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Introductory Chemistry - 1st Canadian Edition: Reaction Mechanisms

Introductory Chemistry - 1st Canadian Edition
Reaction Mechanisms
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table of contents
  1. Cover
  2. Title Page
  3. Copyright
  4. Table Of Contents
  5. Acknowledgments
  6. Dedication
  7. About BCcampus Open Education
  8. Chapter 1. What is Chemistry
    1. Some Basic Definitions
    2. Chemistry as a Science
  9. Chapter 2. Measurements
    1. Expressing Numbers
    2. Significant Figures
    3. Converting Units
    4. Other Units: Temperature and Density
    5. Expressing Units
    6. End-of-Chapter Material
  10. Chapter 3. Atoms, Molecules, and Ions
    1. Acids
    2. Ions and Ionic Compounds
    3. Masses of Atoms and Molecules
    4. Molecules and Chemical Nomenclature
    5. Atomic Theory
    6. End-of-Chapter Material
  11. Chapter 4. Chemical Reactions and Equations
    1. The Chemical Equation
    2. Types of Chemical Reactions: Single- and Double-Displacement Reactions
    3. Ionic Equations: A Closer Look
    4. Composition, Decomposition, and Combustion Reactions
    5. Oxidation-Reduction Reactions
    6. Neutralization Reactions
    7. End-of-Chapter Material
  12. Chapter 5. Stoichiometry and the Mole
    1. Stoichiometry
    2. The Mole
    3. Mole-Mass and Mass-Mass Calculations
    4. Limiting Reagents
    5. The Mole in Chemical Reactions
    6. Yields
    7. End-of-Chapter Material
  13. Chapter 6. Gases
    1. Pressure
    2. Gas Laws
    3. Other Gas Laws
    4. The Ideal Gas Law and Some Applications
    5. Gas Mixtures
    6. Kinetic Molecular Theory of Gases
    7. Molecular Effusion and Diffusion
    8. Real Gases
    9. End-of-Chapter Material
  14. Chapter 7. Energy and Chemistry
    1. Formation Reactions
    2. Energy
    3. Stoichiometry Calculations Using Enthalpy
    4. Enthalpy and Chemical Reactions
    5. Work and Heat
    6. Hess’s Law
    7. End-of-Chapter Material
  15. Chapter 8. Electronic Structure
    1. Light
    2. Quantum Numbers for Electrons
    3. Organization of Electrons in Atoms
    4. Electronic Structure and the Periodic Table
    5. Periodic Trends
    6. End-of-Chapter Material
  16. Chapter 9. Chemical Bonds
    1. Lewis Electron Dot Diagrams
    2. Electron Transfer: Ionic Bonds
    3. Covalent Bonds
    4. Other Aspects of Covalent Bonds
    5. Violations of the Octet Rule
    6. Molecular Shapes and Polarity
    7. Valence Bond Theory and Hybrid Orbitals
    8. Molecular Orbitals
    9. End-of-Chapter Material
  17. Chapter 10. Solids and Liquids
    1. Properties of Liquids
    2. Solids
    3. Phase Transitions: Melting, Boiling, and Subliming
    4. Intermolecular Forces
    5. End-of-Chapter Material
  18. Chapter 11. Solutions
    1. Colligative Properties of Solutions
    2. Concentrations as Conversion Factors
    3. Quantitative Units of Concentration
    4. Colligative Properties of Ionic Solutes
    5. Some Definitions
    6. Dilutions and Concentrations
    7. End-of-Chapter Material
  19. Chapter 12. Acids and Bases
    1. Acid-Base Titrations
    2. Strong and Weak Acids and Bases and Their Salts
    3. Brønsted-Lowry Acids and Bases
    4. Arrhenius Acids and Bases
    5. Autoionization of Water
    6. Buffers
    7. The pH Scale
    8. End-of-Chapter Material
  20. Chapter 13. Chemical Equilibrium
    1. Chemical Equilibrium
    2. The Equilibrium Constant
    3. Shifting Equilibria: Le Chatelier’s Principle
    4. Calculating Equilibrium Constant Values
    5. Some Special Types of Equilibria
    6. End-of-Chapter Material
  21. Chapter 14. Oxidation and Reduction
    1. Oxidation-Reduction Reactions
    2. Balancing Redox Reactions
    3. Applications of Redox Reactions: Voltaic Cells
    4. Electrolysis
    5. End-of-Chapter Material
  22. Chapter 15. Nuclear Chemistry
    1. Units of Radioactivity
    2. Uses of Radioactive Isotopes
    3. Half-Life
    4. Radioactivity
    5. Nuclear Energy
    6. End-of-Chapter Material
  23. Chapter 16. Organic Chemistry
    1. Hydrocarbons
    2. Branched Hydrocarbons
    3. Alkyl Halides and Alcohols
    4. Other Oxygen-Containing Functional Groups
    5. Other Functional Groups
    6. Polymers
    7. End-of-Chapter Material
  24. Chapter 17. Kinetics
    1. Factors that Affect the Rate of Reactions
    2. Reaction Rates
    3. Rate Laws
    4. Concentration–Time Relationships: Integrated Rate Laws
    5. Activation Energy and the Arrhenius Equation
    6. Reaction Mechanisms
    7. Catalysis
    8. End-of-Chapter Material
  25. Chapter 18. Chemical Thermodynamics
    1. Spontaneous Change
    2. Entropy and the Second Law of Thermodynamics
    3. Measuring Entropy and Entropy Changes
    4. Gibbs Free Energy
    5. Spontaneity: Free Energy and Temperature
    6. Free Energy under Nonstandard Conditions
    7. End-of-Chapter Material
  26. Appendix A: Periodic Table of the Elements
  27. Appendix B: Selected Acid Dissociation Constants at 25°C
  28. Appendix C: Solubility Constants for Compounds at 25°C
  29. Appendix D: Standard Thermodynamic Quantities for Chemical Substances at 25°C
  30. Appendix E: Standard Reduction Potentials by Value
  31. Glossary
  32. About the Authors
  33. Versioning History

Reaction Mechanisms

Jessie A. Key

Learning Objectives

  • To gain an understanding of reaction mechanisms, including the concepts of elementary steps and molecularity.
  • To become familiar with reaction potential energy diagrams.
  • To gain an understanding of rate-determining steps in multi-step reactions.

For us to truly understand a chemical reaction, including its rate, it would be ideal to see the exact bond-making and bond-breaking steps that occur at the molecular level — the reaction mechanism. Unfortunately, we cannot watch reactions occurring at the molecular level, but we can infer these events using kinetics and other chemical methods.

Elementary Steps

Each event that occurs in a chemical reaction as a result of an effective collision is known as an elementary step. The total number of molecules that participate in the effective collision of an elementary step is known as its molecularity. Molecularity can be used to classify elementary steps into three categories:

  • Unimolecular: Only one molecule participates
  • Bimolecular: Two molecules participate
  • Termolecular: Three molecules participate

There are only three main categories of molecularity because it is rare that more than three molecules participate simultaneously in an effective collision.

Elementary Steps and Rate Laws

A complete chemical reaction may occur in one or more elementary steps, each having its own rate law. The rate of a single elementary step can be derived directly from its stoichiometric equation, since it is an individual effective collision describing a single bond-breaking or bond-forming event. This explains why the rate law of an overall reaction, potentially involving several steps, does not necessarily correlate to the stoichiometry of its balanced chemical equation. For example:

\ce{5Br-(aq)}+\ce{BrO3^-(aq)}+\ce{6H+(aq)}\rightarrow\ce{3Br2(\ell)}+\ce{3H2O(\ell)}

\text{Rate}=k[\ce{Br-}][\ce{BrO3-}][\ce{H+}]^2

However, the rate law for an elementary step is determined from its molecularity: the number of molecules involved in the single effective collision (Table 17.2 “Elementary Steps and Their Rate Laws”). For the following elementary step:

    \begin{align*} A&\rightarrow B \\ \text{Rate}&=k[A] \end{align*}

This is a unimolecular step, and as the concentration of reactant A molecules increases, the number of effective collisions also increases.

Table 17.2 Elementary Steps and Their Rate Laws
Elementary StepMolecularityRate Law
A → BUnimolecularRate = k[A]
2A → CBimolecularRate = k[A]2
2A + D → ETermolecularRate = k[A]2[D]

Multi-step Mechanisms

The overall reaction process often corresponds to a series of two or more elementary steps, which must always add up to give the overall balanced chemical equation. For example, in the following elimination reaction (a type of reaction typically discussed in introductory organic chemistry courses):

\ce{C4H9Br}+\ce{H2O}\rightarrow\ce{C4H8}+\ce{H3O+}+\ce{Br-}

This reaction process proceeds in two elementary steps and would therefore be called a two-step mechanism. In the first step, bromide leaves from the starting material to give the cation C4H9+. In the second step, C4H9+ reacts with water to generate the product C4H8 and H3O+.

    \begin{align*} \text{Step 1: }\ce{C4H9Br}&\leftrightarrow \ce{C4H9+}+\ce{Br-}\hspace{4em}\text{(slow)} \\ \text{Step 2: }\ce{C4H9+}+\ce{H2O}&\leftrightarrow \ce{C4H8}+\ce{H3O+} \\ \text{Net: }\ce{C4H9Br}+\ce{H2O}&\rightarrow\ce{C4H8}+\ce{H3O+}+\ce{Br-} \end{align*}

The cation C4H9+ is called an intermediate, since it does not appear in the overall balanced equation and is generated in one elementary step but used up in a subsequent step. A potential energy diagram for this multi-step reaction can be drawn as shown in Figure 17.12 “Multi-step Reaction Potential Energy Diagram.” Notice each step has its own activation energy, and transition state (or activated complex), which is the highest-energy transitional point in the elementary step. Transition states are very unstable (high energy) as bonds are in the process of breaking or forming, and therefore transition states cannot be isolated. Intermediates are more stable than transition states and can sometimes be isolated and characterized by certain techniques.

Multistep reaction potential energy diagram.
Figure 17.12 “Multi-step Reaction Potential Energy Diagram.” Multi-step reaction potential energy diagram showing the intermediate.

The Rate-Determining Step

For multi-step mechanisms, there is often one step that is significantly slower than the other steps. This slowest step is referred to as the rate-determining step, as it limits the rate of the entire reaction. An analogy that illustrates this concept is an hourglass having two different sized openings. The rate of the sand falling to the bottom-most chamber is determined by the smaller of the two openings (see Figure 17.13 “Rate-Determining Point in an Hourglass”). Similarly, the rate law of the overall reaction is determined from its rate-determining slowest step.

Double hourglass with one opening smaller than the other which determines rate.
Figure 17.13 “Rate-Determining Point in an Hourglass.” Double hourglass with one opening smaller than the other, which determines rate.

Example 17.9

The following reaction occurs in a two-step mechanism:

    \begin{align*} \text{A}\rightarrow \text{B}+\text{C} \hspace{2em}\text{ slow} \\ \text{A}+\text{C}\rightarrow \text{B}+\text{D}\hspace{2em}\text{ fast} \end{align*}

  1. Determine the overall reaction equation.
  2. Write the rate law for the overall reaction.

Solution

  1. Add the two elementary steps together and cancel out any intermediates to give the overall reaction:

    2A → 2B + D

  2. Rate = k[A]2

Key Takeaways

  • The overall reaction process often corresponds to a series of more than one elementary step, which must always add up to give the overall balanced chemical equation.
  • Each step has its own activation energy and transition state.
  • The slowest step of a multi-step reaction is the rate-determining step.

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Reaction Mechanisms by Jessie A. Key is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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Copyright © 2014

                                by Jessie A. Key

            Introductory Chemistry - 1st Canadian Edition by Jessie A. Key is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.
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