Electrons, Atoms, and Molecules in Inorganic Chemistry: A Worked Examples Approach

763 Pages·2017·5.31 MB·English

by  Joseph J. Stephanos

Electrons, Atoms, and Molecules in
Inorganic Chemistry

Electrons, Atoms,
and Molecules in
Inorganic Chemistry
A Worked Examples Approach
Joseph J. Stephanos
Anthony W. Addison
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To our Students in Chemistry

Contents
Preface XIII 2.5 The Angular Equation 47
2.6 The <!>-Equation 48
2.7 The 8-Equation 51
1. Particle Wave Duality
2.8 The Radial Equation 57
1.1 Cathode and Anode Rays 2.9 The Final Solution for the Full Wave
1.2 Charge of the Electron 4 Function, 111n tm(r, 0, (/J) 66
1.3 Mass of Electron and Proton 6 2.10 The Orthonormal Properties of the
1.4 Rutherford's Atomic Model 9 Real Wave Functions 71
1.5 Quantum of Energy 10 2.11 The Quantum Numbers: n, I, and m 76
1
1.6 Hydrogen Atom Line-Emission Spectra; The Principle Quantum Number, n 76
Electrons in Atoms Exist Only in Very The Quantum Numbers I and Angular
Specific Energy States 13 Momentum 76
1.7 Bohr's Quantum Theory of the The Angular Momentum Quantum
Hydrogen Atom 15 Numbers, I and m 78
1.8 The Bohr-Sommerfeld Model 18 Picture and Represent Precisely m
1
1.9 The Corpuscular Nature of Electrons, Vectors of p- and d-Orbitals 78
Photons, and Particles of Very Small Mass 18 2.12 The Spin Quantum Number, s 84
1.10 Relativity Theory: Mass and Energy, 2.13 The Boundary Surface of s-Orbital 85
Momentum, and Wavelength 2.14 The Boundary Surface of p-Orbitals 87
Interdependence 21 2.15 The Boundary Surface of d-Orbitals 91
1.11 The Corpuscular Nature of 2.16 Calculating the Most Probable Radius 99
Electromagnetic Waves 21 2.17 Calculating the Mean Radius
The Photoelectric Effect 22 of an Orbital 100
The Compton Effect 25 2.18 The Structure of Many-Electron Atoms 108
1.12 de Broglie's Considerations 26 2.19 The Pauli Exclusion Principle 109
1.13 Werner Heisenberg's Uncertainty 2.20 Slater Determinant 111
Principle, or the Principle of 2.21 Penetration and Shielding 113
Indeterminacy 27 2.22 The Building-Up Principle 11 7
1.14 The Probability of Finding an Electron 2.23 Term Structure for Polyelectron
and the Wave Function 28 Atoms 121
1.15 Atomic and Subatomic Particles 29 2.24 Term Wave Functions and Single
Elementary Particles 29 Electron Wave Functions 129
Suggestions for Further Reading 32 2.25 Spin-Orbital Coupling 131
2.26 Spin-Orbital Coupling in External
2. Electrons in Atoms Magnetic Field 133
Suggestions for Further Reading 144
2.1 The Wave Function (the Schri:idinger
Equation) 37
3. Chemical Bonding
2.2 Properties of the Wave Function 39
2.3 Schri:idinger Equation of the 3.1 Electronegativity and Electropositivity 149
Hydrogen Atom 40 3.2 Electronegativity and Electropositivity
2.4 Transformation of the Schri:idinger Trends 150
Equation From Cartesians to Spherical 3.3 Molecular and Nonmolecular
Polar Coordinates 41 Compounds 151
vii
viii Contents
3.4 Types of Bonds 152 Macrocyclic Effect 193
3.5 Metallic Bonding and General Solvation Enthalpy Differences 196
Properties of Metals 152 Donor Atom Basicity 196
Conductivity and Mobility of Electrons 153 Cavity Size 197
Luster and Free Electron Irradiation 154 Solvent Competition 197
Malleability, Cohesive Force, Number Steric Effect 198
of Valence Electrons 154 Stability and Metal Oxidation State 198
Theories of Bonding in Metals 155 Stability and Metal Ionization Potential 201
Free Electron Theory 155 3.9 Intermolecular Interactions 204
Bond Lengths 156 van der Waals Forces 204
Crystal Structures of Metals (Metallic ion-Induced Dipole Forces,
Structures) 156 ion-Dipole Forces, and Hydrogen
Alloy and Metallic Compounds 158 Bonding 206
3.6 Ionic Bonding 159 3.10 Covalent Networks and
Lattice Energy and Cohesion Giant Molecules 212
of Atomic Lattice 159 Graphite, Fullerenes, Graphene, Carbon
Born-Haber Cycle and Heat of Formation 163 Nanotubes, and Asbestos 214
Ionic Crystal Structures and the Radius Suggestions for Further Reading 225
Ratio 164
Stoichiometric and Nonstoichiometric 4. Molecular Symmetry
Defects 169
Ionic Character and Covalency 4.1 Molecular Symmetry 228
Interference 170 4.2 The Symmetry Elements 230
Ionic Character and Melting Point 1 71 Identity, E 230
Solubility of the Ionic Salts 171 Proper Rotation Axis, Cn 230
3.7 Covalent Bonding 173 Plane of Symmetry, a 233
The Lewis Structures and Octet Rule 173 (Pntpr of Symmetry, i 2.15
Exceptions to the Octet Rule 173 Sn: Improper Rotation Axis 236
Bonding and Polarity 174 4.3 The Symmetry and Point Group 238
3.8 Coordinate Covalent Bond 4.4 Some Immediate Applications 239
(Dative Bonding) 175 Dipole Moments and Polarity 239
Coordination Number and the Chirality 244
"18-Eiectron Rule" 176 Equivalent Atoms: (Or Group of Atoms) 244
Ligand Denticity 176 Crystal Symmetry 245
Nomenclature of Complexes 176 4.5 Group Theory: Properties of the
Complex Formation 178 Groups and Their Elements 250
Coordinative Comproportionation 4.6 Similarity Transforms, Conjugation,
Reaction 181 and Classes 252
Complexation Equilibrium 182 4.7 Matrix Representation 254
Multiligand Complexation 183 Matrices and Vectors 254
Stepwise Formation Constants and the Matrix Representation of Symmetry
Sequential Analysis 184 Operation 255
Complex Stability 186 Matrix Representation of Point Group 258
Hard and Soft Interactions, HSAB 186 Irreducible Representations 260
Chemical Features of Hard and Soft Ions, Irreducible and Degenerate
and Classification 189 Representations 261
Rule of Interactions 190 4.8 Motion Representations of the
Hard-Hard and Soft-Soft Interactions 190 Groups 262
Hard-Soft Interaction and Anion Translation Motion 262
Polarizabi I ity 190 Rotational Motion 264
Chelate Effect 191 4.9 Symmetry Properties of Atomic
Entropy and Chelate Formation 192 Orbitals 266
Stability and the Geometry of the Mullikan Notation 266
Chelate Ring 193 Atomic Orbital Representation 267
Contents ix
4.10 Character Tables 269 6.5 Heterodiatomic Molecules 347
Properties of the Characters of 6.6 Polyatomic Molecules 349
Representations 270 6.7 Molecular Orbitals for a Centric Molecule 351
4.11 Relation Between any Reducible and 6.8 Properties Derived From Molecular
Irreducible Representations 272 Wave Function 366
The Direct Product 274 6.9 Band Theory: Molecule Orbital Theory
4.12 Group Theory and Quantum and Metallic Bonding Orbit 394
Mechanics: Irreducible Representations 6.10 Conductors, Insulators, and
and Wave Function 275 Semiconductors 397
Suggestions for Further Reading 280 Suggestions for Further Reading 401
7. Crystal Field Theory
5. Valence Bond Theory and Orbital
Hybridization
7.1 The Advantages and Disadvantages of
Valence Bond Theory 405
5.1 Valence Bond Theory 282
7.2 Bases of Crystal Field Theory 405
5.2 VSEPR Theory and Molecular
d-Orbitals in Cubic Crystal Field 405
Geometry 283
f-Orbitals in Cubic Crystal Field 406
5.3 lsoelectronic Species 284
7.3 The Crystal Field Potential 407
5.4 Procedures to Diagram Molecular
Octahedral Crystal field Potential, Voct. 407
Structure 284
Square Planar Crystal Field Potential, Vsq.PI. 412
5.5 Valence Bond Theory and Metallic
Tetragonal Crystal Field Potential, VTetrag. 415
Bonds 288
Tetrahedral Crystal Field Potential, Vrd 417
5.6 Orbital Hybridization 290
7.4 Zero-Order Perturbation Theory 419
5.7 Rehybridization and Complex Formation 291
The Linear Combination of Atomic
5.8 Hybridization and o--/rr-Bonding 294
Orbitals, LCAO-MO, and Energy
5.9 Orbital Hybridization and Molecular
Cillc:uliltion 419
Symmetry 296
The Perturbation Theory for Degenerate
Trigonal Planar Hybridization 296
Systems 421
The Extend of d-Orbital Participation in
The Splitting of d-Orbitals in Octahedral
Molecular Bonding 301
Crystal Field, Voct. 423
Trigonal Bipyramidal Hybridization 301
The Splitting of d-Orbitals in Tetrahedral
Tetragonal Pyramidal Hybridization 303
Crystal Field, Vrd 430
Square Planar Hybridization 304
The Splitting of d-Orbitals in Tetragonal
Tetrahedral Hybridization 306
Crystal Field, Vo.h 435
Octahedral Hybridization 308
7.5 Types of Interactions That Affect the
5.10 Hybrid Orbitals as Symmetry
Crystal Field Treatment 442
Adapted Linear Combination of Atomic
7.6 Free Jon in Weak Crystal Fields 442
Orbitals (SALC) 311
Problems and the Required
5.11 Molecular Wave Function as Symmetry
Approximations 442
Adapted Linear Combination of Atomic
The Effect of the Crystal Field on S Term 442
Orbitals (SALC) 322
The Effect of the Cubic Crystal Field on
Suggestions for Further Reading 330
P Term 442
The Effect of a Cubic Crystal Field on
6. Molecular Orbital Theory
D Term 44f)
6.1 Molecular Orbital Theory Versus The Effect of a Cubic Crystal Field
Valence Bond Theory 332 on F Term 447
6.2 Molecular Orbital Wave Function and The Effect of a Cubic Crystal Field on G,
Symmetry 333 H, and I 455
6.3 The Linear Combination of Atomic 7.7 Strong Field Approach 457
Orbitals-Molecular Orbital (LCAO-MO) Determinantal Wave Functions 457
and Hi.ickel Approximations 333 The Determinantal Wave Functions of d2
6.4 Atomic Orbitals Combinations for the in Strong Field of Tetragonal Structure,
Second Row Diatomic Molecules 338 Trans-ML Z 457
4 2