Physical Chemistry

Statistical mechanics, kinetics and quantum theory as one account of matter

About this course

Chemistry derived from physics — the Boltzmann distribution and partition functions, thermodynamics of real systems, reaction rates and mechanisms, the quantum postulates applied to atoms and molecules, and spectroscopy.

What you will be able to do

  • Derive thermodynamic quantities from the Boltzmann distribution and partition functions
  • Analyse phase equilibria and mixtures, including non-ideal gases
  • Derive rate laws from mechanisms and interpret them with collision and transition-state theory
  • Solve the exactly solvable quantum systems and apply them to atoms and bonding
  • Interpret rotational, vibrational, electronic and magnetic resonance spectra

What this course covers

  • Mechanisms as candidates, not proofs
  • Elementary steps and molecularity vs. order
  • The steady-state approximation and its exact error
  • Rate laws as mechanistic evidence: pre-equilibria and radical chains
  • The logic of mechanistic disproof
  • Scope, summary, and preview of collision and transition-state theory
  • The Lindemann mechanism and pressure-dependent reaction order
  • Correspondence Principle and the Classical Limit
  • The Four Postulates of Quantum Mechanics
  • Quantization from Boundary Conditions
  • Uncertainty as Algebra, Not Measurement Disturbance
  • Size and Energy of the Hydrogen Atom from Uncertainty
  • Measurement Problem and Interpretations
  • Energy–Time Uncertainty and Spectral Linewidths
  • Statistical mechanics core claim
  • Equipartition and heat capacity as mode counting
  • Degrees of freedom counting procedure
  • Failure of equipartition for vibration
  • Arrhenius factor as a Boltzmann fraction
  • Boltzmann populations and spectral appearance
  • Reading molecular structure from a heat capacity
  • The Transition Dipole Moment and Selection Rules
  • Normal Modes and Infrared Activity
  • Vibrational Band Structure: P, Q, and R Branches
  • The Greenhouse Effect as Applied Selection Rules
  • Symmetry as the Unifying Principle of Spectroscopy
  • Reading a Real HCl Spectrum: Four Independent Quantities
  • Fitting vs. Predicting: Central Epistemological Lesson
  • Virial Expansion as Honest Gas Description
  • Boyle Temperature: Attraction vs. Molecular Volume
  • Van der Waals Equation: Fit vs. Prediction
  • Law of Corresponding States
  • Practical Decision Procedure for Real Gases
  • Worked Example: Nitrogen at 600 bar
  • Electronic Transitions and the Frank-Condon Principle
  • Intensity, Beer-Lambert Law, and Selection Rules for Color
  • Zeeman Effect and the NMR Sensitivity Puzzle
  • Chemical Shift, Spin-Spin Coupling, and Structure Determination
  • Collision rate from kinetic theory
  • Arrhenius equation derived from collision theory
  • The steric factor and the pattern of collision-theory failure
  • The harpoon mechanism
  • Transition state theory and the universal frequency kT/h
  • Steric factor reinterpreted as entropy of activation
  • Synthesis: collision theory vs. transition state theory compared
  • Counting arrangements to define a distribution
  • Method of the most probable distribution
  • Deriving the Boltzmann distribution via Stirling and Lagrange multipliers
  • Identifying β = 1/kT and the statistical meaning of temperature
  • kT in four unit currencies
  • The barometric formula as a Boltzmann factor
  • Practical procedure and limits for applying the Boltzmann distribution
  • Primary kinetic isotope effect from zero-point energy
  • Quantization from boundary conditions
  • Harmonic oscillator and zero-point energy
  • Rigid rotor: levels, degeneracy, and spectrum
  • Bond length and force constant from spectra
  • Three level patterns as spectroscopic fingerprints
  • Three motions against kT: thermal population and partition functions
  • CP − CV exact relation
  • Thermodynamic potentials and natural variables
  • Maxwell relations from mixed partial derivatives
  • Four-step procedure for unmeasurable quantities
  • Thermodynamic equation of state and internal pressure
  • Physical content of thermodynamic formalism
  • Joule–Thomson effect and inversion temperature
  • Catalyst as alternative path, not lowered barrier
  • Langmuir adsorption isotherm derived via steady state
  • Langmuir and Michaelis-Menten as identical functions
  • Enzyme kinetics and the diffusion-limit ceiling
  • Catalyst cannot shift equilibrium: thermodynamic and detailed-balance arguments
  • Two hard limits bounding catalysis
  • Entropy half of catalysis: proximity and orientation
  • Hydrogen atom: three quantum numbers and degeneracy
  • Periodic table shape from N-squared degeneracy
  • The variational principle: proof and recipe
  • Variational treatment of helium and the orbital approximation
  • Screening, Slater's rules, and where screening fails
  • Orbital energies are not fixed numbers
  • Master summary: what orbitals and configurations actually are
  • Clausius-Clapeyron and vapour pressure prediction
  • Chemical potential and equilibrium condition
  • Chemical potential: what equilibrium does and does not equalise
  • Clapeyron equation and phase-boundary slopes
  • Raoult's law, Henry's law, and distillation
  • Colligative properties as four faces of one fact
  • Worked application: road-salting and eutectic limit
  • Partition function definition and physical interpretation
  • Thermodynamic quantities from ln Q
  • Effect of energy zero on computed quantities
  • Practical procedure, checks, and cautions
  • Sackur–Tetrode equation and absolute entropy
  • Equilibrium constant from partition functions
  • Worked example: argon absolute entropy
  • The partition function bridge: entropy from spectroscopy
  • Five standard molar entropies vs. calorimetry
  • Heat capacity as a smooth ramp, not a staircase
  • Equilibrium constant from spectroscopic constants alone
  • Residual entropy: when disagreement is the result
  • Course synthesis: productive failure as method
  • Born–Oppenheimer approximation and molecular structure
  • Two pictures of a bond: MO theory and valence bond theory
  • MO theory's dissociation failure and its structural origin
  • Oxygen paramagnetism: MO prediction vs Lewis structure
  • Bond order: electron counting, half-integers, and predictive power
  • Synthesis: convergence of MO and VB, and working rules

Syllabus

  1. Statistical Foundations

    1. L1 · What Physical Chemistry Is For
    2. L2 · The Boltzmann Distribution
    3. L3 · Partition Functions

  2. Thermodynamics of Real Systems

    1. L4 · Real Gases, Properly
    2. L5 · Thermodynamic Machinery
    3. L6 · Phase Equilibria and Mixtures

  3. Kinetics

    1. L7 · Rate Laws and Mechanisms
    2. L8 · Collision Theory and Transition States
    3. L9 · Catalysis and Surfaces

  4. Quantum Chemistry

    1. L10 · The Postulates, Minimally
    2. L11 · Exactly Solvable Systems
    3. L12 · Atoms, Beyond Hydrogen
    4. L13 · Molecules and Bonding

  5. Spectroscopy and Synthesis

    1. L14 · Spectroscopy I — Rotation and Vibration
    2. L15 · Spectroscopy II — Electronic and Magnetic
    3. L16 · Statistical Thermodynamics, and the Course as One Argument