Physical Chemistry

by Delmar Larsen

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This Physical Chemistry textbook addressed the study of macroscopic, and particulate phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mechanics, analytical dynamics and chemical equilibria.

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LibreTexts Inc
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Chemistry, Physical and Theoretical Chemistry Textbook Maps
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CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
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Tweens profiles and older, judged from its title and subjects

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.E: 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.E: 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.E: The Schrödinger Equation and a Particle in a Box (Exercises)
  35. 3.S: 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.E: Postulates and Principles of Quantum Mechanics (Exercises)
  44. 4.S: 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.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
  56. 5.S: 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.E: The Hydrogen Atom (Exercises)
  66. 6.S: 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.E: Approximation Methods (Exercises)
  73. 7.S: 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.E: Multielectron Atoms (Exercises)
  87. 8.S: 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.E: Chemical Bond in Diatomic Molecules (Exercises)
  106. 9.S: 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.E: Bonding in Polyatomic Molecules (Exercises)
  116. 10.S: 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 (Double Zeta and Split-Valence)
  121. 11.4: Orbital Polarization and Diffuse Terms in Basis Sets
  122. 11.E: 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.E: Group Theory - The Exploitation of Symmetry (Exercises)
  140. 12.S: Group Theory - The Exploitation of Symmetry (Summary)
  141. 12.T: Character Tables
  142. 12.T: 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.E: Molecular Spectroscopy (Exercises)
  159. 13.S: 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.E: Nuclear Magnetic Resonance Spectroscopy (Exercises)
  171. 14.S: 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.E: Lasers, Laser Spectroscopy, and Photochemistry (Exercises)
  181. 15.S: Lasers, Laser Spectroscopy, and Photochemistry (Summary)
  182. 16: The Properties of Gases
  183. 16.1: All Dilute Gases Behave Ideally
  184. 16.2: van der Waals and Redlich-Kwong Equations of State
  185. 16.3: A Cubic Equation of State
  186. 16.4: The Law of Corresponding States
  187. 16.5: The Second Virial Coefficient
  188. 16.6: The Repulsive Term in the Lennard-Jones Potential
  189. 16.7: Van der Waals Constants in Terms of Molecular Parameters
  190. 16.E: The Properties of Gases (Exercises)
  191. 16.S: The Properties of Gases (Summary)
  192. 17: Boltzmann Factor and Partition Functions
  193. 17.1: The Boltzmann Factor is used to Approximate the Fraction of Particles in a Large System
  194. 17.2: The Boltzmann Distribution represents a Thermally Equilibrated Distribution
  195. 17.3: The Average Ensemble Energy is Equal to the Observed Energy of a System
  196. 17.4: Heat Capacity at Constant Volume is the Change in Internal Energy with Temperature
  197. 17.5: Pressure can be Expressed in Terms of the Canonical Partition Function
  198. 17.6: The Partition Function of Distinguishable, Independent Molecules is the Product of the Molecular Partition Functions
  199. 17.7: Partition Functions of Indistinguishable Molecules Must Avoid Over Counting States
  200. 17.8: Partition Functions can be Decomposed into Partition Functions of Each Degree of Freedom
  201. 17.E: Boltzmann Factor and Partition Functions (Exercises)
  202. 17.S: Boltzmann Factor and Partition Functions (Summary)
  203. 18: Partition Functions and Ideal Gases
  204. 18.1: Translational Partition Functions of Monotonic Gases
  205. 18.2: Most Atoms are in the Ground Electronic State
  206. 18.3: The Energy of a Diatomic/Polyatomic Molecule Can Be Approximated as a Sum of Separate Terms
  207. 18.4: Most Molecules are in the Ground Vibrational State
  208. 18.5: Most Molecules are Rotationally Excited at Ordinary Temperatures
  209. 18.6: Rotational Partition Functions of Diatomic Gases Contain a Symmetry Number
  210. 18.7: Vibrational Partition Functions of Polyatomic Molecules Include the Partition Function for Each Normal Coordinate
  211. 18.8: Rotational Partition Functions of Polyatomic Molecules Depend on the Sphar of the Molecule
  212. 18.9: Molar Heat Capacities
  213. 18.10: Ortho and Para Hydrogen
  214. 18.11: The Equipartition Principle
  215. 18.E: Partition Functions and Ideal Gases (Exercises)
  216. 19: The First Law of Thermodynamics
  217. 19.1: Overview of Classical Thermodynamics
  218. 19.2: Pressure-Volume Work
  219. 19.3: Work and Heat are not State Functions
  220. 19.4: Energy is a State Function
  221. 19.5: An Adiabatic Process is a Process in which No Energy as Heat is Transferred
  222. 19.6: The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion
  223. 19.7: Work and Heat Have a Simple Molecular Interpretation
  224. 19.8: Pressure-Volume Work
  225. 19.9: Heat Capacity is a Path Function
  226. 19.10: Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition
  227. 19.11: Enthalpy Changes for Chemical Equations are Additive
  228. 19.12: Heats of Reactions Can Be Calculated from Tabulated Heats of Formation
  229. 19.13: The Temperature Dependence of ΔH
  230. 19.14: Enthalpy is a State Function
  231. 19.E: The First Law of Thermodynamics (Exercises)
  232. 20: Entropy and The Second Law of Thermodynamics
  233. 20.1: Energy Does not Determine Spontaneity
  234. 20.2: Nonequilibrium Isolated Systems Evolve in a Direction That Increases Their Energy Dispersal
  235. 20.3: Unlike heat, Entropy is a State Function
  236. 20.4: The Second Law of Thermodynamics
  237. 20.5: The Famous Equation of Statistical Thermodynamics is S=k ln W
  238. 20.6: We Must Always Devise a Reversible Process to Calculate Entropy Changes
  239. 20.7: Thermodynamics Provides Insight into the Conversion of Heat into Work
  240. 20.8: Entropy Can Be Expressed in Terms of a Partition Function
  241. 20.9: The Statistical Definition of Entropy is Analogous to the Thermodynamic Definition
  242. 20.E: Entropy and The Second Law of Thermodynamics (Exercises)
  243. 21: Entropy and the Third Law of Thermodynamics
  244. 21.1: Entropy Increases with Increasing Temperature
  245. 21.2: The 3rd Law of Thermodynamics Puts Entropy on an Absolute Scale
  246. 21.3: The Entropy of a Phase Transition can be Calculated from the Enthalpy of the Phase Transition
  247. 21.4: The Debye Function is Used to Calculate the Heat Capacity at Low Temperatures
  248. 21.5: Practical Absolute Entropies Can Be Determined Calorimetrically
  249. 21.6: Practical Absolute Entropies of Gases Can Be Calculated from Partition Functions
  250. 21.7: Standard Entropies Depend Upon Molecular Mass and Structure
  251. 21.8: Spectroscopic Entropies sometimes disgree with Calorimetric Entropies
  252. 21.9: Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions
  253. 21.E: Entropy and the Third Law of Thermodynamics (Exercises)
  254. 22: Helmholtz and Gibbs Energies
  255. 22.1: Helmholtz Energy
  256. 22.2: Gibbs Energy Determines the Direction of Spontaneity at Constant Pressure and Temperature
  257. 22.3: The Maxwell Relations
  258. 22.4: The Enthalpy of an Ideal Gas is Independent of Pressure
  259. 22.5: Thermodynamic Functions have Natural Variables
  260. 22.6: The Standard State for a Gas is an Ideal Gas at 1 Bar
  261. 22.7: The Gibbs-Helmholtz Equation
  262. 22.8: Fugacity Measures Nonideality of a Gas
  263. 23: Phase Equilibria
  264. 23.1: A Phase Diagram Summarizes the Solid-Liquid-Gas Behavior of a Substance
  265. 23.2: Gibbs Energies and Phase Diagrams
  266. 23.3: The Chemical Potentials of a Pure Substance in Two Phases in Equilibrium
  267. 23.4: The Clausius-Clapeyron Equation
  268. 23.5: Chemical Potential Can be Evaluated From a Partition Function
  269. 23.E: Phase Equilibria (Exercises)
  270. 24: Solutions I - Volatile Solutes
  271. 24.1: A Mixture is a Combination of Two or More Substances
  272. 24.2: The Gibbs-Duhem Equation Relates Chemical Potential and Composition at Equilibrium
  273. 24.3: Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears
  274. 24.4: Ideal Solutions obey Raoult's Law
  275. 24.5: Most Solutions are Not Ideal
  276. 24.6: Vapor Pressures of Volatile Binary Solutions
  277. 24.7: Activities of Nonideal Solutions
  278. 24.8: Activities are Calculated with Respect to Standard States
  279. 24.9: Gibbs Energy of Mixing of Binary Solutions in Terms of the Activity Coefficient
  280. 24.E: Solutions I- Liquid-Liquid Solutions (Exercises)
  281. 25: Solutions II - Nonvolatile Solutes
  282. 25.1: Standard State of Nonvolatile Solutions
  283. 25.2: The Activities of Nonvolatile Solutes
  284. 25.3: Colligative Properties Depend only on Number Density
  285. 25.4: Osmotic Pressure can Determine Molecular Masses
  286. 25.5: Electrolytes Solutions are Nonideal at Low Concentrations
  287. 25.6: The Debye-Hückel Theory
  288. 25.7: Extending Debye-Hückel Theory to Higher Concentrations
  289. 25.8: Homework Problems
  290. 26: Chemical Equilibrium
  291. 26.1: Equilibrium Results when Gibbs Energy is Minimized
  292. 26.2: An Equilibrium Constant is a Function of Temperature Only
  293. 26.3: Standard Gibbs Energies of Formation Can Be Used to Calculate Equilibrium Constants
  294. 26.4: Gibbs Energy of a Reaction vs. Extent of Reaction is a Minimum at Equilibrium
  295. 26.5: Reaction Quotient and Equilibrium Constant Ratio Determines Reaction Direction
  296. 26.6: The Sign of ΔG and not ΔG° Determines the Direction of Reaction Spontaneity
  297. 26.7: The van 't Hoff Equation
  298. 26.8: Equilibrium Constants in Terms of Partition Functions
  299. 26.9: Molecular Partition Functions and Related Thermodynamic Data Are Extensively Tabulated
  300. 26.10: Real Gases Are Expressed in Terms of Partial Fugacities
  301. 26.11: Thermodynamic Equilibrium Constants Are Expressed in Terms of Activities
  302. 26.12: Activities are Important for Ionic Species
  303. 26.13: Homework Problems
  304. 27: The Kinetic Theory of Gases
  305. 27.1: The Average Translational Kinetic Energy of a Gas
  306. 27.2: The Gaussian Distribution of One Component of the Molecular Velocity
  307. 27.3: The Distribution of Molecular Speeds is Given by the Maxwell-Boltzmann Distribution
  308. 27.4: The Frequency of Collisions with a Wall
  309. 27.5: The Maxwell-Boltzmann Distribution Has Been Verified Experimentally
  310. 27.6: Mean Free Path
  311. 27.7: Rates of Gas-Phase Chemical Reactions
  312. 27.E: The Kinetic Theory of Gases (Exercises)
  313. 28: Chemical Kinetics I - Rate Laws
  314. 28.1: The Time Dependence of a Chemical Reaction is Described by a Rate Law
  315. 28.2: Rate Laws Must Be Determined Experimentally
  316. 28.3: First-Order Reactions Show an Exponential Decay of Reactant Concentration with Time
  317. 28.4: Different Rate Laws Predict Different Kinetics
  318. 28.5: Reactions can also be Reversible
  319. 28.6: The Rate Constants of a Reversible Reaction Can Be Determined Using Relaxation Techniques
  320. 28.7: Rate Constants Are Usually Strongly Temperature Dependent
  321. 28.8: Transition-State Theory Can Be Used to Estimate Reaction Rate Constants
  322. 28.E: Chemical Kinetics I - Rate Laws (Exercises)
  323. 29: Chemical Kinetics II- Reaction Mechanisms
  324. 29.1: A Mechanism is a Sequence of Elementary Reactions
  325. 29.2: The Principle of Detailed Balance
  326. 29.3: Multiple Mechanisms are often Indistinguishable
  327. 29.4: The Steady-State Approximation
  328. 29.5: Rate Laws Do Not Imply Unique Mechanism
  329. 29.6: The Lindemann Mechanism
  330. 29.7: Some Reaction Mechanisms Involve Chain Reactions
  331. 29.8: A Catalyst Affects the Mechanism and Activation Energy
  332. 29.9: The Michaelis-Menten Mechanism for Enzyme Catalysis
  333. 29.E: Chemical Kinetics II- Reaction Mechanisms (Exercises)
  334. 30: Gas-Phase Reaction Dynamics
  335. 30.1: The Rate of Bimolecular Gas-Phase Reaction Can Be Estimated Using Hard-Sphere Collision Theory and an Energy-Dependent Reaction Cross Section
  336. 30.2: A Reaction Cross Section Depends Upon the Impact Parameter
  337. 30.3: The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules
  338. 30.4: The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction
  339. 30.5: A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System
  340. 30.6: Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines
  341. 30.7: Reactions Can Produce Vibrationally Excited Molecules
  342. 30.8: The Velocity and Angular Distribution of the Products of a Reactive Collision
  343. 30.9: Not All Gas-Phase Chemical Reactions are Rebound Reactions
  344. 30.10: The Potential-Energy Surface Can Be Calculated Using Quantum Mechanics
  345. 30.E: Gas-Phase Reaction Dynamics (Exercises)
  346. 31: Solids and Surface Chemistry
  347. 31.1: The Unit Cell is the Fundamental Building Block of a Crystal
  348. 31.2: The Orientation of a Lattice Plane is Described by its Miller Indices
  349. 31.3: The Spacing Between Lattice Planes Can Be Determined from X-Ray Diffraction Measurements
  350. 31.4: The Total Scattering Intensity is Related to the Periodic Structure of the Electron Density in the Crystal
  351. 31.5: The Structure Factor and the Electron Density Are Related by a Fourier Transform
  352. 31.6: Atoms and Molecules can Physisorb or Chemisorb to a Surface
  353. 31.7: Isotherms are Plots of Surface Coverage as a Function of Gas Pressure at Constant Temperature
  354. 31.8: Using Langmuir Isotherms to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions
  355. 31.9: The Structure of a Surface is Different from that of a Bulk Solid
  356. 31.10: The Haber-Bosch Reaction Can Be Surface Catalyzed
  357. 31.E: Homework Problems
  358. 32: Math Chapters
  359. 32.1: Complex Numbers
  360. 32.2: Probability and Statistics
  361. 32.3: Partial Differentiation
  362. 32.4: Numerical Methods
  363. 32.5: Vectors
  364. 32.6: Spherical Coordinates
  365. 32.7: Determinants
  366. 32.8: Matrices
  367. 32.9: Series and Limits
  368. 32.10: Fourier Analysis
  369. 32.10.1: Fourier Analysis in Matlab
  370. 32.10.2: Fourier Synthesis of Periodic Waveforms
  371. 32.11: The Binomial Distribution and Stirling's Appromixation
  372. 33: Appendices
  373. 33.1: Deriving Planck's Distribution Law
  374. 33.2: Bra-Ket Notation
  375. Back Matter
  376. Index
  377. Glossary
  378. Detailed Licensing