Section 7: Phase Diagrams, Gibbs Rule, & Multicomponent Systems

Phase Definition

A homogeneous, physically distinct, and mechanically separable portion of a system that is uniform throughout.

Phase Visibility

The visible, distinct part of a system that maintains identical chemical and physical properties throughout its boundary.

Two-Phase Abundance Examples

Ice + liquid water constitutes 2 phases; oil + water constitutes 2 phases.

Phase Diagram Definition

A graph plotting pressure versus temperature to map out the exact environmental boundaries where solid, liquid, gas, and supercritical fluid phases remain stable.

Gibbs Phase Rule Definition

A mathematical rule used to determine the exact number of independent variables (temperature, pressure, concentration) needed to define a system.

Gibbs Phase Rule Variables

F is degrees of freedom, C is number of components, and P is number of phases present.

Gibbs Phase Rule Equation

Expressed mathematically as F = (C - P) + 2.

Gibbs Phase Rule Degree Examples

Liquid water + water vapor yields F=1; liquid hexane + liquid water yields F=2; liquid ethanol + liquid water yields F=3.

One-Component System Diagram Shape

Represented by a distinct "Y-curve" on a single-component H2O phase diagram.

One-Component System F Value (1 Phase)

Yields F = 2, meaning both pressure and temperature must be known to define the system.

One-Component System F Value (2 Phases)

Yields F = 1, meaning either pressure or temperature must be known to define the system.

One-Component System F Value (3 Phases)

Yields F = 0, meaning the system is invariant and coordinates are locked.

Water Diagram Triple Point Coordinates

Occurs at exactly 0.006 atmospheres of pressure and 0.01°C.

Water Diagram Critical Point Coordinates

Occurs at exactly 218 atmospheres of pressure and 374°C.

Two-Component System Alternative Name

Frequently called a condensed system.

Two-Component System Pressure Rule

The vapor phase is completely ignored by setting pressure to a constant atmospheric value, leaving temperature and concentration as variables.

Two-Component System Subclasses

Subdivided into systems containing liquid-liquid phases and systems containing solid-liquid phases (Eutectic Mixtures).

Liquid-Liquid System Diagram Curve

Represented by a distinct "U or D curve" called a binodal curve.

Binodal Curve Boundaries

Inside the curve represents a two-phase split system; outside the curve represents a uniform single-phase system.

Critical Solution Temperature Definition

The upper consolute temperature threshold above which any proportion of components blends into a uniform single-phase system.

Tie Line Definition

A horizontal line drawn across a two-phase region on a phase diagram that shows the exact composition of each separated layer at a specific temperature.

Tie Line Boundaries

The two outer ends of a tie line represent the exact composition of the two conjugate phases.

Conjugate Phases Definition

The two distinct liquid layers that form simultaneously when a partially miscible mixture separates.

Phenol + Water System Constants

Exhibits an upper critical solution temperature of 66°C; a mixture inside splits into an 11% phenol layer and a 63% phenol layer.

Triethylamine + Water System Constant

Exhibits a lower critical solution temperature boundary established at exactly 18.5°C.

Nicotine + Water System Constant

Features a double-consolute loop creating a closed two-phase region bounded between 60.8°C and 208°C.

Eutectic Mixture Definition

A solid-liquid system of two or more compounds that features a combined melting point strictly lower than that of any of its individual components.

Eutectic Formula Rule

Melting point of components A+B is strictly less than the melting point of pure A or pure B.

Eutexia Definition

The physical phenomenon of depression or lowering of a melting point driven by the blending of specific components.

Pharmaceutical Eutectic Examples

EMLA (Lidocaine + Prilocaine), Thymol + Salol, Camphor + Menthol, and Menthol + Phenol.

EMLA Acronym

Represents Eutectic Mixture of Local Anesthetics.

Eutectic Point Definition

The unique minimum temperature and composition coordinates where the liquid phase and solid phases of a mixture coexist in equilibrium.

Liquidus Line

The temperature boundary curve above which the entire multi-component system exists entirely as a liquid phase.

Solidus Line

The temperature boundary curve below which the entire multi-component system exists entirely as a solid phase.

Three-Component System Alternative Name

Commonly called a ternary system.

Three-Component System Phase Triangle

A system consisting of 3 components existing in phase equilibrium where temperature and pressure are both held constant.

Ternary System Co-solvent Mechanism

Consists of two liquids that are partially miscible, where the third component acts as a co-solvent with high affinity for both layers.

Ternary Triangle Apex Coordinates

Represents an absolute 100% concentration of that single isolated component.

Ternary Triangle Base Coordinates

Located directly opposite any apex, representing a 0% concentration of that specific component.

One-Component System Main Pharmaceutical Use

Leveraged for freeze-drying, drying protocols, and precise phase change control.

Two-Component Liquid-Liquid Main Pharmaceutical Use

Applied during miscibility studies, optimal co-solvent selection, and phase separation tracking.

Two-Component Solid-Liquid Main Pharmaceutical Use

Crucial for formulating eutectic mixtures, lowering melting points, and troubleshooting compounding issues.

Three-Component System Main Pharmaceutical Use

Extensively used to map and formulate stable emulsions, microemulsions, and specialized surfactant/co-solvent vehicles.