Phase equilibria is the study of the conditions (temperature, pressure, composition) under which different phases of matter coexist in thermodynamic equilibrium. Phase diagrams provide a graphical representation of these relationships and are essential tools in materials science, chemistry, and engineering.
Phase and Phase Transitions
A phase is a homogeneous region of matter with uniform physical and chemical properties, with the three primary phases being solid, liquid, and gas. Phase transitions include melting (solid to liquid), freezing (liquid to solid), vaporization (liquid to gas), condensation (gas to liquid), sublimation (solid to gas), and deposition (gas to solid). During a phase transition at constant pressure, the temperature remains constant as heat is absorbed as latent heat or enthalpy of phase change.
Gibbs Phase Rule
The phase rule relates the number of phases (P), components (C), and degrees of freedom (F): F = C - P + 2. Degrees of freedom (F) are the number of intensive variables (T, P, composition) that can be changed independently without altering the number of phases. For a one-component system (C = 1), F = 3 - P, so at the triple point (P = 3), F = 0 (invariant); along a phase boundary (P = 2), F = 1 (univariant); and within a single phase (P = 1), F = 2 (bivariant).
One-Component Phase Diagrams
The phase diagram for water shows three phases: ice (solid), liquid water, and steam (gas), and the solid-liquid boundary has a negative slope due to the lower density of ice compared to liquid water. The phase diagram for carbon dioxide has a positive solid-liquid boundary, and the triple point is at 5.11 atm and -56.6°C; CO2 sublimes at atmospheric pressure. The critical point marks the temperature and pressure above which the liquid and gas phases become indistinguishable, forming a supercritical fluid — for water, Tc = 374°C and Pc = 218 atm, while for CO2, Tc = 31°C and Pc = 73 atm.
The Clausius-Clapeyron Equation
The Clausius-Clapeyron equation describes the temperature dependence of vapor pressure: dP/dT = ΔH/TΔV, where ΔH is the enthalpy of vaporization and ΔV is the volume change. For liquid-vapor equilibrium, the integrated form is ln(P2/P1) = -ΔHvap/R × (1/T2 - 1/T1). The equation is used to calculate the enthalpy of vaporization from vapor pressure measurements at different temperatures.
Binary Phase Diagrams
Temperature-composition (T-x) diagrams show phase behavior of two-component mixtures as a function of composition at constant pressure. Ideal solutions follow Raoult’s Law: Pi = x_iPi*, where Pi is the partial pressure of component i, x_i is its mole fraction, and Pi* is its vapor pressure; positive deviations indicate weaker A-B interactions, while negative deviations indicate stronger A-B interactions. Eutectic systems have a eutectic point, which is the lowest melting composition in a binary system — the eutectic mixture melts at a single temperature lower than either pure component, and for NaCl/H2O the eutectic composition is 23.3% NaCl at -21.1°C. Azeotropic systems are liquid mixtures that boil at a constant composition; ethanol-water forms a minimum-boiling azeotrope at 95.6% ethanol (78.2°C), while nitric acid-water forms a maximum-boiling azeotrope.
Liquid-Liquid and Solid-Liquid Equilibria
Partially miscible liquids such as water and phenol show an upper critical solution temperature (UCST) above which the two liquids are completely miscible. Liquid-liquid phase diagrams can also show a lower critical solution temperature (LCST), as seen in water-triethylamine and polymer solutions. Solid-liquid phase diagrams for eutectic systems are used in metallurgy to understand alloy behavior and in pharmacy to design pharmaceutical cocrystals.
Supercritical Fluids
Above the critical temperature and pressure, substances exist as supercritical fluids with properties intermediate between liquids and gases — density near that of a liquid and viscosity near that of a gas. Supercritical CO2 is widely used for decaffeination of coffee, extraction of essential oils, and as a solvent in green chemistry. Supercritical water is used for biomass gasification and waste destruction due to its unique solvation properties.
