Chapter
Early Development of Analysis
Julius Wilhelm Richard Dedekind (1831–1916CE)
Leopold Kronecker (1823–91CE)
1.2.2.3 God Made the Integers, All Else Is the Work of Man
“All Else Is the Work of Man”
1.2.2.4 Classification of Real and Imaginary Numbers
1.2.3 Nature Is Recursion Relationships
1.5 A Prime Example of the Application of Mathematics to the Underlying Reality of Nature
1.5.2 The Distribution of Prime Numbers
Karl Friedrich Gauss (1777–1855CE)
Leonhard Euler (1707–83CE)
Bernard Riemann (1826–66CE)
1.6 Parallels in the Mathematical Descriptions of Prime Numbers and Nature
1.7 Mathematics and Truth
2 - Five Important Equations in Thermodynamics
Inexact and Exact Differential Equations
State Functions and Reference Tables
Intensive and Extensive Properties of a System
The Five Important Equations
Heat as a Substance—Phlogiston and Caloric Theories
Mechanical Heat as Energy of Motion
2.2 The Experimental Form of the First Law of Thermodynamics
2.3 The Calculus Form of the First Law of Thermodynamics
2.4 Steam Power and the Industrial Revolution
2.5 The Carnot Cycle and Heat, Work, and Entropy
Nicolas Léonard Sadi Carnot
Benoit Paul Émile Clapeyron
2.5.1 Entropy: The Quantification of the Carnot Cycle by Application of the First Law of Thermodynamics
2.5.2 Entropy Is a State Function
2.6 The Carnot Cycle and the Second Law of Thermodynamics
2.7 The Second Law of Thermodynamics and the Arrow of Time
2.8.1 Thermodynamic Interpretation of Entropy
2.8.2 Molecular Interpretation of Entropy
2.9.1 Entropy of Mixing in the Gas Phase
2.9.2 Entropy of Mixing Two Liquids
2.9.2.1 Particles of Unequal Size
2.9.2.2 Particles of Equal Size
2.10 Ambiguity of “Randomness” and “Order” as a Description of Entropy
2.10.1 The Mixing of Two Liquids and the Chess Board
2.10.2 The Transferring of Information and the Chess Board
2.10.3 The Degeneracy of States and the Chess Board
2.10.4 “Order” and “Disorder” Are Generations Apart
2.11 Enthalpy From the First Law of Thermodynamics: The Joule–Thomson Expansion Experiment
2.12 Combined First and Second Laws of Thermodynamics: Work and the Free Energies
2.12.1 Helmholtz Free Energy
2.14 Maxwell Relationships
2.14.3 Helmholtz Free Energy
2.15 Thermodynamic Equation of State
2.16 Isothermal Compressibility and Isobaric Thermal Expansion and the Difference in Heat Capacities Cp−CV
2.17 The Joule–Thomson Coefficient
2.18 Expansion of the Thermodynamic Functions
3 - Gibbs Free Energy, Work, and Equilibrium
3.1 Criteria for Stability of a System—Clausius Inequality
3.2 The Gibbs Free Energy and the Chemical Potential
3.3 The Clausius Equation for a Phase Transition
3.4 Phase Diagrams and the Gibbs Phase Rule
3.5 The Gibbs Free Energy and the Concentration Potential
3.6 The Gibbs Free Energy and Reference States
3.7 The Gibbs Free Energy and Equilibrium
3.8 State Functions, Standard States, and Thermodynamic Calculations
3.9 Temperature Dependence of the Equilibrium Constant
3.10 The Osmotic Pressure—Ideal Solutions
3.11 The Osmotic Pressure and Work
3.12 Bond Energy/Enthalpy and Work
3.13 Burning of Fossil Fuels—Heterogeneous Phases
3.13.1 Coal Versus Natural Gas
3.13.2 Group Energies of Alkanes
3.13.3 Energy Density of Mixed Alcohol–Gasoline Fuels: The E‐fuels
3.13.4 Fossil Fuels, Oxidation States, and Energy Content
3.14 The Chemical Potential With an External Potential
3.14.2 Gravitational Force
3.15 The Anatomy of an Oxidation–Reduction Reaction
3.16 The Gibbs Free Energy and Electric Work
3.16.1 The Hydrogen Electrode
3.16.2 The Nernst Equation
3.17 The Thermodynamic Functions from the Temperature Dependence of Eo
3.18 The Heat Change of a Redox Reaction During the Reaction
3.19 Oxidation–Reduction Reactions and Anaerobic Decomposition
3.19.1 Biochemical Oxygen Demand
3.19.2 Chemical Oxygen Demand
4 - Thermodynamics of the Gas State
4.1.1 Empirical Expression of the Ideal Gas Law
4.1.2 The Ideal Gas Law and the Kinetic Theory of Gases
4.2 Real Gases and the Ideal Gas Law
4.3 From Generalized Differential Equations to Practical Integrated Expressions
4.3.1 Choice of a Theoretical Expression
4.3.2 Choice of Experimental Conditions
4.3.3 Final Step—The Integral Form
4.4 Ideal Gas Law and Dalton's Law of Partial Pressures
4.5 Dalton's Law of Partial Pressures and Gas Phase Chemical Reactions: Dimerization
4.6 Dalton's Law of Partial Pressures and Gas Phase Chemical Reactions: Extent of Reaction
4.7 Adiabatic Expansion/Contraction of an Ideal Gas
4.8 Entropy Change of the Ideal Gas: Reversible and Irreversible Processes
4.9 The Thermodynamic Representation of a Real Gas: Fugacity
4.10 Reference State for a Real Gas
4.11 Determination of the Activity Coefficient for Real Gases
4.11.1 Approximate Method
4.12 Virial Expansion Representation of Real Gases
4.13 Analytical Expressions for Real Gases—The van der Waals Equation
4.14 Internal Pressure and Second Virial Coefficient for the van der Waals Gas
4.15 Activity Coefficient and the van der Waals Gas
4.16 Work, Heat, and the van der Waals Gas for an Isothermal Reversible Process
4.17 The Physics Behind the van der Waals Gas for an Isothermal Reversible Process
4.18 Generalized Relationship Between CP and CV With Application to Ideal and van der Waals Gases
4.19 The Stability of the van der Waals Gas
4.20 Anatomy of the P–V Plot for Real Gases
4.21 The van der Waals Gas and the Critical Point
4.22 The van der Waals Gas and Phase Transitions
4.23 Reduced van der Waals Equation of State
4.24 Relationship Between the Boyle Temperature and the Critical Temperature for a van der Waals Gas
4.25 The Joule–Thomson Inversion Temperature and the van der Waals Gas
4.26 Other Expressions for Real Gas Systems
The Virial Expansion with the Lennard-Jones 6-12 Potential
5 - Thermodynamics of the Liquid State
5.1 The Pressure–Temperature Dependence of the Phase Transition: The Clapeyron and Clausius–Clapeyron Equations
5.1.1 The Clapeyron Equation—Incompressible Phases
5.1.2 Clausius–Clapeyron Equation—Compressible Phases
5.2 Gibbs Free Energy of Mixing for Ideal and Real Solutions
5.2.1 Gibbs Free Energy of Mixing: Ideal Solutions
5.2.2 Gibbs Free Energy of Mixing: Real Solutions
5.3 The Gibbs–Duhem and Duhem–Margules Equations
5.4 Duhem–Margules Equation for Ideal and Real Solutions
5.4.1 Real Solution at the Infinite Dilution Limit
5.4.2 Ideal Solution—Raoult's Law and Henry's Law
5.4.2.1 Different Forms of Henry's Law
5.4.2.2 Gas Solubility and Henry's Law
5.5 Real Solutions and Raoult's and Henry's Laws: A Molecular Interpretation
5.5.1 Molecular Interpretation of Raoult's Law
5.5.2 Molecular Interpretation of Henry's Law
5.5.3 Temperature Dependence of Henry's Law Constant
5.6 Colligative Properties of Solutions Using General Thermodynamic Principles
5.6.1 Changes in the Solvent Upon Introduction of a Solute—Raoult's Law
5.6.2 Solute Effects on the Transition Temperature
5.7 Colligative Properties and Number Average Molecular Weight
5.8 Nonideal Solutions: The Practical Osmotic Coefficient
5.8.1 Thermodynamic Representation of Nonideality
5.8.2 Statistical Mechanics Representation of Nonideality
Molecular Model Representation: Dimer Model for the Activity Coefficient
Molecular Model Representation: Dimer Model for the Practical Osmotic Pressure
Molecular Model Representation: Polymer Model for the Practical Osmotic Pressure
5.9 Solubilities of Gases, Liquids, and Solids
5.10 The Solubility Product
5.10.2 Complex Formation and Solubility
5.11 The Partition Coefficient
5.12 Acid–Base Equilibrium
5.13 Ionic Solutions and Nonideality: The Debye–Hückel Limiting Law
Nonideality and the Mean Ion Activity Coefficient
Nonideality and the Debye–Hückel Limiting Law
6.2 The Lattice Constants and Unit Cell of Crystalline Solids
6.5 Lattice Energy for Ionic Crystals
Madelung Constant for Simple Cubic Structures
6.10 Heat Capacity of Solids
6.11 Adsorption on Lattice Surfaces
7.1.1 Black Body Radiation Spectrum
7.1.2 Photoelectric Effect
7.1.3 Heat Capacity of Solids (ca1860s)
7.2.1 Black Body Radiation Spectrum
7.2.2 Photoelectric Effect
7.2.3 Heat Capacity of Solids
7.4 The Wave–Particle Duality of Light from Planck's Radiation Law
7.5 Symmetrization of Nature—the Wave–Particle Duality of Matter
7.5.1 Ad Hoc Derivation of the de Broglie Wavelength
7.5.2 de Broglie Derivation—1924 Doctoral Thesis
7.5.3 Experimental Verification of the de Broglie Wavelength
7.5.4 Why Can Rory McIlroy Hit a Golf Ball on a Tee?
The de Broglie Wavelength of a Moving Golf Ball
The Resolution of the Rory McIlroy Paradox
7.5.5 The de Broglie Wavelength and the Stability of the Bohr Orbits
7.6 The Schrödinger Wave Equation
7.7 Quantum Mechanics and Linear Operators
7.8 Postulates of Quantum Mechanics
7.9 Heisenberg Matrix Mechanics
7.10 The Heisenberg Indeterminacy Principle (Tolerance Principle)
7.11 The Hamiltonian, the Wave Function, the Probability and Graphics
Kinetic Energy and Curvature
Energy is Conserved—Potential Energy and Curvature
The Slope of the Wave Function
Probability and Potential Energy
Orthonormality of Wave Functions
Bohr Correspondence Principle—the Lore of Large Quantum Numbers
7.12 The Spin Quantum Number
7.13 Superposition of Wave Functions
7.15 What Is the Wave Function?
7.15.1 The 1927 Solvay Conference
7.15.2 The Copenhagen Interpretation
The Copenhagen Interpretation Extension: The Conscious Observer
7.15.3 Beyond the Copenhagen Interpretation
Sum Over Past Histories—Feynman Diagrams
Holistic Universe Interpretation
7.16 Indeterminacy in Measurement
7.17 Indeterminacy in Nature
8 - Quantum Systems With Constant Potential
8.1 The Free Particle in Three Dimensions
8.2 The One-Dimensional Schrödinger Equation With a Step Constant Potential
8.3 The One-Dimensional Schrödinger Equation With a Square Barrier
8.3.2 E﹥V: Transmission Over a Square Barrier
8.4 The One-Dimensional Schrödinger Equation With a Finite Symmetric Square Well
8.4.1 E﹥0: Transmission Over a Square Well
8.4.2 E<0 Bound Particles
8.5 The One-Dimensional Schrödinger Equation for a Particle-in-a-Symmetric Box
8.6 Orthonormal Property of the Particle-in-a-Box Wave Functions
8.7 Spatial Degeneracy in an Arbitrary Three-Dimensional Rectangular Box
8.8 Expectation Values and Probability
8.9 Degeneracy Due to Exchange of Indistinguishable Particles
8.10 Degeneracy Due to Spin of the Particles
8.11 Product Wave Functions in the Bra-Ket Notation
8.12 Real Systems and Perturbation Theory
8.13 First-Order Correction to the Wave Function With the Bra-Ket Notation
8.14 Shapes of Perturbation Potential and the Perturbed Wave Function
8.15 Slater Determinants and Particle Symmetry
9 - Quantum Energies for Central Potentials
9.1 Central Potential Defined
9.2 Polar Coordinate System
9.3 The Hamiltonian Operator in Polar Coordinates
9.4 Solutions to the φ-Equation and θ-Equation: Spherical Harmonics
9.4.1 Generating Equation for Legendre and Associated Legendre Polynomials
9.4.2 Recursion Relationship for Legendre Polynomials
9.5 Rotation Energies of a Rigid Rotor
9.6 Solution to the r-Equation: Inverse Distance Central Potential
9.6.1 Outer Solution: Asymptotic Limit ρ→∞
9.6.2 Inner Solution: Generating Functions for Laguerre and Associated Laguerre Polynomials
9.6.3 Recursion Relationship for Laguerre Polynomials
9.6.4 Normalized Radial Wave Function
9.7 The Energy for the Coulomb Potential From the Recursion Relationship of Coefficients
9.8 Vibrational States and the Harmonic Oscillator
9.8.1 Harmonic Oscillator in Reduced Coordinates
9.8.2 Harmonic Oscillator in the Asymptotic Limit ξ→∞
9.8.3 Harmonic Oscillator: Inner Solution to the Wave Function
9.8.4 Recursion Relationships of Expansion Coefficients and the Energy
9.8.5 Generating Function for the Hermite Polynomials
9.8.6 Recursion Relationship for the Hermite Polynomials
9.9 Transitions Between Rotation–Vibration States: Selection Rules
9.10 Spectral Regions for Pure Rotation Transitions and Pure Vibration Transitions
9.11 The Indeterminacy Principle and the Harmonic Oscillator
9.12 Particles in a Spherical Box
9.12.1 Impenetrable Spherical Shell
9.12.2 Penetrable Spherical Shell
9.13 The Shell Model of Electrons and Nucleons
9.14 Characterization of Nuclei
9.14.2 Atomic Mass Unit Expressed as Energy
9.15 The Stability of the Nucleus
9.16 The Instability of the Nucleus
9.17.2 Carbon-14 and Fossil Fuels
10 - Electronic and Nuclear States
10.1 Quantum Mechanics, Special Relativity, and Description of the Electron
10.1.1 Dirac's Approach to Solve the Relativistic Schrödinger Equation
10.1.2 The Electron “Spin”
10.1.3 Prediction of Antimatter
10.1.5 Time-Dependent Dirac Equation for a Free Particle in One Dimension
10.1.6 The Nodes and Bound Particles
10.1.7 The Electron in an Electric Field—The Beginning of Quantum Electrodynamics
10.1.8 The Relativistic de Broglie Wavelength
10.1.9 Beauty in the Equations
10.2 Paul Dirac—A Concise Picture
10.3 The Schrödinger Atoms and the Periodic Table of the Elements
Ordering of Elements in the Periodic Table of the Elements
Aufbau Principle and the Periodic Table
10.5 Electron Spin: Singlet and Triplet States of Excited Helium
10.6 Spatially Directed Atomic Orbitals: 2px, 2py, and 2pz
10.7 Spatially Directed Bonding Orbitals—Hybridization
10.7.1 The sp hybrid orbital
10.7.2 The sp2 Hybrid Orbitals
10.7.4 The Geometry of the Hybrid Orbitals
10.8 The Chemical Bond: Valence Bond and Molecular Orbital Approaches
10.8.1 The Valence Bond Approach
10.8.2 The Molecular Orbital Approach
10.8.3 Comparison of the VB and LCAO–MO Approaches
10.9 LCAO–MO Description of Double and Triple Bonds
10.10 LCAO–MO for Benzene
Principal of Conservation of Probability
Linear Combination of Atomic Orbitals for the Benzene Ring
10.11 Hückel Molecular Orbital Description of Benzene
10.12 Other Effects That Alter the Electronic Energy States of Atoms and Molecules
10.13 Einstein Model for Steady-State Electronic Transitions
10.14.1 The Particles: Hadrons and Leptons
10.14.2 The Force Carrying Particles: Quarks and Bosons
10.14.3 The Standard Model
10.15 Energy From the Sun: Fusion
10.16 The Liquid Drop Model of the Nucleus and Fission
10.16.1 A Wafer Thin Mint
10.16.2 The Liquid Drop Nucleus and Nuclear Fission
10.17 Nuclear Power Unleashed
10.18 Fossil Fuels and Nuclear Fuels: A Comparison
Heat of Combustion of Methane
10.19 Energy for the Future
11 - Rotation–Vibration Spectra
11.1 The Total Hamiltonian for a Diatomic Molecule
11.2 The Interaction of a Molecule With Light—Absorption, Emission, and Scattering
11.2.1 Infrared Spectroscopy—Absorption and Emission of Light
11.2.2 Raman Spectroscopy—Scattering of Light
11.2.3 Complementary Tools—Infrared and Raman Spectroscopy
11.3 General Construct for Transitions to a New Molecular State
11.4 Selection Rules for a Diatomic Molecule in the Presence of Light
11.4.1 Translation Motion of Molecules and Light Absorption
11.4.2 Rotation Motion of Molecules and Light Absorption
11.4.3 Vibration Motion of Molecules and Light Absorption
11.5 Spectral Regions for Rotation and Vibration Transitions
11.6 Interpretation of the Infrared Spectrum: The Diatomic as an Example
11.7 Vibration–Rotation Modes of Real Diatomic Molecules
11.8 Vibration–Rotation Modes of Multiatom Molecules
12 - Classical Statistical Mechanics
12.1 Gambling—The Origin of Statistical Analysis
12.1.1 Pennies and Particles
12.1.2 Conditional Probabilities
12.1.3 Knowledge and Probabilities
12.2 Casino Games of Chance and the Principles of Statistical Mechanics
12.2.1 “True” Odds and Probabilities
12.2.2 The Lore of Large Numbers
12.2.3 “Perfect” and “Imperfect” and True Probabilities and Odds
12.2.4 The Unusual Luck of Joseph Hobson Jagger
12.2.5 Independent Probabilities for Nonuniform Distributions: Craps
12.2.6 “Or” and “And” Probabilities: Craps
12.2.7 Changing Probabilities: Blackjack and Texas Hold'em
12.2.8 Time and Ensemble Averages: The Slot Machines
12.3 Distributions, Fluctuations, and Averages
12.4 Laplace's Demon and Phase Space
12.4.2 μ-Space, the Dynamics of Individual Bees
12.4.3 γ-Space, the Dynamics of the Swarm of Bees
12.5 The Liouville Theorem
12.6 The Poincaré Recurrence Theorem
12.9 The Microcanonical Ensemble
12.9.1 The Maximum Number of Configurations
12.9.3 Randomness: You Walk Into a Bar……
12.10 The Canonical Ensemble and the Probability
12.11 The Canonical Partition Function and Thermodynamic Functions
12.12 The Canonical Partition Function and the Hamiltonian for the System
12.12.1 The Configuration Integral and the Ursell–Mayer Cluster Diagrams
12.12.2 Validity of Expressions: Check With the Particle in a Box
12.13 The Canonical Partition Function for a System of Particles
12.14 The Canonical Partition Function and the Characteristic Temperature
12.14.1 Translational States
12.14.2 Rotational States
12.14.3 Vibrational States
12.14.4 Electronic States
12.15 The Canonical Ensemble and the Equilibrium Constant
12.16 The Grand Canonical Partition Function
12.17 Coarse Grain, Fine Grain, and Averages
12.18 The Boltzmann H Theorem
12.18.1 The Boltzmann H Function
12.18.2 Collisions: The Mechanism of Change
13 - Quantum Statistical Mechanics
13.1 The Framing of the Problem of Degeneracy
13.1.1 A Tale of Two Electrons
13.2 Fermi–Dirac and Bose–Einstein Statistics and Playing Cards
13.2.1 Bose–Einstein Degeneracy
13.2.2 Fermi–Dirac Degeneracy
13.3 The Grand Partition Function: Maxwell–Boltzmann, Boltzmann, Fermi–Dirac, and Bose–Einstein Statistics
13.4 Occupation Numbers and Fermi–Dirac and Bose–Einstein Statistics
13.5 Comparison of Maxwell–Boltzmann, Fermi–Dirac, and Bose–Einstein Statistics
13.6 Relationships Between Classical Statistical Mechanics and Quantum Statistical Mechanics
13.7 The Quantum Behavior of Helium-4
13.7.1 Bose–Einstein Condensation
13.7.2 Lambda Transition for Helium-4
13.8 Pairwise Interactions Between Bound Polymer Sites: Random and Exact
13.8.1 The Scatchard Model for Binding Isotherms
13.8.2 The Exact Nearest-Neighbor Model for Binding Isotherms
14 - Nonequilibrium Thermodynamics
14.2 Nonequilibrium and Entropy Change: The Dissipation Function
14.3 Diffusion and Dissipation
14.4 Hydrodynamic Flow and the Reynolds Number
14.5 The Friction Factor for Particles at Low Reynolds Numbers
Stokes' Friction Factor for a Sphere
Perrin's Friction Factor for Ellipsoids of Revolution
Friction Factor for Long Cylinders
Friction Factor for Molecules of Arbitrary Shape: The Spherical Subunit Model
Role of Hydrodynamic Shielding
14.6 Mutual, Self, and Tracer Friction Factors
14.7 Fick's Laws of Diffusion—The Mutual Diffusion Coefficient
Spreading of a Drop of Ink
14.8 The Motion of a Particle in a Solvent: The Langevin Equation
Derivation of the Langevin Equation
Asymptotic Limits of the Langevin Equation
Time Course of Mean Square Displacement of Stokes Spheres
14.10 Principle of Minimum Entropy Production
14.11 Onsager Reciprocity Relationships
15 - Reaction Rates and Mechanisms
15.1 Determination of the Order of the Chemical Reaction
15.2 Time Course of the Zeroth-, First-, and Second-Order Reactions
15.2.1 Second-Order Reactions
15.2.2 First-Order Reactions
15.2.3 Zeroth-Order Reactions
15.2.4 Reaction Order and Stoichiometry of the Reaction
15.3 Reaction Mechanisms and Microscopic Reversibility
15.4 Reaction Mechanisms With Decision-Making Steps: Parallel Reactions
15.5 Reaction Mechanisms With Continuing Steps: Consecutive Reactions
15.6 Reaction Mechanisms With Regretful Steps: Reversible Reactions
15.7 Reaction Mechanisms With Consecutive and Reversible Steps
15.8 The Michaelis–Menten Mechanism for Enzyme Kinetics
Graphic Representation of the Michaelis–Menten Model for Enzyme Kinetics
Comments on the Michaelis–Menten Model
Michaelis–Menten Kinetics in the Presence of Other Binding Molecules
15.8.1 The Michaelis–Menten Mechanism: Inhibition
Competitive Inhibition Mechanism
Noncompetitive Inhibition Mechanism
15.8.2 The Michaelis–Menten Mechanism: Activation
15.8.3 The Michaelis–Menten Mechanism: Activator Plus Component X
Derivation of General Expressions for vmax and KM
Simplification of General Expressions for vmax and KM
Can an Activation Mechanism Appear as an Inhibitor Mechanism?
15.9 Collisions and Reaction Kinetics
15.9.1 Pseudo First-Order Reactions: The Lindemann–Christiansen Mechanism
15.9.2 Chain Reactions: Hydrogen Bromide
15.10 Photodissociation Reactions
15.11.1 Catalytic Destruction of Ozone—The Hole Story
15.11.2 The Chapman Cycle Revisited—Microscopic Reversibility
15.12 Hard Sphere Collisions in the Gas Phase: Theory
15.12.1 Generalized Form of Bimolecular Collision Number
15.13 Hard Sphere Collision Model for Gas Phase Reaction Kinetics
15.14 Ad Hoc Modifications to the Hard Sphere Collision Model
15.15 Potential Energy Surface of a Chemical Reaction
15.16 Transition State Theory
15.17 Solution Kinetics—General Considerations
15.18 Diffusion-Controlled Reactions: The Smoluchowski Limit
15.19 Bimolecular Solution Kinetics: The Schurr Model
15.19.1 The Degree of Activation and Diffusion Contributions to Bimolecular Rate Constants
15.19.2 Effect of Rotation on the Forward Reaction Rate Constant
15.20 Temperature and Pressure Dependence of the Rate Constants
15.21 Caldin-Hasinoff: Reaction of Ferroprotoporphyrin IX With Carbon Monoxide
15.22 Nuclear Radiation and Dosage Rates
MS.1.1 Conversions of Units
MS.1.1.1 Change in Velocity Units
MS.1.1.2 Weight to Number
MS.1.1.3 Weight to Concentration
MS.1.1.4 Molar and Molal Concentrations
MS.1.1.5 Dimensional Analysis
MS.1.2.1 Balancing Chemical Equations
MS.1.2.2 Solving Equations for Equilibrium Concentrations
MS.1.2.3 Simple Reactions with Arbitrary Concentrations
MS.1.2.4 Chemical Reactions with Arbitrary Concentrations
MS.2.3 Multivariable Functions
MS.3 Unknown Functions—Taylor Series Expansion
MS.4.1 The Inverse Matrix and the Identity Matrix
MS.4.2 Solving Coupled Equations with Matrices and Vectors
Appendix A: Definitions and Conversion Factors
Appendix B: Universal Constants of Nature
Appendix C: Thermodynamic Functions of Formation of Inorganic Compoundsa
Appendix D: Thermodynamic Functions of Formation of Organic Compounds
Appendix E: Standard State Enthalpies of Phase Transitions
Appendix F: Heat Capacities
Appendix G: Compressibility and Expansion Parameters
Appendix H: Heats of Combustion of Organic Compounds
Appendix I: Heats of Combustion of Common Fuels and Food
Appendix J: Standard Thermodynamic Function of Phase Transitions of Water
Appendix J: Viscosity of Water
Appendix J: Compressibility and Expansion Parameters for Water
Appendix J: Thermal Dependence of Physical Properties—Liquid Water
Appendix J: Thermal Dependence of Physical Properties—Ice
Appendix J: Temperature Dependence of the σt Densitya of Seawater
Appendix J: Density of Seawatera with Ocean Depth
Appendix K: Bond Dissociation Enthalpies and Bond Lengths
Appendix L: Selected Equilibrium Constants
Appendix L: Aqueous Complex Formation Constantsa
Appendix M: Different Forms of Henry's Law Constant at 298K
Appendix M: Temperature Dependence of Solubility of Gases in Water (Mole Fraction X)
Appendix M: Temperature Dependence of Henry's Law Constants kH (atm)
Appendix M: Solubility in Water and Benzene 298K
Appendix M: Temperature Dependence of Carbon Dioxide Solubility
Appendix M: Oxygen Solubility in Freshwater and Seawater in mg/L
Appendix M: Solubility of Oxygen in Seawater (mL of O2 at STP per Liter of Seawater)
Appendix M: Solubility of Nitrogen in Alcohol/Water Mixtures
Appendix M: Solubility of Oxygen in Organic Solvents
Appendix N: Solubility Products at 25°C
Appendix O: Partition Coefficients (Octanol/Water)
Appendix P: Acid–Base Constants
Appendix P: Conjugate Acids and Basesa
Appendix Q: Standard Half-Cell Potentials
Appendix R: Ionization Energies of Elements
Appendix R: Ionization Energies of Elements (kJ/mol)
Appendix S: Infrared Transitions of HCla
Appendix S: Molecular Parameters Diatomic Molecules
Appendix S: Vibrational Frequencies (cm−1) for Bent Triatomic Molecules
Appendix S: Isotope Effect on Vibrational Frequencies of Triatomic Molecules (cm−1)
Appendix S: Vibrational Frequencies of Water (cm−1)
Appendix S: Isotope-Substituted Vibrational Frequencies (cm−1)
Appendix T: Characteristic Parameters for Selected Moleculesa
Appendix U: van der Waals Parameters
Appendix V: Electromagnetic Spectrum
Physical Chemistry
：Concepts and Theory
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