Concise Physical Chemistry

CONCISE PHYSICAL CHEMISTRY......Page 4
CONTENTS......Page 8
Foreword......Page 24
Preface......Page 26
1.1 Empirical Gas Laws......Page 28
1.1.2 Units......Page 29
1.2 The Mole......Page 30
1.3 Equations of State......Page 31
Partial Pressures......Page 32
Molecular Weight Determination......Page 33
1.8 The Maxwell–Boltzmann Distribution......Page 34
Figure 1.2 A Maxwell–Boltzmann Distribution Over Discontinuous Energy Levels.......Page 35
1.9 A Digression on “Space”......Page 36
1.10 The Sum-Over-States or Partition Function......Page 37
Exercise 1.1......Page 39
Exercise 1.2......Page 40
Problems 1.1–1.13......Page 42
Problems 1.15–1.18......Page 43
2.1 The van der Waals Equation......Page 45
2.2 The Virial Equation: A Parametric Curve Fit......Page 46
2.3 The Compressibility Factor......Page 47
Figure 2.1 A Quadratic Least-Squares Fit to an Experimental Data Set for the Compressibility Factor of Nitrogen at 300 K and Low Pressures (Sigmaplot 11.0C ).......Page 48
Figure 2.2 The Second Virial Coefficient of Three Gases as a Function of Temperature.......Page 49
Figure 2.3 The Z = f (p) Curve for Two Different Gases or for the Same Gas at Two Different Temperatures.......Page 50
Figure 2.4 Three Isotherms of a van der Waals Gas.......Page 51
2.4.1 Subcritical Fluids......Page 52
Figure 2.6 Density ρ Curves for Liquid and Gaseous Oxygen.......Page 53
2.6 The Law of Corresponding States, Another View......Page 54
Exercise 2.1......Page 55
Figure 2.8 Boyle’s Law Plot for an Ideal Gas (lower curve) and for Nitrogen (upper curve).......Page 56
Figure 2.9 Experimental Values of pVm = z(p) vs. p for a Real Gas.......Page 57
Table 2.2 Observed Real Gas Behavior Expressed as (p, pVm).......Page 58
Problems 2.1–2.15......Page 59
Figure 2.11 Cubic Real Gas Behavior.......Page 61
3.1 Conservation Laws and Exact Differentials......Page 62
3.1.1 The Reciprocity Relationship......Page 63
3.2 Thermodynamic Cycles......Page 64
3.2.1 Hey, Let’s Make a Perpetual Motion Machine!......Page 65
Figure 3.2 Different Segments of a Curved Rod.......Page 66
Figure 3.3 Pythagorean Approximation to the Short Arc of a Curve.......Page 67
3.5 State Functions......Page 68
3.6 Reversible Processes and Path Independence......Page 69
Figure 3.4 The Energy Change for Reversible Expansion of an Ideal Gas.......Page 70
3.8 Energy and Enthalpy......Page 71
3.9 The Joule and Joule–Thomson Experiments......Page 73
Figure 3.5 Inversion Temperature Ti as a Function of Pressure.......Page 74
Table 3.1 Heat Capacities and γ for Selected Gases.......Page 75
3.11 Adiabatic Work......Page 77
Figure 3.7 Two Expansions of an Ideal Gas.......Page 78
Problems 3.1–3.12......Page 79
Figure 3.9 C = Quarter-Circular Arc.......Page 80
4.1 Calorimetry......Page 83
4.2 Energies and Enthalpies of Formation......Page 84
4.4 Molecular Enthalpies of Formation......Page 85
Figure 4.1 Combustion of C(gr) and CO(g).......Page 86
4.5 Enthalpies of Reaction......Page 87
4.6 Group Additivity......Page 89
4.8 The Schr¨odinger Equation......Page 91
4.9 Variation of  H with T......Page 92
4.10 Differential Scanning Calorimetry......Page 93
Figure 4.3 Schematic Diagram of the Thermal Denaturation of a Water-Soluble Protein.......Page 94
Problems 4.1–4.9......Page 95
5.1 Entropy......Page 98
Figure 5.1 An Engine.......Page 99
5.1.2 The Reaction Coordinate......Page 100
5.2.1 Heating......Page 101
5.2.3 Heating and Expansion......Page 102
5.3.2 Heat Transfer......Page 104
5.4 The Third Law......Page 105
5.4.1 Chemical Reactions (Again)......Page 106
Example 5.1......Page 107
Problems 5.1–5.9......Page 108
6.1 Combining Enthalpy and Entropy......Page 111
6.2 Free Energies of Formation......Page 112
6.3 Some Fundamental Thermodynamic Identities......Page 113
6.5 Pressure Dependence of the Chemical Potential......Page 114
6.6 The Temperature Dependence of the Free Energy......Page 115
Problems 6.1–6.12......Page 117
7.1 The Equilibrium Constant......Page 120
7.2 General Formulation......Page 121
7.3 The Extent of Reaction......Page 123
7.5 Variation of the Equilibrium Constant with Temperature......Page 124
The van’t Hoff Equation......Page 125
7.5.2 Entropy from the van’t Hoff Equation......Page 126
7.7 Chemical Potential: Nonideal Systems......Page 127
7.8 Free Energy and Equilibria in Biochemical Systems......Page 129
7.8.1 Making ATP, the Cell’s Power Supply......Page 130
Example 7.1......Page 131
Problems 7.1–7.7......Page 132
8.1 Equilibrium......Page 135
8.2 Degeneracy and Equilibrium......Page 136
Figure 8.4 A Degenerate Two-Level Equilibrium.......Page 137
Figure 8.5 A Two-Level Equilibrium with Many A and Many B Levels.......Page 138
8.3 Gibbs Free Energy and the Partition Function......Page 139
8.5 The Thermodynamic Functions......Page 140
8.6 The Partition Function of a Simple System......Page 141
8.7 The Partition Function for Different Modes of Motion......Page 143
8.8 The Equilibrium Constant: A Statistical Approach......Page 144
8.9 Computational Statistical Thermodynamics......Page 146
Example 8.1......Page 147
Example 8.2......Page 148
Problems 8.1–8.9......Page 149
9.1 Components, Phases, and Degrees of Freedom......Page 151
9.2 Coexistence Curves......Page 152
Figure 9.1 Pure Water in One Phase (left) and Two Phases (right).......Page 153
Figure 9.2 A Liquid–Vapor Coexistence Curve.......Page 154
9.3 The Clausius–Clapeyron Equation......Page 155
9.4 Partial Molar Volume......Page 156
9.4.1 Generalization......Page 157
Figure 9.7 Volume Behavior of a Nonideal Binary Solution.......Page 158
9.6 Two-Component Phase Diagrams......Page 161
Figure 9.8 A Type I Phase Diagram.......Page 162
Figure 9.9 A Type II Phase Diagram.......Page 163
9.7 Compound Phase Diagrams......Page 164
9.8 Ternary Phase Diagrams......Page 165
Example 9.1......Page 166
Example 9.2......Page 167
Problems 9.1–9.9......Page 168
10.1 First-Order Kinetic Rate Laws......Page 171
Figure 10.1 First-Order Radioactive Decay.......Page 173
10.2 Second-Order Reactions......Page 174
10.3.1 Mathematical Interlude: The Laplace Transform......Page 176
10.3.2 Back to Kinetics: Sequential Reactions......Page 177
10.3.3 Reversible Reactions......Page 178
10.5 Reaction Mechanisms......Page 181
Figure 10.3 An Activation Energy Barrier Between an Unstable Position and a Stable Position.......Page 183
Figure 10.5 An Activation Barrier.......Page 184
10.7 Collision Theory......Page 185
10.8 Computational Kinetics......Page 186
Example 10.2......Page 187
Figure 10.8 The Natural Logarithm of Relative Intensity vs. Time for Radiative Decay.......Page 188
Problems 10.1–10.10......Page 189
11.1 Surface tension......Page 192
Figure 11.2 Stretching a Two-Dimensional Membrane by Moving an Edge of Length l.......Page 193
Figure 11.4 Capillary Rise in a Tube of Radius R.......Page 194
Figure 11.5 Heat Capacity as a Function of Temperature.......Page 195
Figure 11.6 Approximation of Laminar Flow Inside a Tube.......Page 196
11.4 Crystals......Page 197
Figure 11.7 Close Packing of Marbles Between Two Sheets.......Page 198
Figure 11.8 A Less Efficient Packing of Marbles.......Page 199
11.4.1 X-Ray Diffraction: Determination of Interplanar Distances......Page 200
11.4.2 The Packing Fraction......Page 201
Figure 11.12 A Simple Cubic Cell.......Page 202
11.5.1 Covalent Bond Radii......Page 203
11.7 Lattice Energies......Page 204
Exercise 11.1......Page 205
Problems 11.1–11.8......Page 206
Figure 11.15 A Body-Centered Primitive Cubic Cell.......Page 207
12.1 The Ideal Solution......Page 209
12.2 Raoult’s Law......Page 210
12.3 A Digression on Concentration Units......Page 211
Figure 12.3 Consistent Positive Deviations from Raoult’s Law.......Page 212
12.5.1 Henry’s Law Activities......Page 213
12.6 Vapor Pressure......Page 214
12.7 Boiling Point Elevation......Page 215
Figure 12.5 Boiling of Pure Solvent (left) and a Solution of Solvent and Nonvolatile Solute (right).......Page 216
12.8 Osmotic Presure......Page 218
Figure 12.6 Osmotic Pressure,......Page 219
12.9 Colligative Properties......Page 221
Example 12.1......Page 222
Example 12.2......Page 223
Exercise 12.1......Page 225
Problems 12.1–12.10......Page 226
13.1.1 Membrane Potentials......Page 230
Figure 13.2 An Ion-Permeable Membrane (Schematic).......Page 231
13.2 Resistivity, Conductivity, and Conductance......Page 232
13.3 Molar Conductivity......Page 233
Figure 13.3 Kohlrausch’s Law for Conductance of the Strong Electrolytes HCl and NaOAc and the Weak Electrolyte HOAc.......Page 234
13.4 Partial Ionization: Weak Electrolytes......Page 235
13.5 Ion Mobilities......Page 236
Figure 13.4 Moving Boundary Determination of the Mobility of H+.......Page 237
13.8 The Hittorf Cell......Page 238
Figure 13.5 A Three-Compartment Hittorf Cell.......Page 239
13.9 Ion Activities......Page 240
Example 13.1......Page 242
Example 13.3......Page 243
Problems 13.1–13.11......Page 244
14.1 The Daniell Cell......Page 247
14.2 Half-Cells......Page 248
14.3 Half-Cell Potentials......Page 249
14.4 Cell Diagrams......Page 250
14.6 The Nernst Equation......Page 251
14.7 Concentration Cells......Page 252
14.8 Finding E◦......Page 253
14.9 Solubility and Stability Products......Page 255
14.11 The Calomel Electrode......Page 256
Example 14.1......Page 257
Example 14.2......Page 258
Problems 14.1–14.9......Page 259
15.1 The Hydrogen Spectrum......Page 262
15.2 Early Quantum Theory......Page 263
The Hamiltonian Operator......Page 264
Heitler and London......Page 265
Hartree and Fock......Page 266
15.4 The Hartree Independent Electron Method......Page 267
Example 15.1......Page 270
Example 15.2......Page 271
Problems 15.1–15.9......Page 273
16.1 Wave Motion......Page 275
16.2 Wave equations......Page 276
16.3 The Schr¨odinger Equation......Page 277
  is a Vector......Page 278
The Eigenfunction Postulate......Page 279
16.5 The Particle in a One-Dimensional Box......Page 280
Fundamentals and Overtones......Page 281
16.6 The Particle in a Cubic Box......Page 282
Separable Equations......Page 283
16.6.3 Normalization......Page 284
The Radial Equation and Probability “Shells”......Page 285
16.8 Breaking Degeneracy......Page 286
16.8.1 Higher Exact Solutions for the Hydrogen Atom......Page 287
Figure 16.8 Roots of the Radial 3s Wave Function of Atomic Hydrogen as a Function of Distance r......Page 288
Figure 16.10 The Radial Node of the 2p Atomic Orbital.......Page 289
The Hartree Method......Page 290
Problems 16.1–16.9Problems 16.1–16.9......Page 291
17.1 More on the Variational Method......Page 294
17.2 The Secular Determinant......Page 295
17.3 A Variational Treatment for the Hydrogen Atom: The Energy Spectrum......Page 298
The Gaussian Approximation......Page 299
File 17.2 Energies Drawn from the Gaussian gen Output File for the Hydrogen Atom.......Page 300
17.4 Helium......Page 301
17.4.1 An SCF Variational Ionization Potential for Helium......Page 302
17.6 Bosons and Fermions......Page 305
17.7 Slater Determinants......Page 306
17.8 The Aufbau Principle......Page 307
Figure 17.1 Calculated IP1 for Elements 1–10.......Page 308
Table 17.1 Slater’s Rules.......Page 309
Example 17.1......Page 310
Example 17.2......Page 311
Problems 17.1–17.9......Page 312
18.1 The Harmonic Oscillator......Page 314
Figure 18.1 A Classical Harmonic Oscillator.......Page 315
18.2 The Hooke’s Law Potential Well......Page 316
18.4 The Quantum Rigid Rotor......Page 317
Figure 18.3 Energy Levels within a Simple Rotor.......Page 318
18.6 Electronic Spectra......Page 319
Figure 18.5 Absorption Wavelengths of Conjugated Polyalkenes.......Page 320
Figure 18.7 A Charged Capacitor with a Dielectric.......Page 321
Polarizability......Page 322
Figure 18.8 The Total Dipoles of Two Dichloroethene Isomers.......Page 323
18.8 Nuclear Magnetic Resonance (NMR)......Page 324
18.8.1 Spin–Spin Coupling......Page 325
Example 18.1......Page 326
Figure 18.10 Schematic Diagram of a Vibration–Rotation Band.......Page 327
Problems 18.1–18.13......Page 328
Figure 18.11 The Vibration–Rotation Spectrum of CO.......Page 329
19.1 Enthalpy: Additive Methods......Page 332
Bond Additivity......Page 333
19.3 Structure......Page 334
Force Constants and Parameters......Page 335
19.4 Geometry and Enthalpy: Molecular Mechanics......Page 336
Figure 19.4 Visualization of the Output for the Ethane Molecule (PCModel 8.0 C ).......Page 337
File 19.1 Partial MM4 Enthalpy Output for Ethane.......Page 338
19.8 The Outside World......Page 339
19.9 Transition States......Page 340
File 19.2 An Input File for Water.......Page 341
Example 19.3......Page 342
Problems 19.1–19.10......Page 343
20.1 The Molecular Variational Method......Page 345
Figure 20.1 The Hydrogen Molecule Ion, H+......Page 346
Figure 20.2 Bonding and Antibonding Orbitals for H+......Page 348
20.3 Higher Molecular Orbital Calculations......Page 349
20.4 Semiempirical Methods......Page 350
Figure 20.4 The 1s STO (solid line) and a Gaussian Approximation (dotted line).......Page 351
File 20.1 (Input) A Four-Parameter Gaussian File for the Hydrogen Atom.......Page 352
Figure 20.5 Approximation to the 1s Orbital of Hydrogen by 2 Gaussians.......Page 353
File 20.4 (Output) Stored Parameters for the STO-2G Basis Set.......Page 354
Figure 20.6 The G3MP2 Thermochemical Cycle for Determination of  fH298 of Methanol.......Page 355
File 20.5 (Input) A Molecular Orbital Input File for H2., 329 z-Matrix Format......Page 356
File 20.7 (Input) GAMESS File for Hydrogen Molecule.......Page 357
20.10 Split Valence Basis Sets......Page 358
20.12 Heteroatoms: Oxygen......Page 359
File 20.9 Input file for a GAUSSIANC  STO-3G Calculation on Methanol.......Page 360
20.13 Finding  fH298 of Methanol......Page 361
20.15 Post-Hartree–Fock Calculations......Page 363
20.16 Perturbation......Page 364
Scheme 20.1 A Computational Chemical Script.......Page 365
Figure 20.7 Additive Extrapolations in the G3(MP2) Scripted Method.......Page 362
20.18 Density Functional Theory (DFT)......Page 366
Example 20.2......Page 367
Example 20.3......Page 368
Problems 20.1–20.9......Page 369
21.1 Einstein’s Law......Page 371
Table 21.1 Some Experimental Quantum Yields.......Page 372
21.2.1 Lipid Peroxidation......Page 373
21.2.2 Ozone Depletion......Page 374
21.4 Lasers......Page 375
21.6 The Eyring Theory of Reaction Rates......Page 376
Figure 21.2 Eyring Potential Energy Plot for the Reaction H + H–H → H–H + H.......Page 377
Figure 21.4 The Enthalpy of Activation of an Exothermic Reaction.......Page 378
Figure 21.6 Inversion of Optical Activity.......Page 379
21.8 The Steady-State Pseudo-Equilibrium......Page 380
21.9 Entropies of Activation......Page 381
Example 21.1......Page 382
Example 21.2......Page 383
Problems 21.1–21.8......Page 384
References......Page 388
Answers to Selected Odd-Numbered Problems......Page 392
Index......Page 396