea mechanism with n steps has n peaks on its profile
  2. An intermediate is a real species between two stepsit sits in a valley between neighboring peaks
  3. Each step starts from the level the previous step ended atits barrier is measured from that level, not from the reactants
  4. The step with the largest barrier has the fewest successful collisionsit is the slow, rate-determining step

Part 6 · Key ideas

Key ideas

  • A multistep energy profile has one peak per elementary step; valleys between peaks are intermediates.
  • A step's Ea is its peak minus the level it starts from.
  • The step with the largest Ea is the rate-determining step; it need not be the first.
  • The overall energy change is products minus reactants, whatever happens in between.

Part 7 · Misconception

A common mistake

The wrong idea: On a multistep profile, every activation energy is measured from the reactants.

What actually happens: Each step's barrier starts from the level that step begins at: the reactants for step 1, the intermediate for step 2, and so on.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Graph

A two-step reaction

The energy profile for a reaction that happens in two elementary steps:

Step 1: A + B → C   Step 2: C → D

Reaction progress has no units.

0204060801001201401600246810121416Reaction progressPotential energy (kJ/mol)
Data table
Reaction progressEnergy
050
150
250
372.5
4117.5
5140
6125
795
880
987.5
10102.5
11110
1287.5
1342.5
1420
1520
1620

1. Where is the intermediate C on the profile?

  1. In the valley between the two peaks, at 80 kJ/mol
  2. At the first peak, at 140 kJ/mol
  3. At the second peak, at 110 kJ/mol
  4. At the right-hand plateau, at 20 kJ/mol
Show the answer

An intermediate is a real species made in step 1 and used in step 2, so it sits in the local minimum between the two transition states.

  • Correct: In the valley between the two peaks, at 80 kJ/mol: Right: the valley between the steps.
  • At the first peak, at 140 kJ/mol: The first peak is the transition state of step 1, not a species that can be isolated.
  • At the second peak, at 110 kJ/mol: The second peak is the transition state of step 2.
  • At the right-hand plateau, at 20 kJ/mol: The right-hand plateau is the product D.

2. What is the activation energy of step 2, in kJ/mol?

Type a number in kJ/mol.

Show the answer

Step 2 starts at the intermediate (80 kJ/mol) and climbs to the second transition state (110 kJ/mol): Ea = 110 − 80 = 30 kJ/mol.

  • Answer: 30 kJ/mol

3. Which step is rate-determining, and what is the evidence?

  1. Step 1: its barrier, 90 kJ/mol, is larger
  2. Step 2: its transition state comes later in the reaction
  3. Step 2: its barrier ends nearest to the products
  4. Step 1: being first, it is the slowest by rule
Show the answer

Step 1 climbs 140 − 50 = 90 kJ/mol; step 2 climbs 110 − 80 = 30 kJ/mol. The larger barrier means fewer successful collisions, so step 1 is slower and limits the rate.

  • Correct: Step 1: its barrier, 90 kJ/mol, is larger: Right: compares the two activation energies.
  • Step 2: its transition state comes later in the reaction: Position along the reaction coordinate does not decide which step is slower.
  • Step 2: its barrier ends nearest to the products: Where a step ends says nothing about its barrier.
  • Step 1: being first, it is the slowest by rule: The first step is not slowest by rule; here it is slowest because of its barrier.

4. What rate law does this profile predict for the overall reaction A + B → D?

  1. rate = k[A][B]
  2. rate = k[C]
  3. rate = k[A][B][C]
  4. rate = k[D]
Show the answer

Step 1 (A + B → C) is the slow step and comes first, so its rate law is the overall rate law: rate = k[A][B].

  • Correct: rate = k[A][B]: Right: from the slow first step.
  • rate = k[C]: That is the rate law of the fast step, and C is an intermediate.
  • rate = k[A][B][C]: C is an intermediate and does not belong in the rate law.
  • rate = k[D]: D is a product.

5. On a multistep energy profile, what does each peak represent?

  1. The transition state of one elementary step
  2. An intermediate that can be isolated
  3. The products of the overall reaction
  4. A point where no bonds are changing
Show the answer

Each elementary step has its own barrier, so each peak is that step's transition state.

  • Correct: The transition state of one elementary step: Right: one peak per step.
  • An intermediate that can be isolated: Intermediates are in the valleys, not at the peaks.
  • The products of the overall reaction: The products are the final plateau.
  • A point where no bonds are changing: At a peak, bonds are partly broken and partly formed.

6. A three-step reaction profile is drawn. How many valleys lie between the reactant and product plateaus?

  1. 1
  2. 2
  3. 3
  4. 4
Show the answer

There is one valley between each pair of neighboring peaks: three peaks give two valleys, one for each intermediate.

  • 1: One valley would mean two steps.
  • Correct: 2: Right: two intermediates.
  • 3: Three is the number of peaks.
  • 4: Four would mean five steps.

Part 9 · Summary

Summary

A multistep energy profile has one peak, a transition state, for each elementary step, with intermediates in the valleys between them. Each step's activation energy is measured from its own starting level, and the step with the largest barrier is the rate-determining step. The overall energy change is products minus reactants.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections