Starting with just a few basic principles of probability and the distribution of energy, Introduction to Molecular Thermodynamics takes students on an adventure into the inner workings of the molecular world like no other, from probability to Gibbs energy and beyond, following a logical step-by-step progression of ideas.
Preface
To the Instructor
To the Student: How to Study Thermodynamics
Acknowledgments
PART I: PROBABILITY, DISTRIBUTIONS, AND EQUILIBRIUM
1.1 Chemical Change
1.2 Chemical Equilibrium
1.3 Probability Is '(Ways of getting x) / (Ways total)'
1.4 AND Probability Multiplies
1.5 OR Probability Adds
1.6 AND and OR Probability Can Be Combined
1.7 The Probability of 'Not X' Is One Minus the Probability of 'X'
1.8 Probability Can Be Interpreted Two Ways
1.9 Distributions
1.10 For Large Populations, We Approximate
1.11 Relative Probability and Fluctuations
1.12 Equilibrium and the Most Probable Distribution
1.13 Equilibrium Constants Describe the Most Probable Distribution
1.14 Le Chˆatelier's Principle Is Based on Probability
1.15 Determining Equilibrium Amounts and Constants Based on Probability
1.16 Summary
PART II: THE DISTRIBUTION OF ENERGY
2.1 Real Chemical Reactions
2.2 Temperature and Heat Energy
2.3 The Quantized Nature of Energy
2.4 Distributions of Energy Quanta in Small Systems
2.5 Calculating W Using Combinations
2.6 Why Equations 2.1 and 2.2 Work
2.7 Determining the Probability of a Particular Distribution of Energy
2.8 The Most Probable Distribution Is the Boltzmann Distribution
2.9 The Effect of Temperature
2.10 The Effect of Energy Level Separation
2.11 Why Is the Boltzmann Distribution the Most Probable?
2.12 Determining the Population of the Lowest Level
2.13 Estimating the Fraction of Particles That Will React
2.14 Estimating How Many Levels Are Populated
2.15 Summary
PART III: ENERGY LEVELS IN REAL CHEMICAL SYSTEMS
3.1 Historical Perspective
3.2 The Modern Viewpoint
3.3 Planck, Einstein, and de Broglie
3.4 The 'Wave' Can Be Thought of in Terms of Probability
3.5 Electronic Energy
3.6 Vibrational Energy
3.7 Rotational Energy
3.8 Translational Energy
3.9 Putting It All Together
3.10 Chemical Reactions
3.11 Chemical Equilibrium and Energy Levels
3.12 Color, Fluorescence, and Phosphorescence
3.13 Lasers and Stimulated Emission
3.14 Summary
PART IV: INTERNAL ENERGY (U) AND THE FIRST LAW
4.1 The Internal Energy (U)
4.2 Internal Energy (U) Is a State Function
4.3 Microscopic Heat (q) and Work (w)
4.4 'Heating' vs. 'Adding Heat'
4.5 The First Law of Thermodynamics: U = q + w
4.6 Macroscopic Heat and Heat Capacity: q = CT
4.7 Macroscopic Work: w =−PV
4.8 In Chemical Reactions, Work Can Be Ignored
4.9 Calorimeters Allow the Direct Determination of U
4.10 Don't Forget the Surroundings!
4.11 Engines: Converting Heat into Work
4.12 Biological and Other Forms of Work
4.13 Summary
PART V: BONDING AND INTERNAL ENERGY
5.1 The Chemical Bond
5.2 Hess's Law
5.3 The Reference Point for Changes in Internal Energy Is 'Isolated Atoms'
5.4 Two Corollaries of Hess's Law
5.5 Mean Bond Dissociation Energies and Internal Energy
5.6 Estimating rU for Chemical Reactions Using Bond Dissociation Energies
5.7 Using Bond Dissociation Energies to Understand Chemical Reactions
5.8 The 'High-Energy Phosphate Bond' and Other Anomalies
5.9 Computational Chemistry and the Modern View of Bonding
5.10 Beyond Covalent Bonding
5.11 Summary
PART VI: THE EFFECT OF TEMPERATURE ON EQUILIBRIUM
6.1 Chemical Reactions as Single Systems: Isomerizations
6.2 The Temperature Effect on Isomerizations
6.3 K vs. T for Evenly Spaced Systems
6.4 Experimental Data Can Reveal Energy Level Information
6.5 Application to Real Chemical Reactions
6.6 The Solid/Liquid Problem
6.7 Summary
PART VII: ENTROPY (S) AND THE SECOND LAW
7.1 Energy Does Not Rule
7.2 The Definition of Entropy: S = k ln W
7.3 Changes in Entropy: S = k ln(W2/W1)
7.4 The Second Law of Thermodynamics: Suniverse > 0
7.5 Heat and Entropy Changes in the Surroundings: Ssur = qsur/T
7.6 Measuring Entropy Changes
7.7 Standard Molar Entropy: S◦
7.8 Entropy Comparisons Are Informative
7.9 The Effect of Ground State Electronic Degeneracy on Molar
7.10 Determining the Standard Change in Entropy for a Chemical Reaction
7.11 Another Way to Look at S
7.12 Summary
PART VIII: THE EFFECT OF PRESSURE AND CONCENTRATION ON ENTROPY
8.1 Introduction
8.2 Impossible? or Just Improbable?
8.3 Ideal Gases and Ideal Solutions
8.4 The Volume Effect on Entropy: S = nR ln(V2/V1)
8.5 The Entropy of Mixing Is Just the Entropy of Expansion
8.6 The Pressure Effect for Ideal Gases: S =−nR ln(P2/P1)
8.7 Concentration Effect for Solutions: S =−nR ln([X]2/[X]1)
8.8 Adjustment to the Standard State: Sx = S◦x − R ln Px and Sx = S◦x − R ln[X]
8.9 The Reaction Quotient: rS = rS◦ − R ln Q
8.10 Solids and Liquids Do Not Appear in the Reaction Quotient
8.11 The Evaporation of Liquid Water
8.12 A Microscopic Picture of Pressure Effects on Entropy
8.13 Summary
PART IX: ENTHALPY (H) AND THE SURROUNDINGS
9.1 Heat Is Not a State Function
9.2 The Definition of Enthalpy: H = U + PV
9.3 Standard Enthalpies of Formation, fH◦
9.4 Using Hess's Law and fH◦ to Get rH◦ for a Reaction
9.5 Enthalpy vs. Internal Energy
9.6 High Temperature Breaks Bonds
9.7 Summary
PART X: GIBBS ENERGY (G)
10.1 The Second Law Again, with a Twist
10.2 The Definition of Gibbs Energy: G = H − T S
10.3 Plotting G vs. T (G–T Graphs)
10.4 Comparing Two or More Substances Using G–T Graphs
10.5 Equilibrium Is Where rG = 0
10.6 The 'Low Enthalpy/High Entropy Rule'
10.7 A Quantitative Look at Melting Points: 0 = fusH − TmpfusS
10.8 The Gibbs Energy of a Gas Depends upon Its Pressure
10.9 Vapor Pressure, Barometric Pressure, and Boiling
10.10 Summary
PART XI: THE EQUILIBRIUM CONSTANT (K )
11.1 Introduction
11.2 The Equilibrium Constant
11.3 Determining the Values of rH◦ and rS◦ Experimentally
11.4 The Effect of Temperature on Keq
11.5 A Qualitative Picture of the Approach to Equilibrium
11.6 Le Chˆatelier's Principle Revisited
11.7 Determining Equilibrium Pressures and Concentrations
11.8 Equilibration at Constant Pressure (optional)
11.9 Standard Reaction Gibbs Energies, rG◦T
11.10 The Potential for Change in Entropy of the Universe isR ln K/Q
11.11 Beyond Ideality: 'Activity'
11.12 Summary
PART XII: APPLICATIONS OF GIBBS ENERGY: PHASE CHANGES
12.1 Review
12.2 Evaporation and Boiling
12.3 Sublimation and Vapor Deposition
12.4 Triple Points
12.5 Critical Points and Phase Diagrams
12.6 Solubility: 0 = rH◦ − T (rS◦ − R ln[X]sat)
12.7 Impure Liquids: S = S◦ − R ln x
12.8 Summary
PART XIII: APPLICATIONS OF GIBBS ENERGY: ELECTROCHEMISTRY
13.1 Introduction
13.2 Review: Gibbs Energy and Entropy
13.3 Including Internal Energy and ElectricalWork in the Big Picture
13.4 Electrical Work Is Limited by the Gibbs Energy
13.5 The Gibbs Energy Change Can Be Positive
13.6 The Electrical Connection: −G = Qelec × Ecell = I × t × Ecell
13.7 The Chemical Connection: Qrxn = n × F
13.8 Gibbs Energy and Cell Potential: rG=−nFEcell
13.9 Standard State for Cell Potential: E◦cell,T
13.10 Using Standard Reduction Potentials to Predict Reactivity
13.11 Equilibrium Constants from Cell Potentials: 0=−nFE◦cell,T + RT ln K
13.12 Actual Cell Voltages and the Nernst Equation: −nFEcell =−nFE◦cell,T + RT ln Q
13.13 Detailed Examples
13.14 Summary
APPENDIX A Symbols and Constants
APPENDIX B Mathematical Tricks
APPENDIX C Table of Standard Reduction Potentials
APPENDIX D Table of Standard Thermodynamic Data (25°C and 1 bar)
APPENDIX E Thermodynamic Data for the Evaporation of Liquid Water
Answers to Selected Exercises
Index
ROBERT HANSON is a Professor of Chemistry at St. Olaf College, in Northfield, Minnesota, USA, where he has been teaching since 1986. Trained as an organic chemist with Gilbert Stork at Columbia University, USA, he shares a patent with 2001 Nobel Prize winner K.Barry Sharpless for the asymmetric epoxidation of allylic alcohols. His interest in thermodynamics goes back to early training at the California Institute of Technology, from which he got a B.S. degree in 1979.
SUSAN GREEN has had the privilege of being both a student and a professor at St. Olaf College in Northfield, Minnesota, USA, where she was first introduced to the idea of teaching thermodynamics to first-year students. She trained as a physical chemist at the University of Minnesota, USA, studying the vibrational and electronic structure of small metal oxides as well as trying her hand at analytical chemistry.
Description
Starting with just a few basic principles of probability and the distribution of energy, Introduction to Molecular Thermodynamics takes students on an adventure into the inner workings of the molecular world like no other, from probability to Gibbs energy and beyond, following a logical step-by-step progression of ideas.
Contents
Preface
To the Instructor
To the Student: How to Study Thermodynamics
Acknowledgments
PART I: PROBABILITY, DISTRIBUTIONS, AND EQUILIBRIUM
1.1 Chemical Change
1.2 Chemical Equilibrium
1.3 Probability Is '(Ways of getting x) / (Ways total)'
1.4 AND Probability Multiplies
1.5 OR Probability Adds
1.6 AND and OR Probability Can Be Combined
1.7 The Probability of 'Not X' Is One Minus the Probability of 'X'
1.8 Probability Can Be Interpreted Two Ways
1.9 Distributions
1.10 For Large Populations, We Approximate
1.11 Relative Probability and Fluctuations
1.12 Equilibrium and the Most Probable Distribution
1.13 Equilibrium Constants Describe the Most Probable Distribution
1.14 Le Chˆatelier's Principle Is Based on Probability
1.15 Determining Equilibrium Amounts and Constants Based on Probability
1.16 Summary
PART II: THE DISTRIBUTION OF ENERGY
2.1 Real Chemical Reactions
2.2 Temperature and Heat Energy
2.3 The Quantized Nature of Energy
2.4 Distributions of Energy Quanta in Small Systems
2.5 Calculating W Using Combinations
2.6 Why Equations 2.1 and 2.2 Work
2.7 Determining the Probability of a Particular Distribution of Energy
2.8 The Most Probable Distribution Is the Boltzmann Distribution
2.9 The Effect of Temperature
2.10 The Effect of Energy Level Separation
2.11 Why Is the Boltzmann Distribution the Most Probable?
2.12 Determining the Population of the Lowest Level
2.13 Estimating the Fraction of Particles That Will React
2.14 Estimating How Many Levels Are Populated
2.15 Summary
PART III: ENERGY LEVELS IN REAL CHEMICAL SYSTEMS
3.1 Historical Perspective
3.2 The Modern Viewpoint
3.3 Planck, Einstein, and de Broglie
3.4 The 'Wave' Can Be Thought of in Terms of Probability
3.5 Electronic Energy
3.6 Vibrational Energy
3.7 Rotational Energy
3.8 Translational Energy
3.9 Putting It All Together
3.10 Chemical Reactions
3.11 Chemical Equilibrium and Energy Levels
3.12 Color, Fluorescence, and Phosphorescence
3.13 Lasers and Stimulated Emission
3.14 Summary
PART IV: INTERNAL ENERGY (U) AND THE FIRST LAW
4.1 The Internal Energy (U)
4.2 Internal Energy (U) Is a State Function
4.3 Microscopic Heat (q) and Work (w)
4.4 'Heating' vs. 'Adding Heat'
4.5 The First Law of Thermodynamics: U = q + w
4.6 Macroscopic Heat and Heat Capacity: q = CT
4.7 Macroscopic Work: w =−PV
4.8 In Chemical Reactions, Work Can Be Ignored
4.9 Calorimeters Allow the Direct Determination of U
4.10 Don't Forget the Surroundings!
4.11 Engines: Converting Heat into Work
4.12 Biological and Other Forms of Work
4.13 Summary
PART V: BONDING AND INTERNAL ENERGY
5.1 The Chemical Bond
5.2 Hess's Law
5.3 The Reference Point for Changes in Internal Energy Is 'Isolated Atoms'
5.4 Two Corollaries of Hess's Law
5.5 Mean Bond Dissociation Energies and Internal Energy
5.6 Estimating rU for Chemical Reactions Using Bond Dissociation Energies
5.7 Using Bond Dissociation Energies to Understand Chemical Reactions
5.8 The 'High-Energy Phosphate Bond' and Other Anomalies
5.9 Computational Chemistry and the Modern View of Bonding
5.10 Beyond Covalent Bonding
5.11 Summary
PART VI: THE EFFECT OF TEMPERATURE ON EQUILIBRIUM
6.1 Chemical Reactions as Single Systems: Isomerizations
6.2 The Temperature Effect on Isomerizations
6.3 K vs. T for Evenly Spaced Systems
6.4 Experimental Data Can Reveal Energy Level Information
6.5 Application to Real Chemical Reactions
6.6 The Solid/Liquid Problem
6.7 Summary
PART VII: ENTROPY (S) AND THE SECOND LAW
7.1 Energy Does Not Rule
7.2 The Definition of Entropy: S = k ln W
7.3 Changes in Entropy: S = k ln(W2/W1)
7.4 The Second Law of Thermodynamics: Suniverse > 0
7.5 Heat and Entropy Changes in the Surroundings: Ssur = qsur/T
7.6 Measuring Entropy Changes
7.7 Standard Molar Entropy: S◦
7.8 Entropy Comparisons Are Informative
7.9 The Effect of Ground State Electronic Degeneracy on Molar
7.10 Determining the Standard Change in Entropy for a Chemical Reaction
7.11 Another Way to Look at S
7.12 Summary
PART VIII: THE EFFECT OF PRESSURE AND CONCENTRATION ON ENTROPY
8.1 Introduction
8.2 Impossible? or Just Improbable?
8.3 Ideal Gases and Ideal Solutions
8.4 The Volume Effect on Entropy: S = nR ln(V2/V1)
8.5 The Entropy of Mixing Is Just the Entropy of Expansion
8.6 The Pressure Effect for Ideal Gases: S =−nR ln(P2/P1)
8.7 Concentration Effect for Solutions: S =−nR ln([X]2/[X]1)
8.8 Adjustment to the Standard State: Sx = S◦x − R ln Px and Sx = S◦x − R ln[X]
8.9 The Reaction Quotient: rS = rS◦ − R ln Q
8.10 Solids and Liquids Do Not Appear in the Reaction Quotient
8.11 The Evaporation of Liquid Water
8.12 A Microscopic Picture of Pressure Effects on Entropy
8.13 Summary
PART IX: ENTHALPY (H) AND THE SURROUNDINGS
9.1 Heat Is Not a State Function
9.2 The Definition of Enthalpy: H = U + PV
9.3 Standard Enthalpies of Formation, fH◦
9.4 Using Hess's Law and fH◦ to Get rH◦ for a Reaction
9.5 Enthalpy vs. Internal Energy
9.6 High Temperature Breaks Bonds
9.7 Summary
PART X: GIBBS ENERGY (G)
10.1 The Second Law Again, with a Twist
10.2 The Definition of Gibbs Energy: G = H − T S
10.3 Plotting G vs. T (G–T Graphs)
10.4 Comparing Two or More Substances Using G–T Graphs
10.5 Equilibrium Is Where rG = 0
10.6 The 'Low Enthalpy/High Entropy Rule'
10.7 A Quantitative Look at Melting Points: 0 = fusH − TmpfusS
10.8 The Gibbs Energy of a Gas Depends upon Its Pressure
10.9 Vapor Pressure, Barometric Pressure, and Boiling
10.10 Summary
PART XI: THE EQUILIBRIUM CONSTANT (K )
11.1 Introduction
11.2 The Equilibrium Constant
11.3 Determining the Values of rH◦ and rS◦ Experimentally
11.4 The Effect of Temperature on Keq
11.5 A Qualitative Picture of the Approach to Equilibrium
11.6 Le Chˆatelier's Principle Revisited
11.7 Determining Equilibrium Pressures and Concentrations
11.8 Equilibration at Constant Pressure (optional)
11.9 Standard Reaction Gibbs Energies, rG◦T
11.10 The Potential for Change in Entropy of the Universe isR ln K/Q
11.11 Beyond Ideality: 'Activity'
11.12 Summary
PART XII: APPLICATIONS OF GIBBS ENERGY: PHASE CHANGES
12.1 Review
12.2 Evaporation and Boiling
12.3 Sublimation and Vapor Deposition
12.4 Triple Points
12.5 Critical Points and Phase Diagrams
12.6 Solubility: 0 = rH◦ − T (rS◦ − R ln[X]sat)
12.7 Impure Liquids: S = S◦ − R ln x
12.8 Summary
PART XIII: APPLICATIONS OF GIBBS ENERGY: ELECTROCHEMISTRY
13.1 Introduction
13.2 Review: Gibbs Energy and Entropy
13.3 Including Internal Energy and ElectricalWork in the Big Picture
13.4 Electrical Work Is Limited by the Gibbs Energy
13.5 The Gibbs Energy Change Can Be Positive
13.6 The Electrical Connection: −G = Qelec × Ecell = I × t × Ecell
13.7 The Chemical Connection: Qrxn = n × F
13.8 Gibbs Energy and Cell Potential: rG=−nFEcell
13.9 Standard State for Cell Potential: E◦cell,T
13.10 Using Standard Reduction Potentials to Predict Reactivity
13.11 Equilibrium Constants from Cell Potentials: 0=−nFE◦cell,T + RT ln K
13.12 Actual Cell Voltages and the Nernst Equation: −nFEcell =−nFE◦cell,T + RT ln Q
13.13 Detailed Examples
13.14 Summary
APPENDIX A Symbols and Constants
APPENDIX B Mathematical Tricks
APPENDIX C Table of Standard Reduction Potentials
APPENDIX D Table of Standard Thermodynamic Data (25°C and 1 bar)
APPENDIX E Thermodynamic Data for the Evaporation of Liquid Water
Answers to Selected Exercises
Index
Authors
ROBERT HANSON is a Professor of Chemistry at St. Olaf College, in Northfield, Minnesota, USA, where he has been teaching since 1986. Trained as an organic chemist with Gilbert Stork at Columbia University, USA, he shares a patent with 2001 Nobel Prize winner K.Barry Sharpless for the asymmetric epoxidation of allylic alcohols. His interest in thermodynamics goes back to early training at the California Institute of Technology, from which he got a B.S. degree in 1979.
SUSAN GREEN has had the privilege of being both a student and a professor at St. Olaf College in Northfield, Minnesota, USA, where she was first introduced to the idea of teaching thermodynamics to first-year students. She trained as a physical chemist at the University of Minnesota, USA, studying the vibrational and electronic structure of small metal oxides as well as trying her hand at analytical chemistry.
|