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Introductory Chemistry - 1st Canadian Edition: Measuring Entropy and Entropy Changes

Introductory Chemistry - 1st Canadian Edition
Measuring Entropy and Entropy Changes
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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

Measuring Entropy and Entropy Changes

Jessie A. Key

Learning Objectives

  • To gain an understanding of methods of measuring entropy and entropy change.

As the temperature of a sample decreases, its kinetic energy decreases and, correspondingly, the number of microstates possible decreases. The third law of thermodynamics states: at absolute zero (0 K), the entropy of a pure, perfect crystal is zero. In other words, at absolute zero, there is only one microstate and according to Boltzmann’s equation:

S=k \ln W = k\ln 1=0

Using this as a reference point, the entropy of a substance can be obtained by measuring the heat required to raise the temperature a given amount, using a reversible process. Reversible heating requires very slow and very small increases in heat.

\Delta S=\dfrac{q_{\text{rev}}}{T}

Example 18.1

Determine the change in entropy (in J/K) of water when 425 kJ of heat is applied to it at 50°C. Assume the change is reversible and the temperature remains constant.

Solution

\Delta\text{S}=\dfrac{q_{\text{rev}}}{T}=\dfrac{425\text{ kJ}}{323.15\text{ K}}=\dfrac{4.25\times10^5\text{ J}}{323.15\text{ K}}=1.32\times 10^5\text{ J/K}

Standard Molar Entropy, S°

The standard molar entropy, S°, is the entropy of 1 mole of a substance in its standard state, at 1 atm of pressure. These values have been tabulated, and selected substances are listed in Table 18.1a to c “Standard Molar Entropies of Selected Substances at 298 K”.[1]

Table 18.1a Standard Molar Entropies of Selected Gases at 298 K
GasS°[J/(mol·K)]
He126.2
H2130.7
Ne146.3
Ar154.8
Kr164.1
Xe169.7
H2O188.8
N2191.6
O2205.2
CO2213.8
I2260.7
Table 18.1b Standard Molar Entropies of Selected Liquids at 298 K
LiquidS°[J/(mol·K)]
H2O70.0
CH3OH126.8
Br2152.2
CH3CH2OH160.7
C6H6173.4
CH3COCl200.8
C6H12 (cyclohexane)204.4
C8H16 (isooctane)329.3
Table 18.1c Standard Molar Entropies of Selected Solids at 298 K
SolidS°[J/(mol·K)]
C (diamond)2.4
C (graphite)5.7
LiF35.7
SiO2 (quartz)41.5
Ca41.6
Na51.3
MgF257.2
K64.7
NaCl72.1
KCl82.6
I2116.1

Several trends emerge from standard molar entropy data:

  • Larger, more complex molecules have higher standard molar enthalpy values than smaller or simpler molecules. There are more possible arrangements of atoms in space for larger, more complex molecules, increasing the number of possible microstates.
  • Gases tend to have much larger standard molar enthalpies than liquids, and liquids tend to have larger values than solids, when comparing the same or similar substances.
  • The standard molar entropy of any substance increases as the temperature increases. This can be seen in Figure 18.3 “Entropy vs. Temperature of a Single Substance.” Large jumps in entropy occur at the phase changes: solid to liquid and liquid to gas. These large increases occur due to sudden increased molecular mobility and larger available volumes associated with the phase changes.
Generalized plot of entropy versus temperature of a single substance.
Figure 18.3 “Entropy vs. Temperature of a Single Substance.” This is a generalized plot of entropy versus temperature for a single substance. (Source: UC Davis ChemWiki by University of California\CC-BY-SA-3.0)

Standard Entropy Change of a Reaction, ΔS°

The entropy change of a reaction where the reactants and products are in their standard state can be determined using the following equation:

\Delta S^{\circ}=\underset{\text{products}}{\sum nS^{\circ}}-\underset{\text{reactants}}{\sum mS^{\circ}}

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

Example 18.2

Determine the change in the standard entropy, ΔS°, for the synthesis of carbon dioxide from graphite and oxygen:

C(s) + O2(g) → CO2(g)

Solution

    \begin{align*} \Delta S^{\circ}&=\underset{\text{products}}{\sum nS^{\circ}}-\underset{\text{reactants}}{\sum mS^{\circ}} \\ &=(213.8\text{ J/mol K})-(205.2\text{ J/mol K}+ 5.7\text{ J/mol K}) \\ &=+2.9\text{ J/mol K} \end{align*}

Entropy Changes in the Surroundings

The second law of thermodynamics states that a spontaneous reaction will result in an increase of entropy in the universe. The universe comprises both the system being examined and its surroundings.

\Delta S_{\text{universe}}=\Delta S_{\text{sys}}+\Delta S_{\text{surr}}

Standard entropy change can also be calculated by the following:

\Delta S^{\circ}{}_{\text{universe}}=\Delta S^{\circ}{}_{\text{sys}}+\Delta S^{\circ}{}_{\text{surr}}

The change in entropy of the surroundings is essentially just a measure of how much energy is being taken in or given off by the system. Under isothermal conditions, we can express the entropy change of the surroundings as:

\Delta\text{S}_\text{surr}=\dfrac{{-q}_{\text{sys}}}{T}\text{ or }\Delta\text{S}_\text{surr}=\dfrac{-\Delta H_{\text{sys}}}{T}\hspace{1em}\text{(at constant pressure)}

Example 18.3

For the previous example, the change in the standard entropy, ΔS°, for the synthesis of carbon dioxide from graphite and oxygen, use the previously calculated ΔS°sys and standard enthalpy of formation values to determine S°surr and ΔS°universe.

Solution

First we should solve for the ΔH°sys using the standard enthalpies of formation values:

    \begin{align*} \Delta H^{\circ}{}_{\text{sys}}&=\Delta H^{\circ}{}_{\text{f}}[\ce{CO2(g)}]-\Delta H^{\circ}{}_{\text{f}}[\ce{C(s)}+\ce{O2(g)}] \\ &=(-393.5\text{ kJ/mol})-(0\text{ kJ/mol}+0\text{ kJ/mol}) \\ &=-393.5\text{ kJ/mol} \end{align*}

Now we can convert this to the ΔS°surr:

\Delta S^{\circ}{}_{\text{surr}}=\dfrac{-\Delta H_{\text{sys}}}{T}=\dfrac{-393.5\text{ kJ/mol}}{298\text{ K}}=-1.32\text{ kJ/mol K}

Finally, solve for ΔS°universe:

    \begin{align*} \Delta S^{\circ}{}_{\text{universe}}&=\Delta S^{\circ}{}_{\text{sys}}+\Delta S^{\circ}{}_{\text{surr}} \\ &=(+2.9\text{ J/mol K})+(-1.32\times 10^3\text{ J/mol K}) \\ &=-1.3\times 10^3\text{ J/mol K} \end{align*}

Key Takeaways

  • At absolute zero (0 K), the entropy of a pure, perfect crystal is zero.
  • The entropy of a substance can be obtained by measuring the heat required to raise the temperature a given amount, using a reversible process.
  • The standard molar entropy, S°, is the entropy of 1 mole of a substance in its standard state, at 1 atm of pressure.

  1. These tables are based on a table from UC Davis ChemWiki by University of California\CC-BY-SA-3.0 ↵

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Measuring Entropy and Entropy Changes 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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