Physical Chemistry

  1. Statistical Mechanics
    1. Fundamental Concepts
      1. Microscopic vs Macroscopic Descriptions
        1. Molecular Level Properties
          1. Bulk Properties
          2. Microstates and Macrostates
            1. Definition and Examples
              1. Counting Microstates
                1. Degeneracy
                2. Statistical Ensembles
                  1. Microcanonical Ensemble (N, V, E)
                    1. Canonical Ensemble (N, V, T)
                      1. Grand Canonical Ensemble (μ, V, T)
                        1. Isobaric-Isothermal Ensemble (N, P, T)
                        2. The Ergodic Hypothesis
                          1. Time Averages vs Ensemble Averages
                          2. Probability Distributions
                            1. The Boltzmann Distribution
                              1. Derivation from Maximum Entropy
                                1. Applications to Energy States
                              2. The Partition Function
                                1. Canonical Partition Function (Q)
                                  1. Physical Interpretation
                                    1. Calculation Methods
                                    2. Molecular Partition Function (q)
                                      1. Relationship to Q for Independent Particles
                                        1. Factorization into Translational, Rotational, Vibrational, and Electronic Parts
                                        2. Translational Partition Function
                                          1. Three-Dimensional Translation
                                            1. Temperature and Volume Dependence
                                            2. Rotational Partition Function
                                              1. Linear Molecules
                                                1. Nonlinear Molecules
                                                  1. High and Low Temperature Limits
                                                  2. Vibrational Partition Function
                                                    1. Harmonic Oscillator Model
                                                      1. High and Low Temperature Limits
                                                        1. Characteristic Vibrational Temperature
                                                        2. Electronic Partition Function
                                                          1. Ground State Dominance
                                                            1. Excited Electronic States
                                                          2. Thermodynamic Properties from Statistical Mechanics
                                                            1. Internal Energy
                                                              1. Relationship to Partition Function
                                                                1. Contributions from Different Modes
                                                                2. Heat Capacity
                                                                  1. Constant Volume Heat Capacity
                                                                    1. Contributions from Translation, Rotation, and Vibration
                                                                    2. Entropy
                                                                      1. Statistical Definition
                                                                        1. Sackur-Tetrode Equation
                                                                        2. Helmholtz and Gibbs Energies
                                                                          1. Relationships to Partition Functions
                                                                          2. Pressure and Chemical Potential
                                                                            1. Statistical Mechanical Expressions
                                                                          3. Applications of Statistical Mechanics
                                                                            1. Ideal Gases
                                                                              1. Monatomic Gases
                                                                                1. Diatomic Gases
                                                                                  1. Polyatomic Gases
                                                                                  2. Heat Capacity Calculations
                                                                                    1. Temperature Dependence
                                                                                      1. Classical vs Quantum Behavior
                                                                                      2. Chemical Equilibrium
                                                                                        1. Equilibrium Constants from Partition Functions
                                                                                          1. Temperature Dependence
                                                                                          2. The Equipartition Theorem
                                                                                            1. Classical Limit
                                                                                              1. Quantum Corrections
                                                                                                1. Applications and Limitations
                                                                                                2. Phase Transitions
                                                                                                  1. Order-Disorder Transitions
                                                                                                    1. Ising Model

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                                                                                                4. Molecular Spectroscopy

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                                                                                                6. Chemical Kinetics