Essentials of Physical Chemistry

Foreword Author List of Constants Introduction: Mathematics and Physics Review Ideal and Real Gas Behavior Introduction to the "First Encounter with Physical Chemistry" Phenomenological Derivation of the Ideal Gas Equation Charles' (Jacques-Alexandre-Cesar Charles) Law Useful Units Molecular Weight from Gas Density (the Dumas Bulb Method) Dalton's Law of Partial Pressures Nonideal Gas Behavior Supercritical Fluid Chromatography Summary Problems References Viscosity of Laminar Flow Introduction Measurement of Viscosity Viscosity of Blood Staudinger's Rule for Polymer Molecular Weight Summary Problems Bibliography References The Kinetic Molecular Theory of Gases Introduction Kinetic Molecular Theory of Gases Weighted Averaging: A Very Important Concept Summary Problems References The First Law of Thermodynamics Introduction Historical Development of Thermodynamics Definitions First Law of Thermodynamics Isothermal Processes Enthalpy and Heat Capacities Adiabatic Processes Adiabatic Nozzle Expansion Spectroscopy Diesel Engine Compression Calorimetry and Thermochemistry Hess's Law of Heat Summation Standard Heats of Formation at 298.15 K and 1.000 Bar Pressure Temperature Dependence of Reaction Enthalpies Polynomial Curve Fitting Application to I"H0rxn (T > 289.15 K) Other Types of Thermochemistry Perspective Key Formulas and Equations Problems Testing, Grading, and Learning? References The Second and Third Laws of Thermodynamics Introduction Carnot Cycle/Engine Efficiency of Real Heat Engines Entropy and Spontaneity Summary of the Second Law of Thermodynamics Eight Basic Equations of Thermodynamics Third Law of Thermodynamics Simple Statistical Treatment of Liquids and Gases Summary Testing, Grading, and Learning? Problems Bibliography References Gibbs' Free Energy and Equilibria Introduction Temperature Dependence of Equilibrium Constants van't Hoff Equation Vapor Pressure of Liquids Phase Equilibria How Ice Skates Work Gibbs Phase Rule Iodine Triple Point (CP--CV) for Liquids and Solids Open Systems: Gibbs--Duhem Equation for Partial Molal Volumes Chemical Potential for Open Systems Modeling Liquids Summary Problems Testing, Grading, and Learning? Bibliography References Basic Chemical Kinetics Introduction First-Order Reactions Promethium: An Introduction to Nuclear Chemistry Madame Curie and Radioactivity Radium Second-Order Rate Processes: [A] = [B] Second-Order Rate Processes: [A] ae [B] Arrhenius Activation Energy The Classic A --> B --> C Consecutive First-Order Reaction Splitting the Atom Problems References More Kinetics and Some Mechanisms Introduction Beyond Arrhenius to the Eyring Transition State Example Graphical--Analytical Method for I"Ha! and I"Sa! Summary of Graphical Method Results at T = 25 C Further Consideration of SN1 Solvolysis Chain Reactions and the Steady State Enzyme Kinetics Example: A Hypothetical Enzyme Kinetics Conclusions Problems Testing, Grading, and Learning? Bibliography References Basic Spectroscopy Introduction Planck's Discovery Balmer's Integer Formula A Very Useful Formula Preliminary Summary of the Bohr Atom Significance of the Bohr Quantum Number n Orbital Screening X-Ray Emission Forensic/Analytical Use of Auger X-Rays X-Ray Fluorescence X-Ray Diffraction Electronic Absorption Spectroscopy/Spectrophotometry Interpreting Electronic Spectra General Principles of Spectroscopy Problems Bibliography References Early Experiments in Quantum Physics Introduction Stefan--Boltzmann Law: Relating Heat and Light--Part I Blackbody Radiation: Relating Heat and Light--Part II Photoelectric Effect De Broglie Matter Waves Davisson--Germer Experiment Summary Problems References The Schrodinger Wave Equation Introduction Definition of a Commutator Postulates of Quantum Mechanics Particle on a Ring Comparison of PIB and POR Applications Additional Theorems in Quantum Mechanics Summary Problems Study, Test, and Learn? References The Quantized Harmonic Oscillator, Vibrational Spectroscopy Introduction Harmonic Oscillator Details Harmonic Oscillator Results Reduced Mass Isotope Shift in the Vibrational Fundamental Frequency Hermite Recursion Rule Infrared Dipole Selection Rule 3N - 6 or 3N - 5 Vibrations? Raman Spectroscopy Summary Problems References The Quantized Rigid Rotor and the Vib-Rotor Introduction Three-Dimensional Particle-in-a-Box Rigid Rotor Angular Wave Functions Angular Momentum Rotational Spectrum of CO Fourier Transform Spectrometry FT-IR Imaging and Microscopy Dipole Requirement Vib-Rotor Infrared Spectroscopy Bond Length of H-3517Cl Summary Problems References The Schrodinger Hydrogen Atom Introduction Strategy to Solve the Problem Associated Laguerre Polynomials Interpretation Pictures of Angular Orbitals Powell Equivalent d-Orbitals Unsold's Theorem Aufbau Principle and the Scaled H atom Term Symbols and Spin Angular Momentum Hund's Rule |L, Sz) versus |J, Jz) Coupling Summary Problems References Quantum Thermodynamics Introduction (Energy) Partition Function Average Translation Energy in One Dimension Average Rotational Energy of a Diatomic Molecule Average Vibrational Energy High-Temperature Limit for Vibrational Heat Capacity Heat Capacity of a Polyatomic Species: Water Combining Partition Functions Statistical Formulas for Other Thermodynamic Functions Statistical Formula for S(T) Sakur--Tetrode Formula for Absolute Entropy of a Gas Summary Problems References Approximate Methods and Linear Algebra Introduction Simple First-Order Perturbation Theory Principles of Perturbation Theory Variation Method Molecular Orbitals and the Secular Equation Chemical Bonds of Ethylene Elementary Linear Algebra Unitary Similarity Diagonalization of a Square Hermitian Matrix Jacobi Algorithm for Diagonalization Using a Computer Order Matters! Summary Problems Testing, Grading, and Learning! Study, Test, and Learn? References Electronic Structure of Molecules Introduction Hartree--Fock--Roothan LCAO Calculations Chemical Effects in Orbital Screening Many-Electron Wave Functions Atomic Units Roothaan's LCAO Hartree--Fock Equation Practical Implementation and Examples Dipole Moment of BH Excited States of BH Mesoionic Bond Orders Summary Problems References Point Group Theory and Electrospray Mass Spectrometry Introduction Basic Point Group Theory Calculation of Molecular Vibrations Future Development of Electrospray Mass Spectrometry? "Making Elephants Fly" Summary Problems References Essentials of Nuclear Magnetic Resonance Introduction Early NMR Spectrometers NMR Spin Hamiltonian Forensic Application of 1D-NMR Nuclear Magnetic Resonance: Pulse Analysis Rotating Coordinate System Detection of Magnetic Fields Bloch Equations Complex Fourier Transform 2D-NMR COSY Coherent Spectroscopy Product Operator COSY Analysis Using Dr. Brown's Automated Software Anatomy of a 2D Experiment Summary Problems References Appendix A: Relation between Legendre and Associated Legendre Polynomials Appendix B: The Hartree--Fock--Roothaan SCF Equation Appendix C: Gaussian Lobe Basis Integrals Appendix D: Spin-Orbit Coupling in the H Atom Index Use of PCLOBE