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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 ¿¿¿¿: 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 ¿rCp 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 ¿rS¿ 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 ¿mixG 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-Huckel 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 Schrodinger equation 467
20.5 Operators and eigenvalues 469
20.6 Solving the Schr ¿ odinger 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 Schr ¿ odinger 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 Huckel 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
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
Much of chemistry is motivated by asking 'how'. How do I make a primary alcohol? React a Grignard reagent with formaldehyde. How do I get a solution containing phenolphthalein to change from colorless to pink? Add base. How do I make solid barium sulfate? Add enough barium chloride dissolved in water to a solution of sodium sulfate and the barium sulfate precipitates out. 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. In acidic solutions, the protonated form of phenolphthalein absorbs light in the ultraviolet range but is transparent in the visible range. When base is added, the phenolphthalein is converted to a deprotonated form which absorbs in the green part of the visible spectrum, peaking at 553 nm. The absorption of light occurs when an electron is promoted from its ground state to an excited state. BaCl2 and Na2SO4 are both highly soluble in water. BaSO4 is less soluble in water. When enough Ba2+ and SO42- are present in water, it is energetically more favorable for them to form a solid compound, which is denser than water and, therefore, precipitates to the bottom of the beaker. If you are interested in asking why and not just how, then you need to understand physical chemistry.
Introductory chemistry - general chemistry and an introduction to synthesis - has introduced all the major, sweeping, most important aspects of chemistry. In most cases you have been presented these ideas without foundations; that is, you have been told that certain phenomena occur - such as chemical bonding or phase transitions - but you have only had hints given to you about why these phenomena occur. You have been introduced to special cases and single-temperature results. However, you have not been given the machinery to move away from ideal cases, or to change parameters so as to predict what will happen next. Let us jog your memory about some key concepts (and perhaps add a few details I wish you would have been taught). This will illuminate where we have to go and motivate the discussion of much of our machinery building. It will also highlight some areas in which the simplifications of introductory chemistry sometimes border on myth building. The role of physical chemistry is to tear down mirages of explanation in order to construct the machinery that results in fundamental understanding. To a large extent, physical chemistry is the study and mastery of k, K, n, and ?, (rate constant, equilibrium constant, moles, and wavefunction) and how they respond to t, T, and p (time, temperature, and pressure). That is, we want to understand the time evolution and response to experimental conditions of chemical systems. Along the way perhaps the three most important constants that we will have to understand the implications of are kB, h and NA (the constants of Boltzmann, Planck, and Avogadro, respectively) and how they relate to the energy, propensity for change and our ability to probe systems at the atomic level.
Our chemical universe is made up of atoms and molecules. For the purposes of this course we are going to limit ourselves to electrons, protons and neutrons, and not worry about any internal structure of these particles (though we will mention the Higgs boson a couple of times, so don't get the blues!). Atoms are composed of a nucleus, where the protons and neutrons reside, and electrons that occupy the space outside of the nucleus. The space occupied by the electrons is called an orbital. Orbitals have specific shapes; you should recall the spherical s orbitals and dumbbell-shaped p orbitals (as usually represented in chemistry). The d orbitals and f orbitals are more complex yet. Atoms are neutral; that is, the number of negatively charged electrons exactly balances the number of positively charged protons. Neutrons carry no charge. An atom can be excited, for instance by the absorption of light. If the photons in the light are energetic enough, an electron can be removed from the atom to form a positive ion. Negative ions are formed when an atom captures an extra electron from some external source.
Certain atoms will form molecules when they interact with each other. Molecules have well-defined stoichiometries (ratios of how many atoms combine) and well-defined geometries with characteristic bond distances and bond angles. As molecules become bigger and bigger they may be able to take on several different configurations (isomers).
Figure 1.1 A potential energy diagram for the ground electronic state of the O2 molecule.
A molecule is held together by chemical bonds. An especially wicked misconception held by many is that energy is released when a chemical bond is broken. As shown in Fig. 1.1, energy is released when a chemical bond is formed. Chemical bond formation between two atoms must be an exothermic process or else it would never occur. Conversely then, it takes energy to break a chemical bond, and this is an endothermic process. Chemical bonds in molecules come in two broadly defined flavors. In a covalent bond, electrons are shared. If they are shared equally, a nonpolar bond is formed, but if they are shared unequally a polar bond is formed. Unless the geometry of the molecules has a special symmetry that makes charge distributions cancel out, polar bonds lead to polar molecules, that is, molecules that exhibit dipole moments. In ionic bonds, electrostatic forces hold together the positive and negative charges on ions formed by the transfer of at least one complete electron.
The motions of subatomic particles are governed by quantum mechanics, not classical mechanics. Classical mechanics describes everyday particles: billiard balls and apples falling on the heads of drowsy natural philosophers. Quantum mechanics is different. The energy states of electrons are governed by quantum mechanics. Electrons occupy atomic orbitals in atoms and molecular orbitals in molecules. Because covalent bonding is due to electrons and their sharing by atoms, bonding is inherently quantum mechanical in nature.
Moving from a single molecule or atom to collections of particles, the influences of intermolecular forces become important. There are a number of different types of intermolecular interactions: dipole-dipole, van der Waals and hydrogen bonding are some of the most common. The three most commonly encountered phases in chemistry are gases, liquids, and solids. In this course, we will not have to worry about the other two: plasmas and Bose-Einstein condensates, which are most likely to be encountered at very high or very low temperatures, respectively.
You are already familiar with the concept of an ideal gas and its equation of state
Intermolecular interactions are absent in an ideal gas. Even in a real gas, intermolecular interactions are weak as long as the pressure and temperature are far from the conditions that induce condensation. Gas-phase molecules are free to translate, rotate, and vibrate. There are also electronic excitations, but usually these are not accessible by thermal excitations. The places where we can put energy (translations, rotations, vibrations, and electronic states) are called degrees of freedom.
Throughout this book you will find directed practice, short exercises for the reader to collect their thoughts and reinforce concepts. Calculate the volume in m3 of one mole of ideal gas at standard temperature and pressure (STP is defined as T = 273.15 K and 100 kPa) and standard ambient temperature (T = 298.15 K) and atmospheric pressure (p = 101.325 kPa), denoted SATP.
[Answers: 0.0227 m3, 0.0245 m3]
As the temperature is lowered or the pressure increased, the particles in a gas are pushed together, and eventually intermolecular interactions will lead to condensation. Most commonly, a gas will condense into a liquid. Intermolecular interactions are much more important in liquids than gases because the molecules are much closer together. That the molecules are much closer together means that their density is much higher, and that they collide with each other much more frequently than gas-phase molecules. Liquid-phase molecules are still free to translate, rotate and vibrate, but the spectra associated with these degrees of freedom look different than when they are in the gas phase. Liquids are commonly classified as to whether they are polar or nonpolar. Like tends to dissolve like, and polar solvents are capable of dissolving ionic compounds (electrolytes) into their constituent ions. Nonelectrolytes dissolve without the formation of ions. Electrolyte solutions can conduct electrical currents.
At yet lower temperature and higher pressure, liquids condense into solids. Solids are usually denser than liquids, but there is not nearly as big a change during this phase transition as the one from the gas phase to a condensed phase. The atoms and molecules in a solid can no longer translate and rotate freely. There are still vibrations and electronic excitations. Solids are often classified by their electronic structure according to their electrical conductivity properties: metals conduct well and have no band gap between their valence and conduction bands, insulators conduct poorly because they have a large band gap; semiconductors are somewhere in...
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