Chemical and Statistical Thermodynamics I

60 lessons, pages 3041–3100.

From Molecules to Macroscopic Thermodynamics — Why statistical thermodynamics bridges energy levels and bulk properties
Microstates, Configurations and Weight — Counting arrangements of quanta and the dominant configuration
The Boltzmann Distribution — Population ratios and the factor exp(−ε/kT)
Boltzmann's Entropy Formula — S = k ln W and the statistical meaning of entropy
The Molecular Partition Function — Defining q as a sum over states and its role as a normaliser
Interpreting q: Accessible States — q as the effective number of thermally accessible states and its limits
Degeneracy and the Partition Function — Summing over levels with degeneracy factors
Two-Level Systems — Populations, energy and the Schottky heat-capacity peak
The Translational Partition Function — Particle in a box, thermal wavelength and q = V/Λ³
The Rotational Partition Function — Rigid rotor levels, rotational temperature and the high-temperature limit
Symmetry Numbers and Nuclear Spin — Why homonuclear molecules divide q by σ and ortho/para hydrogen
The Vibrational Partition Function — Harmonic oscillator sum, vibrational temperature and zero-point energy
The Electronic Partition Function — Ground-state degeneracy and low-lying excited states
Factorising the Molecular Partition Function — Separable energy modes and q = q_T q_R q_V q_E
The Canonical Ensemble and Q — Ensembles, the canonical partition function and fluctuations
Indistinguishable Particles and N! — Relating Q to q for localised and gaseous systems
Internal Energy from the Partition Function — U − U(0) as a temperature derivative of ln Q
Heat Capacity from Partition Functions — Mode contributions, equipartition and quantum freeze-out
Statistical Entropy and the Sackur–Tetrode Equation — Entropy from Q and the absolute entropy of a monatomic gas
Helmholtz Energy, Pressure and Gibbs Energy from Q — A = −kT ln Q and deriving the ideal gas equation
Equilibrium Constants from Partition Functions — Standard molar partition functions and K for gas-phase reactions
Partition Functions: Worked Problems — Multi-step calculations of populations, energies and entropies
Partial Molar Quantities — Partial molar volume and how properties depend on composition
Defining the Chemical Potential — μ as partial molar Gibbs energy and the fundamental equation dG = V dp − S dT + Σμdn
The Gibbs–Duhem Equation — Why chemical potentials in a mixture cannot change independently
Chemical Potential of an Ideal Gas — μ = μ° + RT ln(p/p°) and the standard state
Fugacity and Real Gases — Fugacity coefficients and departures from ideality
Chemical Potential and Spontaneous Matter Flow — Matter moves from high to low chemical potential
Thermodynamics of Mixing Ideal Gases — Gibbs energy, entropy and enthalpy of mixing
Ideal Solutions and Raoult's Law — Chemical potential of solvent and the ideal solution model
Ideal-Dilute Solutions and Henry's Law — Solute behaviour and Henry's law constants
Activity and Activity Coefficients — Real solutions, activity conventions and excess functions
Colligative Properties from Chemical Potential — Lowering of solvent μ and boiling and freezing point shifts
Osmotic Pressure and the van 't Hoff Equation — Deriving Π = [B]RT from equal chemical potentials
Chemical Potential and Reaction Equilibrium — Reaction Gibbs energy, extent of reaction and ΔrG° = −RT ln K
Temperature Dependence of Equilibrium Constants — The van 't Hoff equation and the Gibbs–Helmholtz relation
Chemical Potential: Worked Problems — Mixing, solutions, osmosis and equilibrium calculations
Phase Stability and Chemical Potential — The stable phase has the lowest chemical potential
Temperature and Pressure Dependence of Chemical Potential — Slopes −S_m and V_m and why phases melt and boil
The Clapeyron Equation — Slopes of phase boundaries from ΔH and ΔV
The Clausius–Clapeyron Equation — Vapour pressure and temperature for liquid–vapour boundaries
One-Component Phase Diagrams — Phase boundaries, triple points and critical points
Phase Diagrams of Water and Carbon Dioxide — Negative melting slope, sublimation and supercritical fluids
Phases, Components and Degrees of Freedom — Precise definitions of P, C and F
Deriving the Gibbs Phase Rule — F = C − P + 2 from counting variables and equal μ conditions
Applying the Phase Rule to One-Component Systems — Invariant, univariant and bivariant regions
Counting Components with Reactions and Constraints — Independent species, chemical equilibria and stoichiometric restrictions
Two-Component Vapour–Liquid Diagrams — Pressure–composition and temperature–composition diagrams
The Lever Rule — Relative amounts of phases from tie lines
Fractional Distillation and Azeotropes — Theoretical plates and maximum- and minimum-boiling azeotropes
Partially Miscible Liquids — Liquid–liquid phase diagrams and critical solution temperatures
Solid–Liquid Diagrams: Simple Eutectics — Eutectic composition, cooling curves and solder alloys
Compound Formation and Incongruent Melting — Congruent compounds and peritectic behaviour
Solid Solutions — Complete miscibility in the solid state and zone refining
Three-Component Systems: Triangular Diagrams — Reading ternary compositions and liquid–liquid tie lines
Classifying Phase Transitions — Ehrenfest classification, first-order and continuous transitions
A Statistical View of Phase Equilibrium — Chemical potential from partition functions and vapour pressure
Phase Rule and Phase Diagrams: Worked Problems — Degrees of freedom, lever rule and Clapeyron calculations
Linking Partition Functions, Chemical Potential and Phase Rule — One framework from molecular states to phase diagrams
Chemical and Statistical Thermodynamics: Unit Review — Integrating partition functions, chemical potential and the phase rule