# Physical Chemistry: How Chemistry Works

# Physical Chemistry: How Chemistry Works

ISBN: 978-1-118-75112-1

Nov 2016

744 pages

## Description

Much of chemistry is motivated by asking 'How'? *How do I make a primary alcohol? React a Grignard reagent with formaldehyde*. Physical chemistry is motivated by asking 'Why'? *The Grignard reagent and formaldehyde follow a molecular dance known as a reaction mechanism in which stronger bonds are made at the expense of weaker bonds*. **If you are interested in asking 'why' and not just 'how', then you need to understand physical chemistry.**

*Physical Chemistry: How Chemistry Works* takes a fresh approach to teaching in physical chemistry. This modern textbook is designed to excite and engage undergraduate chemistry students and prepare them for how they will employ physical chemistry in real life. The student-friendly approach and practical, contemporary examples facilitate an understanding of the physical chemical aspects of any system, allowing students of inorganic chemistry, organic chemistry, analytical chemistry and biochemistry to be fluent in the essentials of physical chemistry in order to understand synthesis, intermolecular interactions and materials properties. For students who are deeply interested in the subject of physical chemistry, the textbook facilitates further study by connecting them to the frontiers of research.

- Provides students with the physical and mathematical machinery to understand the physical chemical aspects of any system.
- Integrates regular examples drawn from the literature, from contemporary issues and research, to engage students with relevant and illustrative details.
- Important topics are introduced and returned to in later chapters: key concepts are reinforced and discussed in more depth as students acquire more tools.
- Chapters begin with a preview of important concepts and conclude with a summary of important equations.
- Each chapter includes worked examples and exercises: discussion questions, simple equation manipulation questions, and problem-solving exercises.
- Accompanied by supplementary online material: worked examples for students and a solutions manual for instructors.
- Written by an experienced instructor, researcher and author in physical chemistry, with a voice and perspective that is pedagogical and engaging.

## Related Resources

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### Student

Preface xv

About the companion website xvii

**1 Introduction 1**

1.1 Atoms and molecules 1

1.2 Phases 2

1.3 Energy 3

1.4 Chemical reactions 4

1.5 Problem solving 5

1.6 Some conventions 7

Exercises 11

Further reading 14

**2 Ideal gases 15**

2.1 Ideal gas equation of state 16

2.2 Molecular degrees of freedom 18

2.3 Translational energy: Distribution and relation to pressure 21

2.4 Maxwell distribution of molecular speeds 23

2.5 Principle of equipartition of energy 24

2.6 Temperature and the zeroth law of thermodynamics 25

2.7 Mixtures of gases 27

2.8 Molecular collisions 27

Exercises 29

Further reading 30

**3 Non-ideal gases and intermolecular interactions 31**

3.1 Non-ideal behavior 31

3.2 Interactions of matter with matter 32

3.3 Intermolecular interactions 34

3.4 Real gases 39

3.5 Corresponding states 42

3.6 Supercritical fluids 43

Exercises 43

Further reading 44

**4 Liquids, liquid crystals, and ionic liquids 45**

4.1 Liquid formation 45

4.2 Properties of liquids 45

4.3 Intermolecular interaction in liquids 47

4.4 Structure of liquids 50

4.5 Internal energy and equation of state of a rigid sphere liquid 52

4.6 Concentration units 53

4.7 Diffusion 55

4.8 Viscosity 57

4.9 Migration 59

4.10 Interface formation 60

4.11 Liquid crystals 62

4.12 Ionic liquids 64

Exercises 66

Further reading 67

**5 Solids, nanoparticles, and interfaces 68**

5.1 Solid formation 68

5.2 Electronic structure of solids 70

5.3 Geometrical structure of solids 72

5.4 Interface formation 76

5.5 Glass formation 78

5.6 Clusters and nanoparticles 78

5.7 The carbon family: Diamond, graphite, graphene, fullerenes, and carbon nanotubes 80

5.8 Porous solids 83

5.9 Polymers and macromolecules 84

Exercises 86

Endnotes 86

Further reading 86

**6 Statistical mechanics 87**

6.1 The initial state of the universe 88

6.2 Microstates and macrostates of molecules 89

6.3 The connection of entropy to microstates 91

6.4 The constant α: Introducing the partition function 93

6.5 Using the partition function to derive thermodynamic functions 94

6.6 Distribution functions for gases 96

6.7 Quantum statistics for particle distributions 98

6.8 The Maxwell–Boltzmann speed distribution 102

6.9 Derivation of the ideal gas law 103

6.10 Deriving the Sackur–Tetrode equation for entropy of a monatomic gas 104

6.11 The partition function of a diatomic molecule 106

6.12 Contributions of each degree of freedom to thermodynamic functions 106

6.13 The total partition function and thermodynamic functions 111

6.14 Polyatomic molecules 113

Exercises 115

Endnotes 116

Further reading 116

**7 First law of thermodynamics 117**

7.1 Some definitions and fundamental concepts in thermodynamics 118

7.2 Laws of thermodynamics 118

7.3 Internal energy and the first law 119

7.4 Work 121

7.5 Intensive and extensive variables 123

7.6 Heat 124

7.7 Non-ideal behavior changes the work 125

7.8 Heat capacity 126

7.9 Temperature dependence of Cp 127

7.10 Internal energy change at constant volume 129

7.11 Enthalpy 130

7.12 Relationship between CV and Cp and partial differentials 131

7.13 Reversible adiabatic expansion/compression 133

Exercises 136

Endnotes 138

Further reading 138

**8 Second law of thermodynamics 139**

8.1 The second law of thermodynamics 140

8.2 Thermodynamics of a hurricane 141

8.3 Heat engines, refrigeration, and heat pumps 145

8.4 Definition of entropy 148

8.5 Calculating changes in entropy 150

8.6 Maxwell's relations 152

8.7 Calculating the natural direction of change 154

Exercises 157

Endnotes 159

Further reading 159

**9 Third law of thermodynamics and temperature dependence of heat capacity, enthalpy and entropy 160**

9.1 When and why does a system change? 160

9.2 Natural variables of internal energy 161

9.3 Helmholtz and Gibbs energies 162

9.4 Standard molar Gibbs energies 163

9.5 Properties of the Gibbs energy 164

9.6 The temperature dependence of ΔrCp and H 168

9.7 Third law of thermodynamics 170

9.8 The unattainability of absolute zero 171

9.9 Absolute entropies 172

9.10 Entropy changes in chemical reactions 173

9.11 Calculating ΔrS· at any temperature 175

Exercises 177

Further reading 180

**10 Thermochemistry: The role of heat in chemical and physical changes 181**

10.1 Stoichiometry and extent of reaction 181

10.2 Standard enthalpy change 182

10.3 Calorimetry 184

10.4 Phase transitions 187

10.5 Bond dissociation and atomization 190

10.6 Solution 191

10.7 Enthalpy of formation 192

10.8 Hess's law 192

10.9 Reaction enthalpy from enthalpies of formation 193

10.10 Calculating enthalpy of reaction from enthalpies of combustion 194

10.11 The magnitude of reaction enthalpy 195

Exercises 196

Further reading 200

**11 Chemical equilibrium 201**

11.1 Chemical potential and Gibbs energy of a reaction mixture 201

11.2 The Gibbs energy and equilibrium composition 202

11.3 The response of equilibria to change 204

11.4 Equilibrium constants and associated calculations 209

11.5 Acid–base equilibria 212

11.6 Dissolution and precipitation of salts 216

11.7 Formation constants of complexes 219

11.8 Thermodynamics of self-assembly 222

Exercises 224

Endnote 228

Further reading 228

**12 Phase stability and phase transitions 229**

12.1 Phase diagrams and the relative stability of solids, liquids, and gases 229

12.2 What determines relative phase stability? 232

12.3 The p–T phase diagram 234

12.4 The Gibbs phase rule 237

12.5 Theoretical basis for the p–T phase diagram 238

12.6 Clausius–Clapeyron equation 240

12.7 Surface tension 242

12.8 Nucleation 246

12.9 Construction of a liquid–vapor phase diagram at constant pressure 250

12.10 Polymers: Phase separation and the glass transition 252

Exercises 254

Endnotes 255

Further reading 256

**13 Solutions and mixtures: Nonelectrolytes 257**

13.1 Ideal solution and the standard state 258

13.2 Partial molar volume 258

13.3 Partial molar Gibbs energy = chemical potential 259

13.4 The chemical potential of a mixture and ΔmixG 261

13.5 Activity 263

13.6 Measurement of activity 264

13.7 Classes of solutions and their properties 269

13.8 Colligative properties 273

13.9 Solubility of polymers 277

13.10 Supercritical CO2 279

Exercises 281

Endnote 282

Further reading 282

**14 Solutions of electrolytes 283**

14.1 Why salts dissolve 283

14.2 Ions in solution 284

14.3 The thermodynamic properties of ions in solution 287

14.4 The activity of ions in solution 289

14.5 Debye–Hückel theory 290

14.6 Use of activities in equilibrium calculations 292

14.7 Charge transport 295

Exercises 298

Further reading 299

**15 Electrochemistry: The chemistry of free charge exchange 300**

15.1 Introduction to electrochemistry 301

15.2 The electrochemical potential 306

15.3 Electrochemical cells 310

15.4 Potential difference of an electrochemical cell 312

15.5 Surface charge and potential 318

15.6 Relating work functions to the electrochemical series 319

15.7 Applications of standard potentials 321

15.8 Biological oxidation and proton-coupled electron transfer 326

Exercises 329

Endnotes 331

Further reading 332

**16 Empirical chemical kinetics 333**

16.1 What is chemical kinetics? 333

16.2 Rates of reaction and rate equations 335

16.3 Elementary versus composite reactions 336

16.4 Kinetics and thermodynamics 337

16.5 Kinetics of specific orders 338

16.6 Reaction rate determination 345

16.7 Methods of determining reaction order 346

16.8 Reversible reactions and the connection of rate constants to equilibrium constants 348

16.9 Temperature dependence of rates and the rate constant 350

16.10 Microscopic reversibility and detailed balance 353

16.11 Rate-determining step (RDS) 354

Exercises 355

Endnotes 359

Further reading 359

**17 Reaction dynamics I: Mechanisms and rates 360**

17.1 Linking empirical kinetics to reaction dynamics 360

17.2 Hard-sphere collision theory 361

17.3 Activation energy and the transition state 364

17.4 Transition-state theory (TST) 366

17.5 Composite reactions and mechanisms 368

17.6 The rate of unimolecular reactions 372

17.7 Desorption kinetics 374

17.8 Langmuir (direct) adsorption 378

17.9 Precursor-mediated adsorption 380

17.10 Adsorption isotherms 381

17.11 Surmounting activation barriers 382

Exercises 386

Endnotes 389

Further reading 390

**18 Reaction dynamics II: Catalysis, photochemistry and charge transfer 391**

18.1 Catalysis 392

18.2 Heterogeneous catalysis 393

18.3 Acid–base catalysis 402

18.4 Enzyme catalysis 403

18.5 Chain reactions 407

18.6 Explosions 410

18.7 Photochemical reactions 411

18.8 Charge transfer and electrochemical dynamics 415

Exercises 428

Endnotes 431

Further reading 431

**19 Developing quantum mechanical intuition 433**

19.1 Classical electromagnetic waves 434

19.2 Classical mechanics to quantum mechanics 443

19.3 Necessity for an understanding of quantum mechanics 444

19.4 Quantum nature of light 448

19.5 Wave–particle duality 449

19.6 The Bohr atom 453

Exercises 458

Endnotes 460

Further reading 461

**20 The quantum mechanical description of nature 462**

20.1 What determines if a quantum description is necessary? 463

20.2 The postulates of quantum mechanics 463

20.3 Wavefunctions 464

20.4 The Schrödinger equation 467

20.5 Operators and eigenvalues 469

20.6 Solving the Schrödinger equation 471

20.7 Expectation values 475

20.8 Orthonormality and superposition 477

20.9 Dirac notation 480

20.10 Developing quantum intuition 481

Exercises 486

Endnotes 488

Further reading 488

**21 Model quantum systems 489**

21.1 Particle in a box 490

21.2 Quantum tunneling 495

21.3 Vibrational motion 497

21.4 Angular momentum 500

Exercises 511

Endnotes 513

Further reading 513

**22 Atomic structure 514**

22.1 The hydrogenl atom 515

22.2 How do you make it better? the Dirac equation 518

22.3 Atomic orbitals 520

22.4 Many-electron atoms 524

22.5 Ground and excited states of He 528

22.6 Slater–Condon theory for approximating atomic energy levels 530

22.7 Electron configurations 533

Exercises 536

Endnotes 538

Further reading 538

**23 Introduction to spectroscopy and atomic spectroscopy 539**

23.1 Fundamentals of spectroscopy 540

23.2 Time-dependent perturbation theory and spectral transitions 544

23.3 The Beer–Lambert law 547

23.4 Electronic spectra of atoms 550

23.5 Spin–orbit coupling 551

23.6 Russell–Saunders (LS) coupling 554

23.7 jj-coupling 559

23.8 Selection rules for atomic spectroscopy 560

23.9 Photoelectron spectroscopy 561

Exercises 566

Endnotes 569

Further reading 569

**24 Molecular bonding and structure 570**

24.1 Born–Oppenheimer approximation 571

24.2 Valence bond theory 573

24.3 Molecular orbital theory 576

24.4 The hydrogen molecular ion H+2 577

24.5 Solving the H2 Schrödinger equation 580

24.6 Homonuclear diatomic molecules 585

24.7 Heteronuclear diatomic molecules 588

24.8 The variational principle in molecular orbital calculations 591

24.9 Polyatomic molecules: The Hückel approximation 593

24.10 Density functional theory (DFT) 597

Exercises 598

Endnotes 601

Further reading 601

**25 Molecular spectroscopy and excited-state dynamics: Diatomics 602**

25.1 Introduction to molecular spectroscopy 603

25.2 Pure rotational spectra of molecules 604

25.3 Rovibrational spectra of molecules 609

25.4 Raman spectroscopy 614

25.5 Electronic spectra of molecules 617

25.6 Excited-state population dynamics 622

25.7 Electron collisions with molecules 628

Exercises 629

Endnotes 632

Further reading 633

**26 Polyatomic molecules and group theory 634**

26.1 Absorption and emission by polyatomics 635

26.2 Electronic and vibronic selection rules 637

26.3 Molecular symmetry 641

26.4 Point groups 645

26.5 Character tables 647

26.6 Dipole moments 650

26.7 Rovibrational spectroscopy of polyatomic molecules 652

26.8 Excited-state dynamics 656

Exercises 665

Endnotes 667

Further reading 667

**27 Light–matter interactions: Lasers, laser spectroscopy, and photodynamics 668**

27.1 Lasers 669

27.2 Harmonic generation (SHG and SFG) 673

27.3 Multiphoton absorption spectroscopy 675

27.4 Cavity ring-down spectroscopy 682

27.5 Femtochemistry 685

27.6 Beyond perturbation theory limit: High harmonic generation 688

27.7 Attosecond physics 690

27.8 Photosynthesis 691

27.9 Color and vision 694

Exercises 697

Endnotes 698

Further reading 699

Appendix 1 Basic calculus and trigonometry 700

Appendix 2 The method of undetermined multipliers 703

Appendix 3 Stirling's theorem 705

Appendix 4 Density of states of a particle in a box 706

Appendix 5 Black-body radiation: Treating radiation as a photon gas 708

Appendix 6 Definitions of symbols used in quantum mechanics and quantum chemistry 710

Appendix 7 Character tables 712

Appendix 8 Periodic behavior 714

Appendix 9 Thermodynamic parameters 717

Index 719