Chemistry
Phase equilibria and diagrams
Gibbs phase rule, unary diagrams, eutectics, and the lever rule.
Basics
Phase rule
Gibbs’s phase rule is F = C − P + 2. F is degrees of freedom, C independent components, P phases. For one-component water the triple point has F=0 so T and P are fixed. In binaries people often hold pressure fixed and write F = C − P + 1. Lines and regions on a diagram make those counts visible. This is a class sketch; non-ideal systems need activities.
Unary phase diagram
On a P–T diagram for water or CO₂, curves are where two phases coexist. Beyond the critical point sits a supercritical fluid with no liquid–gas distinction. Water’s melting curve sloping left means higher pressure lowers the melting point. Sublimation is solid to gas without a liquid. Labels differ by substance.
Binary eutectic
When two components barely mix as solids, a eutectic appears: liquid plus two solids coexist at that composition and temperature. Above the liquidus everything is liquid; between liquidus and solidus, liquid plus solid; below the solidus, solid. Lead–tin solder is the textbook case. A flat hold on a cooling curve flags the eutectic.
Lever rule
In a two-phase field, where bulk composition sits between the two phases sets the phase fractions. The longer arm is the lesser phase — mass balance drawn like a seesaw. Stay consistent with mole or mass fraction on the axis. Apply it only on a tie line (isotherm).
Formulas
Gibbs phase rule
Condensed systems at fixed P often use +1.
Symbols
-
Fdegrees of freedom -
Cnumber of components -
Pnumber of phases
Clausius–Clapeyron (sketch)
Slope of a coexistence curve. For vapor, ΔV≈V_gas.
Symbols
-
ΔHenthalpy of transition -
ΔVvolume change
Lever rule
Bulk w and phase compositions w_α, w_β. Mass-fraction example.
Symbols
-
f_αfraction of phase α -
woverall composition
Key table
| Water triple point | 273.16 K, 611.657 Pa — an anchor of the temperature scale |
|---|---|
| Critical point (water) | about 647 K, 22.1 MPa |
| Eutectic solder | Sn–Pb eutectic freezes all at once near 183 °C |
In this field
Atoms and the periodic table
Atomic structure, nucleus and electrons, periods and groups.
Chemical bonding
Ionic, covalent, and metallic bonds, plus molecular shape.
The mole and stoichiometry
Moles, molar mass, empirical formulas, and yield.
Gases and acids–bases
Ideal gas, pH, and buffers.
Thermo, equilibrium, kinetics
Enthalpy, Gibbs energy, K, and rate laws.
Electrochemistry and organic basics
Oxidation numbers, cells, Nernst, functional groups.
Nuclear chemistry
Radioactivity, half-life, binding energy.
Solutions and kinetics
Concentration, colligative properties, rate laws.
Analytical chemistry
Titration, spectroscopy, and chromatography — measuring what is present and how much.
Polymers and solids
Crystals and glasses, metal–ionic–covalent solids, polymer chains and the glass transition.
Coordination compounds
Ligands, coordination number, crystal field, colour, and an 18-electron sketch.
Electrochemical cells
Galvanic versus electrolytic, Nernst, Faraday, and a corrosion sketch.