Phase Diagrams

Overview

Phase diagrams are graphical representations showing the physical states of a substance as a function of temperature and pressure. They indicate conditions for phase transitions and equilibrium between phases.

States of Matter

State	Description	Properties
Solid	Fixed shape and volume	Particles in fixed positions
Liquid	Fixed volume, variable shape	Particles close but mobile
Gas	Variable shape and volume	Particles far apart, fast moving

Key Features of Phase Diagrams

Phase Regions

Areas representing solid, liquid, and gas phases.

Phase Boundaries

Lines separating phases where two phases coexist in equilibrium.

Triple Point

Where all three phases coexist in equilibrium.

Critical Point

Beyond this point, liquid and gas become indistinguishable (supercritical fluid).

Phase Boundaries

Solid-Liquid Line (Fusion Curve)

• Melting/freezing equilibrium
• Shows how melting point changes with pressure
• Usually slopes right (positive slope)
• Water: slopes left (negative slope) - anomaly!

Liquid-Gas Line (Vaporization Curve)

• Boiling/condensation equilibrium
• Shows how boiling point changes with pressure
• Ends at critical point

Solid-Gas Line (Sublimation Curve)

• Sublimation/deposition equilibrium
• Below triple point pressure

Phase Transitions

Transition	From → To	Energy Change
Melting	Solid → Liquid	Absorbs heat
Freezing	Liquid → Solid	Releases heat
Vaporization	Liquid → Gas	Absorbs heat
Condensation	Gas → Liquid	Releases heat
Sublimation	Solid → Gas	Absorbs heat
Deposition	Gas → Solid	Releases heat

Triple Point

• Unique T and P where all three phases coexist
• For water: 0.01°C, 0.006 atm (611.73 Pa)
• For CO₂: -56.6°C, 5.11 atm

Critical Point

• Beyond this, no distinction between liquid and gas
• Critical temperature ($T_c$): Above this, gas cannot be liquefied by pressure alone
• Critical pressure ($P_c$): Pressure needed to liquefy gas at $T_c$

Substance	$T_c$ (°C)	$P_c$ (atm)
Water	374	218
CO₂	31	73
O₂	-119	50

Reading Phase Diagrams

Determining Phase at Given T, P

1. Locate the point on the diagram
2. The region it falls in indicates the phase

Following Phase Changes

• Move horizontally: constant T, changing P
• Move vertically: constant P, changing T
• Cross boundary lines = phase transition

Example: Water Phase Diagram

Key Points for Water

• Normal melting point: 0°C at 1 atm
• Normal boiling point: 100°C at 1 atm
• Triple point: 0.01°C at 0.006 atm
• Critical point: 374°C at 218 atm
• Negative slope of fusion curve (unusual!)

Example: Carbon Dioxide Phase Diagram

Key Points for CO₂

• At 1 atm, CO₂ sublimates (no liquid phase)
• Dry ice sublimates at -78°C
• Liquid CO₂ only exists above 5.11 atm
• CO₂ fire extinguishers contain supercritical fluid

Heating and Cooling Curves

Plateaus

• Temperature remains constant during phase changes
• All added heat goes into breaking intermolecular forces (latent heat)

Heat Calculations

$$q = mc\Delta T \quad \text{(temperature change)}$$ $$q = n\Delta H_{fus} \quad \text{(melting/freezing)}$$ $$q = n\Delta H_{vap} \quad \text{(vaporization/condensation)}$$

Clausius-Clapeyron Equation

Relates vapor pressure to temperature:

$$\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$

Or:

$$\ln P = -\frac{\Delta H_{vap}}{RT} + C$$

Used to:

• Calculate vapor pressure at different temperatures
• Determine enthalpy of vaporization