Physical Chemistry: A Second Look

by Delmar Larsen

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Chemistry, General Chemistry
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Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: The Dawn of the Quantum Theory
  7. 1.1: Blackbody Radiation Cannot Be Explained Classically
  8. 1.2: Quantum Hypothesis Used for Blackbody Radiation Law
  9. 1.3: Photoelectric Effect Explained with Quantum Hypothesis
  10. 1.4: The Hydrogen Atomic Spectrum
  11. 1.5: The Rydberg Formula and the Hydrogen Atomic Spectrum
  12. 1.6: Matter Has Wavelike Properties
  13. 1.7: de Broglie Waves can be Experimentally Observed
  14. 1.8: The Bohr Theory of the Hydrogen Atom
  15. 1.9: The Heisenberg Uncertainty Principle
  16. 1.10: The Dawn of the Quantum Theory (Exercises)
  17. 2: The Classical Wave Equation
  18. 2.1: The One-Dimensional Wave Equation
  19. 2.2: The Method of Separation of Variables
  20. 2.3: Oscillatory Solutions to Differential Equations
  21. 2.4: The General Solution is a Superposition of Normal Modes
  22. 2.5: A Vibrating Membrane
  23. 2.6: The Classical Wave Equation (Exercises)
  24. 3: The Schrödinger Equation and a Particle in a Box
  25. 3.1: The Schrödinger Equation
  26. 3.2: Linear Operators in Quantum Mechanics
  27. 3.3: The Schrödinger Equation is an Eigenvalue Problem
  28. 3.4: Wavefunctions Have a Probabilistic Interpretation
  29. 3.5: The Energy of a Particle in a Box is Quantized
  30. 3.6: Wavefunctions Must Be Normalized
  31. 3.7: The Average Momentum of a Particle in a Box is Zero
  32. 3.8: The Uncertainty Principle - Estimating Uncertainties from Wavefunctions
  33. 3.9: A Particle in a Three-Dimensional Box
  34. 3.10: The Schrödinger Equation and a Particle in a Box (Exercises)
  35. 3.11: The Schrödinger Equation and a Particle in a Box (Summary)
  36. 4: Postulates and Principles of Quantum Mechanics
  37. 4.1: The Wavefunction Specifies the State of a System
  38. 4.2: Quantum Operators Represent Classical Variables
  39. 4.3: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
  40. 4.4: The Time-Dependent Schrödinger Equation
  41. 4.5: Eigenfunctions of Operators are Orthogonal
  42. 4.6: Commuting Operators Allow Infinite Precision
  43. 4.7: Postulates and Principles of Quantum Mechanics (Exercises)
  44. 4.8: Postulates and Principles of Quantum Mechanics (Summary)
  45. 5: The Harmonic Oscillator and the Rigid Rotor
  46. 5.1: A Harmonic Oscillator Obeys Hooke's Law
  47. 5.2: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
  48. 5.3: The Harmonic Oscillator Approximates Molecular Vibrations
  49. 5.4: The Harmonic Oscillator Energy Levels
  50. 5.5: The Harmonic Oscillator and Infrared Spectra
  51. 5.6: The Harmonic Oscillator Wavefunctions involve Hermite Polynomials
  52. 5.7: Hermite Polynomials are either Even or Odd Functions
  53. 5.8: The Energy Levels of a Rigid Rotor
  54. 5.9: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
  55. 5.10: The Harmonic Oscillator and the Rigid Rotor (Exercises)
  56. 5.11: The Harmonic Oscillator and the Rigid Rotor (Summary)
  57. 6: The Hydrogen Atom
  58. 6.1: The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
  59. 6.2: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
  60. 6.3: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
  61. 6.4: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
  62. 6.5: s-orbitals are Spherically Symmetric
  63. 6.6: Orbital Angular Momentum and the p-Orbitals
  64. 6.7: The Helium Atom Cannot Be Solved Exactly
  65. 6.8: The Hydrogen Atom (Exercises)
  66. 6.9: The Hydrogen Atom (Summary)
  67. 7: Approximation Methods
  68. 7.1: The Variational Method Approximation
  69. 7.2: Linear Variational Method and the Secular Determinant
  70. 7.3: Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters
  71. 7.4: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
  72. 7.5: Approximation Methods (Exercises)
  73. 7.6: Approximation Methods (Summary)
  74. 8: Multielectron Atoms
  75. 8.1: Atomic and Molecular Calculations are Expressed in Atomic Units
  76. 8.2: Perturbation Theory and the Variational Method for Helium
  77. 8.3: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
  78. 8.4: An Electron has an Intrinsic Spin Angular Momentum
  79. 8.5: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
  80. 8.6: Antisymmetric Wavefunctions can be Represented by Slater Determinants
  81. 8.7: Hartree-Fock Calculations Give Good Agreement with Experimental Data
  82. 8.8: Term Symbols Gives a Detailed Description of an Electron Configuration
  83. 8.9: The Allowed Values of J - the Total Angular Momentum Quantum Number
  84. 8.10: Hund's Rules Determine the Term Symbols of the Ground Electronic States
  85. 8.11: Using Atomic Term Symbols to Interpret Atomic Spectra
  86. 8.12: Multielectron Atoms (Exercises)
  87. 8.13: Multielectron Atoms (Summary)
  88. 9: Chemical Bonding in Diatomic Molecules
  89. 9.1: The Born-Oppenheimer Approximation Simplifies the Schrödinger Equation for Molecules
  90. 9.2: The H₂⁺ Prototypical Species
  91. 9.3: The Overlap Integral
  92. 9.4: Chemical Bond Stability
  93. 9.5: Bonding and Antibonding Orbitals
  94. 9.6: A Simple Molecular-Orbital Treatment of H₂ Places Both Electrons in a Bonding Orbital
  95. 9.7: Molecular Orbitals Can Be Ordered According to Their Energies
  96. 9.8: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
  97. 9.9: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
  98. 9.10: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
  99. 9.11: Photoelectron Spectra Support the Existence of Molecular Orbitals
  100. 9.12: Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules
  101. 9.13: SCF-LCAO-MO Wavefunctions are Molecular Orbitals formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently
  102. 9.14: Molecular Term Symbols Describe Electronic States of Molecules
  103. 9.15: Molecular Term Symbols Designate Symmetry
  104. 9.16: Most Molecules Have Excited Electronic States
  105. 9.17: Chemical Bond in Diatomic Molecules (Exercises)
  106. 9.18: Chemical Bonding in Diatomic Molecules (Summary)
  107. 10: Bonding in Polyatomic Molecules
  108. 10.1: Hybrid Orbitals Account for Molecular Shape
  109. 10.2: Hybrid Orbitals in Water
  110. 10.3: BeH₂ is Linear and H₂O is Bent
  111. 10.4: Photoelectron Spectroscopy
  112. 10.5: The pi-Electron Approximation of Conjugation (Hückel Theory)
  113. 10.6: Butadiene is Stabilized by a Delocalization Energy
  114. 10.7: Benzene and Aromaticity
  115. 10.8: Bonding in Polyatomic Molecules (Exercises)
  116. 10.9: Bonding in Polyatomic Molecules (Summary)
  117. 11: Computational Quantum Chemistry
  118. 11.1: Overview of Quantum Calculations
  119. 11.2: Gaussian Basis Sets
  120. 11.3: Extended Basis Sets
  121. 11.4: Orbital Polarization Terms in Basis Sets
  122. 11.5: Computational Quantum Chemistry (Exercises)
  123. 12: Group Theory - The Exploitation of Symmetry
  124. 12.1: The Exploitation of Symmetry Can Help Simplify Numerical Calculations
  125. 12.2: Symmetry Elements and Operations Define the Point Groups
  126. 12.3: Symmetry Operations Define Groups
  127. 12.4: Symmetry Operations as Matrices
  128. 12.5: Molecules can be Represented by Reducible Representations
  129. 12.6: Character Tables Summarize the Properties of a Point Group
  130. 12.7: Characters of Irreducible Representations
  131. 12.8: Using Symmetry to Solve Secular Determinants
  132. 12.9: Generating Operators
  133. 12.10: Molecular Motions of a Molecule can be Represented by a Reducible Reperesentation
  134. 12.11: Reducible Representations are Comprised of Irreducible Representations
  135. 12.12: Normal Modes of Vibrations Describe how Molecules Vibrate
  136. 12.13: Symmetry of Vibrations Describes their Spectroscopic Behavior
  137. 12.14: Symmetry Adapted Linear Combinations are the Sum over all Basis functions
  138. 12.15: Molecular Orbitals can be Constructed on the Basis of Symmetry
  139. 12.16: Group Theory - The Exploitation of Symmetry (Exercises)
  140. 12.17: Group Theory - The Exploitation of Symmetry (Summary)
  141. 12.18: Character Tables
  142. 12.19: Correlation Tables
  143. 13: Molecular Spectroscopy
  144. 13.1: The Electromagnetic Spectrum
  145. 13.2: Rotations Accompany Vibrational Transitions
  146. 13.3: Unequal Spacings in Vibration-Rotation Spectra
  147. 13.4: Unequal Spacings in Pure Rotational Spectra
  148. 13.5: Vibrational Overtones
  149. 13.6: Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
  150. 13.7: The Franck-Condon Principle
  151. 13.8: Rotational Spectra of Polyatomic Molecules
  152. 13.9: Normal Modes in Polyatomic Molecules
  153. 13.10: Irreducible Representation of Point Groups
  154. 13.11: Time-Dependent Perturbation Theory
  155. 13.12: The Selection Rule for the Rigid Rotor
  156. 13.13: The Harmonic Oscillator Selection Rule
  157. 13.14: Group Theory Determines Infrared Activity
  158. 13.15: Molecular Spectroscopy (Exercises)
  159. 13.16: Molecular Spectroscopy (Summary)
  160. 14: Nuclear Magnetic Resonance Spectroscopy
  161. 14.1: Nuclei Have Intrinsic Spin Angular Momenta
  162. 14.2: Magnetic Moments Interact with Magnetic Fields
  163. 14.3: Proton NMR Spectrometers Operate at Frequencies Between 60 MHz and 750 MHz
  164. 14.4: The Magnetic Field Acting upon Nuclei in Molecules is Shielded
  165. 14.5: Chemical Shifts Depend upon the Chemical Environment of the Nucleus
  166. 14.6: Spin-Spin Coupling Can Lead to Multiplets in NMR Spectra
  167. 14.7: Spin-Spin Coupling Between Chemically Equivalent Protons is Not Observed
  168. 14.8: The n+1 Rule Applies Only to First-Order Spectra
  169. 14.9: Second-Order Spectra Can Be Calculated Exactly Using the Variational Method
  170. 14.10: Nuclear Magnetic Resonance Spectroscopy (Exercises)
  171. 14.11: Nuclear Magnetic Resonance Spectroscopy (Summary)
  172. 15: Lasers, Laser Spectroscopy, and Photochemistry
  173. 15.1: Electronically Excited Molecules can Relax by a Number of Processes
  174. 15.2: The Dynamics of Transitions can be Modeled by Rate Equations
  175. 15.3: A Two-Level System Cannot Achieve a Population Inversion
  176. 15.4: Population Inversion can be Achieved in a Three-Level System
  177. 15.5: What is Inside a Laser?
  178. 15.6: The Helium-Neon Laser
  179. 15.7: Modern Applications of Laser Spectroscopy
  180. 15.8: Pulsed Lasers Can by Used to Measure the Dynamics of Photochemical Processes
  181. 15.9: Lasers, Laser Spectroscopy, and Photochemistry (Exercises)
  182. 15.10: Lasers, Laser Spectroscopy, and Photochemistry (Summary)
  183. 16: The Properties of Gases
  184. 16.1: All Dilute Gases Behave Ideally
  185. 16.2: van der Waals and Redlich-Kwong Equations of State
  186. 16.3: A Cubic Equation of State
  187. 16.4: The Law of Corresponding States
  188. 16.5: The Second Virial Coefficient
  189. 16.6: The Repulsive Term in the Lennard-Jones Potential
  190. 16.7: Van der Waals Constants in Terms of Molecular Parameters
  191. 16.8: The Properties of Gases (Exercises)
  192. 16.9: The Properties of Gases (Summary)
  193. 17: Boltzmann Factor and Partition Functions
  194. 17.1: The Boltzmann Factor is used to Approximate the Fraction of Particles in a Large System
  195. 17.2: The Boltzmann Distribution represents a Thermally Equilibrated Distribution
  196. 17.3: The Average Ensemble Energy is Equal to the Observed Energy of a System
  197. 17.4: Heat Capacity at Constant Volume is the Change in Internal Energy with Temperature
  198. 17.5: Pressure can be Expressed in Terms of the Canonical Partition Function
  199. 17.6: The Partition Function of Distinguishable, Independent Molecules is the Product of the Molecular Partition Functions
  200. 17.7: Partition Functions of Indistinguishable Molecules Must Avoid Over Counting States
  201. 17.8: Partition Functions can be Decomposed into Partition Functions of Each Degree of Freedom
  202. 17.9: Boltzmann Factor and Partition Functions (Exercises)
  203. 17.10: Boltzmann Factor and Partition Functions (Summary)
  204. 18: Partition Functions and Ideal Gases
  205. 18.1: Translational Partition Functions of Monotonic Gases
  206. 18.2: Most Atoms are in the Ground Electronic State
  207. 18.3: The Energy of a Diatomic/Polyatomic Molecule Can Be Approximated as a Sum of Separate Terms
  208. 18.4: Most Molecules are in the Ground Vibrational State
  209. 18.5: Most Molecules are Rotationally Excited at Ordinary Temperatures
  210. 18.6: Rotational Partition Functions of Diatomic Gases Contain a Symmetry Number
  211. 18.7: Vibrational Partition Functions of Polyatomic Molecules Include the Partition Function for Each Normal Coordinate
  212. 18.8: Rotational Partition Functions of Polyatomic Molecules Depend on the Sphar of the Molecule
  213. 18.9: Molar Heat Capacities
  214. 18.10: Ortho and Para Hydrogen
  215. 18.11: The Equipartition Principle
  216. 18.12: Partition Functions and Ideal Gases (Exercises)
  217. 19: The First Law of Thermodynamics
  218. 19.1: Overview of Classical Thermodynamics
  219. 19.2: Pressure-Volume Work
  220. 19.3: Work and Heat are not State Functions
  221. 19.4: Energy is a State Function
  222. 19.5: An Adiabatic Process is a Process in which No Energy as Heat is Transferred
  223. 19.6: The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion
  224. 19.7: Work and Heat Have a Simple Molecular Interpretation
  225. 19.8: Pressure-Volume Work
  226. 19.9: Heat Capacity is a Path Function
  227. 19.10: Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition
  228. 19.11: Enthalpy Changes for Chemical Equations are Additive
  229. 19.12: Heats of Reactions Can Be Calculated from Tabulated Heats of Formation
  230. 19.13: The Temperature Dependence of ΔH
  231. 19.14: Enthalpy is a State Function
  232. 19.15: The First Law of Thermodynamics (Exercises)
  233. 20: Entropy and The Second Law of Thermodynamics
  234. 20.1: Energy Does not Determine Spontaneity
  235. 20.2: Nonequilibrium Isolated Systems Evolve in a Direction That Increases Their Energy Dispersal
  236. 20.3: Unlike heat, Entropy is a State Function
  237. 20.4: The Second Law of Thermodynamics
  238. 20.5: The Famous Equation of Statistical Thermodynamics is S=k ln W
  239. 20.6: We Must Always Devise a Reversible Process to Calculate Entropy Changes
  240. 20.7: Thermodynamics Provides Insight into the Conversion of Heat into Work
  241. 20.8: Entropy Can Be Expressed in Terms of a Partition Function
  242. 20.9: The Statistical Definition of Entropy is Analogous to the Thermodynamic Definition
  243. 20.10: Entropy and The Second Law of Thermodynamics (Exercises)
  244. 21: Entropy and the Third Law of Thermodynamics
  245. 21.1: Entropy Increases with Increasing Temperature
  246. 21.2: The 3rd Law of Thermodynamics Puts Entropy on an Absolute Scale
  247. 21.3: The Entropy of a Phase Transition can be Calculated from the Enthalpy of the Phase Transition
  248. 21.4: The Debye Function is Used to Calculate the Heat Capacity at Low Temperatures
  249. 21.5: Practical Absolute Entropies Can Be Determined Calorimetrically
  250. 21.6: Practical Absolute Entropies of Gases Can Be Calculated from Partition Functions
  251. 21.7: Standard Entropies Depend Upon Molecular Mass and Structure
  252. 21.8: Spectroscopic Entropies sometimes disgree with Calorimetric Entropies
  253. 21.9: Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions
  254. 21.10: Entropy and the Third Law of Thermodynamics (Exercises)
  255. 22: Helmholtz and Gibbs Energies
  256. 22.1: Helmholtz Energy
  257. 22.2: Gibbs Energy Determines the Direction of Spontaneity at Constant Pressure and Temperature
  258. 22.3: The Maxwell Relations
  259. 22.4: The Enthalpy of an Ideal Gas is Independent of Pressure
  260. 22.5: Thermodynamic Functions have Natural Variables
  261. 22.6: The Standard State for a Gas is an Ideal Gas at 1 Bar
  262. 22.7: The Gibbs-Helmholtz Equation
  263. 22.8: Fugacity Measures Nonideality of a Gas
  264. 23: Phase Equilibria
  265. 23.1: A Phase Diagram Summarizes the Solid-Liquid-Gas Behavior of a Substance
  266. 23.2: Gibbs Energies and Phase Diagrams
  267. 23.3: The Chemical Potentials of a Pure Substance in Two Phases in Equilibrium
  268. 23.4: The Clausius-Clapeyron Equation
  269. 23.5: Chemical Potential Can be Evaluated From a Partition Function
  270. 23.6: Phase Equilibria (Exercises)
  271. 24: Solutions I - Volatile Solutes
  272. 24.1: A Mixture is a Combination of Two or More Substances
  273. 24.2: The Gibbs-Duhem Equation Relates Chemical Potential and Composition at Equilibrium
  274. 24.3: Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears
  275. 24.4: Ideal Solutions obey Raoult's Law
  276. 24.5: Most Solutions are Not Ideal
  277. 24.6: Vapor Pressures of Volatile Binary Solutions
  278. 24.7: Activities of Nonideal Solutions
  279. 24.8: Activities are Calculated with Respect to Standard States
  280. 24.9: Gibbs Energy of Mixing of Binary Solutions in Terms of the Activity Coefficient
  281. 24.10: Solutions I- Liquid-Liquid Solutions (Exercises)
  282. 25: Solutions II - Nonvolatile Solutes
  283. 25.1: Standard State of Nonvolatile Solutions
  284. 25.2: The Activities of Nonvolatile Solutes
  285. 25.3: Colligative Properties Depend only on Number Density
  286. 25.4: Osmotic Pressure can Determine Molecular Masses
  287. 25.5: Electrolytes Solutions are Nonideal at Low Concentrations
  288. 25.6: The Debye-Hückel Theory
  289. 25.7: Extending Debye-Hückel Theory to Higher Concentrations
  290. 25.8: Homework Problems
  291. 26: Chemical Equilibrium
  292. 26.1: Equilibrium Results when Gibbs Energy is Minimized
  293. 26.2: An Equilibrium Constant is a Function of Temperature Only
  294. 26.3: Standard Gibbs Energies of Formation Can Be Used to Calculate Equilibrium Constants
  295. 26.4: Gibbs Energy of a Reaction vs. Extent of Reaction is a Minimum at Equilibrium
  296. 26.5: Reaction Quotient and Equilibrium Constant Ratio Determines Reaction Direction
  297. 26.6: The Sign of ΔG and not ΔG° Determines the Direction of Reaction Spontaneity
  298. 26.7: The van 't Hoff Equation
  299. 26.8: Equilibrium Constants in Terms of Partition Functions
  300. 26.9: Molecular Partition Functions and Related Thermodynamic Data Are Extensively Tabulated
  301. 26.10: Real Gases Are Expressed in Terms of Partial Fugacities
  302. 26.11: Thermodynamic Equilibrium Constants Are Expressed in Terms of Activities
  303. 26.12: Activities are Important for Ionic Species
  304. 26.13: Homework Problems
  305. 27: The Kinetic Theory of Gases
  306. 27.1: The Average Translational Kinetic Energy of a Gas
  307. 27.2: The Gaussian Distribution of One Component of the Molecular Velocity
  308. 27.3: The Distribution of Molecular Speeds is Given by the Maxwell-Boltzmann Distribution
  309. 27.4: The Frequency of Collisions with a Wall
  310. 27.5: The Maxwell-Boltzmann Distribution Has Been Verified Experimentally
  311. 27.6: Mean Free Path
  312. 27.7: Rates of Gas-Phase Chemical Reactions
  313. 27.8: The Kinetic Theory of Gases (Exercises)
  314. 28: Chemical Kinetics I - Rate Laws
  315. 28.1: The Time Dependence of a Chemical Reaction is Described by a Rate Law
  316. 28.2: Rate Laws Must Be Determined Experimentally
  317. 28.3: First-Order Reactions Show an Exponential Decay of Reactant Concentration with Time
  318. 28.4: Different Rate Laws Predict Different Kinetics
  319. 28.5: Reactions can also be Reversible
  320. 28.6: The Rate Constants of a Reversible Reaction Can Be Determined Using Relaxation Techniques
  321. 28.7: Rate Constants Are Usually Strongly Temperature Dependent
  322. 28.8: Transition-State Theory Can Be Used to Estimate Reaction Rate Constants
  323. 28.9: Chemical Kinetics I - Rate Laws (Exercises)
  324. 29: Chemical Kinetics II- Reaction Mechanisms
  325. 29.1: A Mechanism is a Sequence of Elementary Reactions
  326. 29.2: The Principle of Detailed Balance
  327. 29.3: Multiple Mechanisms are often Indistinguishable
  328. 29.4: The Steady-State Approximation
  329. 29.5: Rate Laws Do Not Imply Unique Mechanism
  330. 29.6: The Lindemann Mechanism
  331. 29.7: Some Reaction Mechanisms Involve Chain Reactions
  332. 29.8: A Catalyst Affects the Mechanism and Activation Energy
  333. 29.9: The Michaelis-Menten Mechanism for Enzyme Catalysis
  334. 29.10: Chemical Kinetics II- Reaction Mechanisms (Exercises)
  335. 30: Gas-Phase Reaction Dynamics
  336. 30.1: The Rate of Bimolecular Gas-Phase Reaction Can Be Estimated Using Hard-Sphere Collision Theory and an Energy-Dependent Reaction Cross Section
  337. 30.2: A Reaction Cross Section Depends Upon the Impact Parameter
  338. 30.3: The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules
  339. 30.4: The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction
  340. 30.5: A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System
  341. 30.6: Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines
  342. 30.7: Reactions Can Produce Vibrationally Excited Molecules
  343. 30.8: The Velocity and Angular Distribution of the Products of a Reactive Collision
  344. 30.9: Not All Gas-Phase Chemical Reactions are Rebound Reactions
  345. 30.10: The Potential-Energy Surface Can Be Calculated Using Quantum Mechanics
  346. 30.11: Gas-Phase Reaction Dynamics (Exercises)
  347. 31: Solids and Surface Chemistry
  348. 31.1: The Unit Cell is the Fundamental Building Block of a Crystal
  349. 31.2: The Orientation of a Lattice Plane is Described by its Miller Indices
  350. 31.3: The Spacing Between Lattice Planes Can Be Determined from X-Ray Diffraction Measurements
  351. 31.4: The Total Scattering Intensity is Related to the Periodic Structure of the Electron Density in the Crystal
  352. 31.5: The Structure Factor and the Electron Density Are Related by a Fourier Transform
  353. 31.6: Atoms and Molecules can Physisorb or Chemisorb to a Surface
  354. 31.7: Isotherms are Plots of Surface Coverage as a Function of Gas Pressure at Constant Temperature
  355. 31.8: Using Langmuir Isotherms to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions
  356. 31.9: The Structure of a Surface is Different from that of a Bulk Solid
  357. 31.10: The Haber-Bosch Reaction Can Be Surface Catalyzed
  358. 31.11: Homework Problems
  359. 32: Math Chapters
  360. 32.1: Complex Numbers
  361. 32.2: Probability and Statistics
  362. 32.3: Partial Differentiation
  363. 32.4: Numerical Methods
  364. 32.5: Vectors
  365. 32.6: Spherical Coordinates
  366. 32.7: Determinants
  367. 32.8: Matrices
  368. 32.9: Series and Limits
  369. 32.10: Fourier Analysis
  370. 32.10.1: Fourier Analysis in Matlab
  371. 32.10.2: Fourier Synthesis of Periodic Waveforms
  372. 32.11: The Binomial Distribution and Stirling's Appromixation
  373. 33: Appendices
  374. 33.1: Deriving Planck's Distribution Law
  375. 33.2: Bra-Ket Notation
  376. 34: Reference Tables
  377. 34.1: Table 1 Regions of the Electromagnetic Spectrum
  378. 34.2: Table 2. Characteristics of Electromagnetic Radiation
  379. 34.3: Table 5. Some Units Commonly Used in Quantum Chemistry
  380. 34.4: Table 8
  381. 34.5: Table 9. The Greek Alphabet
  382. 34.6: Table 10 - Spherical Harmonic Wavefunctions
  383. 34.7: Table 11 Radial functions for one-electron atoms and ions.
  384. 34.8: Table 14. The ground-state electron configurations of the elements.
  385. 34.9: Solubility Products
  386. Back Matter
  387. Index
  388. Glossary
  389. Detailed Licensing
  390. Detailed Licensing