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Introductory Chemistry - 1st Canadian Edition: Reaction Rates

Introductory Chemistry - 1st Canadian Edition
Reaction Rates
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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 Rates

Jessie A. Key

Learning Objectives

  • To gain an understanding of relative reaction rates.
  • To gain an understanding of instantaneous reaction rates and initial reaction rates.

We encounter rates or speeds often in daily life; for example, the rate at which this textbook was typed could be measured in words per minute. This rate is a measure of the change in words typed in the time period of a minute. Similarly, the rate of a chemical reaction is also a measure of change that occurs in a given time period:

\text{Rate of reaction}=\dfrac{\text{Change in Concentration}}{\text{Change in Time}}

For a chemical reaction, we can measure the change in concentration in terms of either the disappearance of starting material or the appearance of the product. For the hypothetical reaction: A + B → C, we can express the average rate of reaction as follows:

\text{Rate of reaction}=-\dfrac{\Delta \ [A]}{\Delta \ t}= -\dfrac{\Delta \ [B]}{\Delta \ t}=  \dfrac{\Delta \ [C]}{\Delta \ t}

Notice that a negative sign is included when expressing reaction rates with respect to the disappearance of starting materials. Reaction rates are always positive, so the decrease in concentration must be corrected for.

When the stoichiometric relationships in the balanced equation are not 1:1, the coefficient for each species must also be corrected for. In the hypothetical reaction 2A + B → 3C, two molecules of A are consumed for every one molecule of B, this means A is consumed twice as fast. To correct for this and express the average rate of reaction for each species, we must divide each by its coefficient in the balanced equation:

\text{Rate of reaction}=-\dfrac{1}{2}\dfrac{\Delta \ [A]}{\Delta \ t}= -\dfrac{\Delta \ [B]}{\Delta \ t}=\dfrac{1}{3}\dfrac{\Delta \ [C]}{\Delta \ t}

Example 17.1

The decomposition of dinitrogen pentoxide 2N2O5(g) → 4NO2(g) + O2(g) was performed in the lab and the rate of formation of NO2 was found to be 0.53 M/s.

  1. What was the rate of formation of O2(g)?
  2. What was the rate of consumption N2O5(g)?

Solution

  1. First determine the rate relationship between NO2(g) and O2(g) using the coefficients of the balanced equation:

    \text{Rate of reaction}=\dfrac{1}{4}\dfrac{\Delta \ [\ce{NO2}]}{\Delta \ t}=\dfrac{\Delta \ [\ce{O2}]}{\Delta \ t}

    Next substitute in the given values and solve for the rate of formation of O2(g):

    Rate of formation of O2(g) = (¼) (0.53 M/s) = 0.13 M/s

  2. First determine the rate relationship between NO2(g) and N2O5(g) using the coefficients of the balanced equation:

    \text{Rate of reaction}=\dfrac{1}{4} \dfrac{\Delta \ [\ce{NO2}]}{\Delta \ t}= -\dfrac{1}{2} \dfrac{\Delta \ [\ce{N2O5}]}{\Delta \ t}

    Next substitute the given values and solve for the rate of consumption of N2O5(g):

    −(½) rate of consumption of N2O5(g) = −(¼) rate of formation NO2(g)

    Rate of consumption of N2O5(g) = −½(0.53 M/s) = 0.27 M/s

Instantaneous Rate

For most chemical reactions, the rate of the reaction tends to decrease as time passes (Figure 17.6 “Reactant Concentration vs. Time”). As the reaction proceeds, more and more of the reactant molecules are consumed to become product, which lowers the concentration of reactant molecules. The reduction in reactant concentration results in fewer effective collisions.

The decrease in reaction rate over time means that average reaction rates do not accurately represent the actual rate of reaction at all time points. Instantaneous reaction rates, the rate of reaction at one instant in time, can be determined from the slope of the tangent at that point in the plot of concentration vs. time. The instantaneous rate at the start of the reaction, t = 0, is of particular interest in kinetics and is known as the initial rate of the reaction.

A plot of reactant concentration vs. time for a hypothetical reaction.
Figure 17.6 “Reactant Concentration vs. Time.” A plot of reactant concentration vs. time for a hypothetical reaction.

Example 17.2

Use Figure 17.6 to determine the instantaneous rate at 3 h.

Solution

The slope of the tangent at 3 h can be determined by drawing a triangle such as the one shown in Figure 17.6, and comparing the ratio of the height of the rise to the run of the length.

\text{Slope}=\dfrac{\text{Rise}}{\text{Run}}= -\dfrac{\Delta \ [\text{Reactant}]}{\Delta \ t}=-\dfrac{4.5-6.5\text{ M}}{4-2\text{ h}}=-\dfrac{-2\text{ M}}{2\text{ h}}=1\dfrac{\text{M}}{\text{h}}

Key Takeaways

  • Reaction rates can be measured by the disappearance of starting material or the appearance of the product over time.
  • Instantaneous reaction rates can be determined from the slope of the tangent at that point in the plot of concentration vs. time.
  • The initial reaction rate is the instantaneous rate at the start of the reaction (at t = 0).

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Reaction Rates 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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