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Introductory Chemistry - 1st Canadian Edition: Gibbs Free Energy

Introductory Chemistry - 1st Canadian Edition
Gibbs Free Energy
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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

Gibbs Free Energy

Jessie A. Key

Learning Objectives

  • To gain an understanding of Gibbs free energy.
  • To understand the relationship between the sign of Gibbs free energy change and the spontaneity of a process.
  • To be able to determine Gibbs free energy using standard free energies of formation.
Portrait of a middle-aged man with a white beard.
Figure 18.4 “J. Willard Gibbs.”

J. Willard Gibbs (1839–1903) proposed a single state function to determine spontaneity:

G=H-TS

where H is the enthalpy of the system, S is the entropy of the system, and G is Gibbs free energy.

The change in Gibbs free energy, ΔG, is the maximum amount of free energy available to do useful work. For an isothermal process, it can be expressed as:

\Delta G=\Delta H-T\Delta S

or at standard conditions:

\Delta G^{\circ}=\Delta H^{\circ}-T\Delta S^{\circ}

This single term, Gibbs free energy (G), allows us to avoid calculating the entropy of the surroundings. It is really just a simplification of our previous method of estimating spontaneity:

    \begin{align*} \Delta S_{\text{universe}}&=\Delta S_{\text{sys}}+\Delta S_{\text{surr}} \\ \\ \Delta S_{\text{universe}}&=\Delta S_{\text{sys}}+\dfrac{-\Delta H_{\text{sys}}}{T} \end{align*}

Multiply both sides of the equation by −T:

    \begin{align*} -T\left(\Delta S_{\text{universe}}\right)&=\left(\Delta S_{\text{sys}}+\dfrac{-\Delta H_{\text{sys}}}{T}\right)-T \\ \\ -T\Delta S_{\text{universe}}&=\Delta H_{\text{sys}}-T\Delta S_{\text{sys}} \end{align*}

Therefore, \Delta G=-T\Delta S_{\text{universe}}.

As a result of this relationship, the sign of Gibbs free energy provides information on the spontaneity of a given reaction:

    \begin{align*} \text{If }\Delta G>0,&\text{ the reaction is nonspontaneous in the direction written.} \\ \text{If }\Delta G=0,&\text{ the reaction is in a state of equilibrium.} \\ \text{If }\Delta G<0,&\text{ the reaction is spontaneous in the direction written.} \end{align*}

The significance of the sign of a change in Gibbs free energy parallels the relationship of terms from the equilibrium chapter: the reaction quotient, Q, and the equilibrium constant, K.

    \begin{align*} \text{If }Q>K,&\text{ the reaction is nonspontaneous in the direction written.}\\ \text{If }Q=K,&\text{ the reaction is in a state of equilibrium.}\\ \text{If }Q<K,&\text{ the reaction is spontaneous in the direction written.}\\ \end{align*}

Example 18.4

Calculate ΔG° for a reaction where ΔH° is equal to 36.2 kJ and ΔS° is equal to 123 J/K at 298 K. Is this a spontaneous reaction?

Solution

    \begin{align*} \Delta G^{\circ}&=\Delta H^{\circ}-T\Delta S^{\circ} \\ &=36.2\text{ kJ}-(298\text{ K}\times 123\text{ J/K}) \\ &=-0.4\text{ kJ} \end{align*}

Therefore the reaction is spontaneous because ΔG° is negative.

Determining ΔG° from Standard Free Energy of Formation

The standard Gibbs free energy change, ΔG°, for a reaction can be calculated from the standard free energies of formation, ΔG°f .

\Delta G^{\circ}{}_{\text{f}}=\underset{\text{products}}{\sum n\Delta G^{\circ}{}_{\text{f}}}-\underset{\text{reactants}}{\sum m\Delta G^{\circ}{}_{\text{f}}}

where n and m are the coefficients in the balanced chemical equation of the reaction.

Standard free energies of formation values are listed in the appendix, “Standard Thermodynamic Quantities for Chemical Substances at 25°C.”

Example 18.5

Calculate the standard free energy change for the following reaction, using standard free energies of formation:

5C(s) + 2SO2(g) → CS2(g) + 4CO(g)

Is this a spontaneous reaction?

Solution

    \begin{align*} \Delta G^{\circ}&=\underset{\text{products}}{\sum n\Delta G^{\circ}{}_{\text{f}}}-\underset{\text{reactants}}{\sum m\Delta G^{\circ}{}_{\text{f}}} \\ &=[(4\times -137.2\text{ kJ/mol})+(67.1\text{ kJ/mol})] \\ &\phantom{=}-[(5\times 0\text{ kJ/mol})+(2\times -300.1\text{ kJ/mol})] \\ &=(-481.7\text{ kJ/mol})-(-600.2\text{ kJ/mol}) \\ &=118.5\text{ kJ/mol} \\ \end{align*}

ΔG° has a positive value, so this is not a spontaneous process.

Key Takeaways

  • The change in Gibbs free energy (ΔG) is the maximum amount of free energy available to do useful work.
  • If ΔG > 0, the reaction is nonspontaneous in the direction written. If ΔG = 0, the reaction is in a state of equilibrium. If ΔG < 0, the reaction is spontaneous in the direction written.
  • The standard Gibbs free energy change, ΔG°, for a reaction can be calculated from the standard free energies of formation, ΔG°f.

Media Attributions

  • “J. W. Gibbs” © unknown is licensed under a Public Domain license

Icon for the Creative Commons Attribution 4.0 International License

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

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Spontaneity: Free Energy and Temperature
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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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