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Physical Chemistry

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.

Physical and Theoretical Chemistry Textbook Maps Chemistry

Tác giả: Delmar Larsen
Nhà xuất bản: LibreTexts Inc
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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01: The Dawn of the Quantum Theory
1.01: Blackbody Radiation Cannot Be Explained Classically
1.02: Quantum Hypothesis Used for Blackbody Radiation Law
1.03: Photoelectric Effect Explained with Quantum Hypothesis
1.04: The Hydrogen Atomic Spectrum
1.05: The Rydberg Formula and the Hydrogen Atomic Spectrum
1.06: Matter Has Wavelike Properties
1.07: de Broglie Waves can be Experimentally Observed
1.08: The Bohr Theory of the Hydrogen Atom
1.09: The Heisenberg Uncertainty Principle
1.E: The Dawn of the Quantum Theory (Exercises)
02: The Classical Wave Equation
2.01: The One-Dimensional Wave Equation
2.02: The Method of Separation of Variables
2.03: Oscillatory Solutions to Differential Equations
2.04: The General Solution is a Superposition of Normal Modes
2.05: A Vibrating Membrane
2.E: The Classical Wave Equation (Exercises)
03: The Schrodinger Equation and a Particle in a Box
3.01: The Schrodinger Equation
3.02: Linear Operators in Quantum Mechanics
3.03: The Schrodinger Equation is an Eigenvalue Problem
3.04: Wavefunctions Have a Probabilistic Interpretation
3.05: The Energy of a Particle in a Box is Quantized
3.06: Wavefunctions Must Be Normalized
3.07: The Average Momentum of a Particle in a Box is Zero
3.08: The Uncertainty Principle - Estimating Uncertainties from Wavefunctions
3.09: A Particle in a Three-Dimensional Box
3.E: The Schrodinger Equation and a Particle in a Box (Exercises)
04: Postulates and Principles of Quantum Mechanics
4.01: The Wavefunction Specifies the State of a System
4.02: Quantum Operators Represent Classical Variables
4.03: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
4.04: The Time-Dependent Schrodinger Equation
4.05: Eigenfunctions of Operators are Orthogonal
4.06: Commuting Operators Allow Infinite Precision
4.E: Postulates and Principles of Quantum Mechanics (Exercises)
05: The Harmonic Oscillator and the Rigid Rotor
5.01: A Harmonic Oscillator Obeys Hooke's Law
5.02: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
5.03: The Harmonic Oscillator Approximates Molecular Vibrations
5.04: The Harmonic Oscillator Energy Levels
5.05: The Harmonic Oscillator and Infrared Spectra
5.06: The Harmonic Oscillator Wavefunctions involve Hermite Polynomials
5.07: Hermite Polynomials are either Even or Odd Functions
5.08: The Energy Levels of a Rigid Rotor
5.09: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
5.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
06: The Hydrogen Atom
6.01: The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
6.02: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
6.03: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
6.04: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
6.05: s-orbitals are Spherically Symmetric
6.06: Orbital Angular Momentum and the p-Orbitals
6.07: The Helium Atom Cannot Be Solved Exactly
6.E: The Hydrogen Atom (Exercises)
07: Approximation Methods
7.01: The Variational Method Approximation
7.02: Linear Variational Method and the Secular Determinant
7.03: Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters
7.04: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
7.E: Approximation Methods (Exercises)
08: Multielectron Atoms
8.01: Atomic and Molecular Calculations are Expressed in Atomic Units
8.02: Perturbation Theory and the Variational Method for Helium
8.03: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
8.04: An Electron has an Intrinsic Spin Angular Momentum
8.05: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
8.06: Antisymmetric Wavefunctions can be Represented by Slater Determinants
8.07: Hartree-Fock Calculations Give Good Agreement with Experimental Data
8.08: Term Symbols Gives a Detailed Description of an Electron Configuration
8.09: The Allowed Values of J - the Total Angular Momentum Quantum Number
8.10: Hund's Rules Determine the Term Symbols of the Ground Electronic States
8.11: Using Atomic Term Symbols to Interpret Atomic Spectra
8.E: Multielectron Atoms (Exercises)
09: Chemical Bonding in Diatomic Molecules
9.01: The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules
9.02: The H Prototypical Species
9.03: The Overlap Integral
9.04: Chemical Bond Stability
9.05: Bonding and Antibonding Orbitals
9.06: A Simple Molecular-Orbital Treatment of H Places Both Electrons in a Bonding Orbital
9.07: Molecular Orbitals Can Be Ordered According to Their Energies
9.08: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
9.09: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
9.10: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
9.11: Photoelectron Spectra Support the Existence of Molecular Orbitals
9.12: Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules
9.13: SCF-LCAO-MO Wavefunctions are Molecular Orbitals formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently
9.14: Molecular Term Symbols Describe Electronic States of Molecules
9.15: Molecular Term Symbols Designate Symmetry
9.16: Most Molecules Have Excited Electronic States
9.E: Chemical Bond in Diatomic Molecules (Exercises)
10: Bonding in Polyatomic Molecules
10.01: Hybrid Orbitals Account for Molecular Shape
10.02: Hybrid Orbitals in Water
10.03: BeH is Linear and HO is Bent
10.04: Photoelectron Spectroscopy
10.05: The pi-Electron Approximation of Conjugation
10.06: Butadiene is Stabilized by a Delocalization Energy
10.07: Benzene and Aromaticity
10.E: Bonding in Polyatomic Molecules (Exercises)
11: Computational Quantum Chemistry
11.01: Overview of Quantum Calculations
11.02: Gaussian Basis Sets
11.03: Extended Basis Sets
11.04: Orbital Polarization Terms in Basis Sets
11.E: Computational Quantum Chemistry (Exercises)
12: Group Theory - The Exploitation of Symmetry
12.01: The Exploitation of Symmetry Can Help Simplify Numerical Calculations
12.02: Symmetry Elements and Operations Define the Point Groups
12.03: Symmetry Operations Define Groups
12.04: Symmetry Operations as Matrices
12.05: Molecules can be Represented by Reducible Representations
12.06: Character Tables Summarize the Properties of a Point Group
12.07: Characters of Irreducible Representations
12.08: Using Symmetry to Solve Secular Determinants
12.09: Generating Operators
12.10: Molecular Motions of a Molecule can be Represented by a Reducible Reperesentation
12.11: Reducible Representations are Comprised of Irreducible Representations
12.12: Normal Modes of Vibrations Describe how Molecules Vibrate
12.13: Symmetry of Vibrations Describes their Spectroscopic Behavior
12.14: Symmetry Adapted Linear Combinations are the Sum over all Basis functions
12.15: Molecular Orbitals can be Constructed on the Basis of Symmetry
12.E: Group Theory - The Exploitation of Symmetry (Exercises)
12.T: Character Tables
12.T: Correlation Tables
13: Molecular Spectroscopy
13.01: The Electromagnetic Spectrum
13.02: Rotations Accompany Vibrational Transitions
13.03: Unequal Spacings in Vibration-Rotation Spectra
13.04: Unequal Spacings in Pure Rotational Spectra
13.05: Vibrational Overtones
13.06: Electronic Spectra Contain Electronic Vibrational and Rotational Information
13.07: The Franck-Condon Principle
13.08: Rotational Spectra of Polyatomic Molecules
13.09: Normal Modes in Polyatomic Molecules
13.10: Irreducible Representation of Point Groups
13.11: Time-Dependent Perturbation Theory
13.12: The Selection Rule for the Rigid Rotor
13.13: The Harmonic Oscillator Selection Rule
13.14: Group Theory Determines Infrared Activity
13.E: Molecular Spectroscopy (Exercises)
14: Nuclear Magnetic Resonance Spectroscopy
14.01: Nuclei Have Intrinsic Spin Angular Momenta
14.02: Magnetic Moments Interact with Magnetic Fields
14.03: Proton NMR Spectrometers Operate at Frequencies Between 60 MHz and 750 MHz
14.04: The Magnetic Field Acting upon Nuclei in Molecules Is Shielded
14.05: Chemical Shifts Depend upon the Chemical Environment of the Nucleus
14.06: Spin-Spin Coupling Can Lead to Multiplets in NMR Spectra
14.07: Spin-Spin Coupling Between Chemically Equivalent Protons is Not Observed
14.08: The n1 Rule Applies Only to First-Order Spectra
14.09: Second-Order Spectra Can Be Calculated Exactly Using the Variational Method
14.E: Nuclear Magnetic Resonance Spectroscopy (Exercises)
15: Lasers Laser Spectroscopy and Photochemistry
15.01: Electronically Excited Molecules can Relax by a Number of Processes
15.02: The Dynamics of Transitions can be Modeled by Rate Equations
15.03: A Two-Level System Cannot Achieve a Population Inversion
15.04: Population Inversion can be Achieved in a Three-Level System
15.05: What is Inside a Laser
15.06: The Helium-Neon Laser
15.07: Modern Applications of Laser Spectroscopy
15.E: Lasers Laser Spectroscopy and Photochemistry (Exercises)
16: The Properties of Gases
16.01: All Dilute Gases Behave Ideally
16.02: van der Waals and Redlich-Kwong Equations of State
16.03: A Cubic Equation of State
16.04: The Law of Corresponding States
16.05: The Second Virial Coefficient
16.06: The Repulsive Term in the Lennard-Jones Potential
16.07: Van der Waals Constants in Terms of Molecular Parameters
16.E: The Properties of Gases (Exercises)
17: Boltzmann Factor and Partition Functions
17.01: The Boltzmann Factor is used to Approximate the Fraction of Particles in a Large System
17.02: The Boltzmann Distribution represents a Thermally Equilibrated Distribution
17.03: The Average Ensemble Energy is Equal to the Observed Energy of a System
17.04: Heat Capacity at Constant Volume is the Change in Internal Energy with Temperature
17.05: Pressure can be Expressed in Terms of the Canonical Partition Function
17.06: The Partition Function of Distinguishable Independent Molecules is the Product of the Molecular Partition Functions
17.07: Partition Functions of Indistinguishable Molecules Must Avoid Over Counting States
17.08: Partition Functions can be Decomposed into Partition Functions of Each Degree of Freedom
17.E: Boltzmann Factor and Partition Functions (Exercises)
18: Partition Functions and Ideal Gases
18.01: Translational Partition Functions of Monotonic Gases
18.02: Most Atoms are in the Ground Electronic State
18.03: The Energy of a Diatomic Polyatomic Molecule Can Be Approximated as a Sum of Separate Terms
18.04: Most Molecules are in the Ground Vibrational State
18.05: Most Molecules are Rotationally Excited at Ordinary Temperatures
18.06: Rotational Partition Functions of Diatomic Gases Contain a Symmetry Number
18.07: Vibrational Partition Functions of Polyatomic Molecules Include the Partition Function for Each Normal Coordinate
18.08: Rotational Partition Functions of Polyatomic Molecules Depend on the Sphar of the Molecule
18.09: Molar Heat Capacities
18.10: Ortho and Para Hydrogen
18.11: The Equipartition Principle
18.E: Partition Functions and Ideal Gases (Exercises)
19: The First Law of Thermodynamics
19.01: Overview of Classical Thermodynamics
19.02: Pressure-Volume Work
19.03: Work and Heat are not State Functions
19.04: Energy is a State Function
19.05: An Adiabatic Process is a Process in which No Energy as Heat is Transferred
19.06: The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion
19.07: Work and Heat Have a Simple Molecular Interpretation
19.08: Pressure-Volume Work
19.09: Heat Capacity is a Path Function
19.10: Relative Enthalpies Can Be Determined from Heat Capacity Data and Heats of Transition
19.11: Enthalpy Changes for Chemical Equations are Additive
19.12: Heats of Reactions Can Be Calculated from Tabulated Heats of Formation
19.13: The Temperature Dependence of H
19.14: Enthalpy is a State Function
19.E: The First Law of Thermodynamics (Exercises)
20: Entropy and The Second Law of Thermodynamics
20.01: Energy Does not Determine Spontaneity
20.02: Nonequilibrium Isolated Systems Evolve in a Direction That Increases Their Energy Dispersal
20.03: Unlike heat Entropy is a State Function
20.04: The Second Law of Thermodynamics
20.05: The Famous Equation of Statistical Thermodynamics is Sk ln W
20.06: We Must Always Devise a Reversible Process to Calculate Entropy Changes
20.07: Thermodynamics Provides Insight into the Conversion of Heat into Work
20.08: Entropy Can Be Expressed in Terms of a Partition Function
20.09: The Statistical Definition of Entropy is Analogous to the Thermodynamic Definition
20.E: Entropy and The Second Law of Thermodynamics (Exercises)
21: Entropy and the Third Law of Thermodynamics
21.01: Entropy Increases With Increasing Temperature
21.02: The 3rd Law of Thermodynamics Puts Entropy on an Absolute Scale
21.03: The Entropy of a Phase Transition can be Calculated from the Enthalpy of the Phase Transition
21.04: The Debye Function is Used to Calculate the Heat Capacity at Low Temperatures
21.05: Practical Absolute Entropies Can Be Determined Calorimetrically
21.06: Practical Absolute Entropies of Gases Can Be Calculated from Partition Functions
21.07: Standard Entropies Depend Upon Molecular Mass and Structure
21.08: Spectroscopic Entropies sometimes disgree with Calorimetric Entropies
21.09: Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions
21.E: Entropy and the Third Law of Thermodynamics (Exercises)
22: Helmholtz and Gibbs Energies
22.01: Helmholtz Energy
22.02: Gibbs Energy Determines the Direction of Spontaneity at Constant Pressure and Temperature
22.03: The Maxwell Relations
22.04: The Enthalpy of an Ideal Gas is Independent of Pressure
22.05: Thermodynamic Functions have Natural Variables
22.06: The Standard State for a Gas is an Ideal Gas at 1 Bar
22.07: The Gibbs-Helmholtz Equation
22.08: Fugacity Measures Nonideality of a Gas
23: Phase Equilibria
23.01: A Phase Diagram Summarizes the Solid-Liquid-Gas Behavior of a Substance
23.02: Gibbs Energies and Phase Diagrams
23.03: The Chemical Potentials of a Pure Substance in Two Phases in Equilibrium
23.04: The Clausius-Clapeyron Equation
23.05: Chemical Potential Can be Evaluated From a Partition Function
23.E: Phase Equilibria (Exercises)
24: Solutions I - Volatile Solutes
24.01: A Mixture is a Combination of Two or More Substances
24.02: The Gibbs-Duhem Equation Relates Chemical Potential and Composition at Equilibrium
24.03: Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears
24.04: Ideal Solutions obey Raoult's Law
24.05: Most Solutions are Not Ideal
24.06: Vapor Pressures of Volatile Binary Solutions
24.07: Activities of Nonideal Solutions
24.08: Activities are Calculated with Respect to Standard States
24.09: Gibbs Energy of Mixing of Binary Solutions in Terms of the Activity Coefficient
24.E: Solutions I- Liquid-Liquid Solutions (Exercises)
25: Solutions II - Nonvolatile Solutes
25.01: Standard State of Nonvolatile Solutions
25.02: The Activities of Nonvolatile Solutes
25.03: Colligative Properties Depend only on Number Density
25.04: Osmotic Pressure can Determine Molecular Masses
25.05: Electrolytes Solutions are Nonideal at Low Concentrations
25.06: The Debye-Huckel Theory
25.07: Extending Debye-Huckel Theory to Higher Concentrations
25.08: Homework Problems
26: Chemical Equilibrium
26.01: Equilibrium Results when Gibbs Energy is Minimized
26.02: An Equilibrium Constant is a Function of Temperature Only
26.03: Standard Gibbs Energies of Formation Can Be Used to Calculate Equilibrium Constants
26.04: Gibbs Energy of a Reaction vs. Extent of Reaction is a Minimum at Equilibrium
26.05: Reaction Quotient and Equilibrium Constant Ratio Determines Reaction Direction
26.06: The Sign of G and not G Determines the Direction of Reaction Spontaneity
26.07: The van 't Hoff Equation
26.08: Equilibrium Constants in Terms of Partition Functions
26.09: Molecular Partition Functions and Related Thermodynamic Data Are Extensively Tabulated
26.10: Real Gases Are Expressed in Terms of Partial Fugacities
26.11: Thermodynamic Equilibrium Constants Are Expressed in Terms of Activities
26.12: Activities are Important for Ionic Species
26.13: Homework Problems
27: The Kinetic Theory of Gases
27.01: The Average Translational Kinetic Energy of a Gas
27.02: The Gaussian Distribution of One Component of the Molecular Velocity
27.03: The Distribution of Molecular Speeds is Given by the Maxwell-Boltzmann Distribution
27.04: The Frequency of Collisions with a Wall
27.05: The Maxwell-Boltzmann Distribution Has Been Verified Experimentally
27.06: Mean Free Path
27.07: Rates of Gas-Phase Chemical Reactions
27.E: The Kinetic Theory of Gases (Exercises)
28: Chemical Kinetics I - Rate Laws
28.01: The Time Dependence of a Chemical Reaction is Described by a Rate Law
28.02: Rate Laws Must Be Determined Experimentally
28.03: First-Order Reactions Show an Exponential Decay of Reactant Concentration with Time
28.04: Different Rate Laws Predict Different Kinetics
28.05: Reactions can also be Reversible
28.06: The Rate Constants of a Reversible Reaction Can Be Determined Using Relaxation Techniques
28.07: Rate Constants Are Usually Strongly Temperature Dependent
28.08: Transition-State Theory Can Be Used to Estimate Reaction Rate Constants
28.E: Chemical Kinetics I - Rate Laws (Exercises)
29: Chemical Kinetics II- Reaction Mechanisms
29.01: A Mechanism is a Sequence of Elementary Reactions
29.02: The Principle of Detailed Balance
29.03: Multiple Mechanisms are often Indistinguishable
29.04: The Steady-State Approximation
29.05: Rate Laws Do Not Imply Unique Mechanism
29.06: The Lindemann Mechanism
29.07: Some Reaction Mechanisms Involve Chain Reactions
29.08: A Catalyst Affects the Mechanism and Activation Energy
29.09: The Michaelis-Menten Mechanism for Enzyme Catalysis
29.E: Chemical Kinetics II- Reaction Mechanisms (Exercises)
30: Gas-Phase Reaction Dynamics
30.01: The Rate of Bimolecular Gas-Phase Reaction Can Be Estimated Using Hard-Sphere Collision Theory and an Energy-Dependent Reaction Cross Section
30.02: A Reaction Cross Section Depends Upon the Impact Parameter
30.03: The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules
30.04: The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction
30.05: A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System
30.06: Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines
30.07: Reactions Can Produce Vibrationally Excited Molecules
30.08: The Velocity and Angular Distribution of the Products of a Reactive Collision
30.09: Not All Gas-Phase Chemical Reactions are Rebound Reactions
30.10: The Potential-Energy Surface Can Be Calculated Using Quantum Mechanics
30.E: Gas-Phase Reaction Dynamics (Exercises)
31: Solids and Surface Chemistry
31.01: The Unit Cell is the Fundamental Building Block of a Crystal
31.02: The Orientation of a Lattice Plane is Described by its Miller Indices
31.03: The Spacing Between Lattice Planes Can Be Determined from X-Ray Diffraction Measurements
31.04: The Total Scattering Intensity is Related to the Periodic Structure of the Electron Density in the Crystal
31.05: The Structure Factor and the Electron Density Are Related by a Fourier Transform
31.06: Atoms and Molecules can Physisorb or Chemisorb to a Surface
31.07: Isotherms are Plots of Surface Coverage as a Function of Gas Pressure at Constant Temperature
31.08: Using Langmuir Isotherms to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions
31.09: The Structure of a Surface is Different from that of a Bulk Solid
31.10: The Haber-Bosch Reaction Can Be Surface Catalyzed
31.E: Homework Problems
32: Math Chapters
32.01: Complex Numbers
32.02: Probability and Statistics
32.03: Vectors
32.04: Spherical Coordinates
32.05: Determinants
32.06: Matrices
32.07: Numerical Methods
32.08: Partial Differentiation
32.09: Series and Limits
32.10: Fourier Analysis
32.10.01: Fourier Analysis in Matlab
32.10.02: Fourier Synthesis of Periodic Waveforms
32.11: The Binomial Distribution and Stirling's Appromixation
33: Appendices
33.01: Deriving Planck's Distribution Law