Phase Equilibria

Study of the equilibrium between different phases of matter and the transitions between them.

Phase

A homogeneous part of a system that is physically distinct and mechanically separable.

System Phase Component Description
Mixture of O₂, N₂, H₂ gases 1 3 Gases well mixed; no visible boundary
Oil + water (unmixed) 2 2 Boundary between two liquids
Alcohol + water (mixed) 1 2 No boundary; miscible
Salt solution 1 2 Salt + water
Saturated CuSO₄ in closed bottle 3 2 Solid, liquid, gas (water vapour)
Steel 1 2 Fe + C 
O
O=C=O
[Cu+2].[O-]S(=O)(=O)[O-]

Phase Rule (Gibbs Phase Rule)

$$F = C - P + 2$$

Where:

  • F = degrees of freedom
  • C = number of components
  • P = number of phases

One-Component Phase Diagrams

Water Phase Diagram

  • Triple point: All three phases coexist (0.01°C, 0.006 atm)
  • Critical point: 374°C, 218 atm (above: supercritical fluid)
  • Normal boiling point: 100°C at 1 atm
  • Normal freezing point: 0°C at 1 atm

CO₂ Phase Diagram

  • Triple point: 5.11 atm, −56.6°C
  • Critical point: 31.1°C, 73 atm
  • Sublimes at 1 atm (dry ice)
  • Solid-liquid line has positive slope (solid denser than liquid)
O=C=O
O

Phase Transitions

Transition Name ΔH
Solid → Liquid Fusion (melting) ΔHfus > 0
Liquid → Solid Freezing ΔHfus < 0
Liquid → Gas Vaporization ΔHvap > 0
Gas → Liquid Condensation ΔHvap < 0
Solid → Gas Sublimation ΔHsub > 0
Gas → Solid Deposition ΔHsub < 0

Clausius-Clapeyron Equation

Describes the temperature dependence of vapor pressure:

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

Raoult's Law

For a component A in solution: $$P_A = X_A P_A^o$$

Where:

  • $X_A$ = mole fraction of component A
  • $P_A^o$ = vapor pressure of pure component A

For a two-component system (A + B), by Dalton's law: $$P_{total} = P_A + P_B = X_A P_A^o + X_B P_B^o$$

Where $X_A + X_B = 1$.

Ideal Solutions

  • A–A ≈ B–B ≈ A–B interactions
  • $ΔH_{soln} = 0$ (thermoneutral)
  • $ΔV = 0$
  • Obeys Raoult's law exactly
  • Example: benzene–toluene
c1ccccc1
Cc1ccccc1

Deviations from Raoult's Law

Deviation Condition $ΔH_{soln}$ $ΔV$ Vapor Pressure Boiling Point
Positive A–A, B–B > A–B +ve (endothermic) +ve (expansion) $P_{actual} > P_{calc}$ Azeotrope has minimum bp
Negative A–B > A–A, B–B −ve (exothermic) −ve (shrinkage) $P_{actual} < P_{calc}$ Azeotrope has maximum bp
  • Positive deviation examples: ethanol–water, ethanol–benzene, NaCl–H₂O (ionic)
  • Negative deviation examples: HCl–water, HNO₃–water, acetone–chloroform
CCO
c1ccccc1
Cl
O
CC(=O)C
C(Cl)(Cl)Cl
O=[N+]([O-])O

Colligative Properties

Properties that depend on the number of solute particles, not their identity.

1. Vapor Pressure Lowering

$$ΔP = X_{solute} × P°_{solvent}$$

2. Boiling Point Elevation

$$ΔT_b = K_b × m$$

3. Freezing Point Depression

$$ΔT_f = K_f × m$$

4. Osmotic Pressure

$$π = MRT$$

[!example] Worked Examples

Vapor pressure lowering: 218 g glucose (RMM 180.2) in 460 mL water at 30°C. $P°{water} = 31.82$ mmHg. $X{glucose} = 0.0453$ → $ΔP = 1.44$ mmHg → $P_{solution} = 30.38$ mmHg.

Freezing point depression: 1.60 g naphthalene (C₁₀H₈) in 20.0 g benzene. $K_f = 4.3$ °C m⁻¹. Pure benzene fp = 5.5°C. $m = 0.624$ mol/kg → $ΔT_f = 2.68$°C → fp = 2.82°C.

Boiling point elevation: 651 g ethylene glycol in 2505 g water. RMM = 62. $K_b = 0.52$ °C/m. $m = 4.19$ mol/kg → $ΔT_b = 2.18$°C → bp = 102.18°C.

Osmotic pressure: 46.0 g glycerin (C₃H₈O₃, RMM 92) per liter at 0°C. $Π = (0.5 / 1.0) × 0.0821 × 273 = 11.21$ atm.

C([C@@H]1[C@H]([C@@H]([C@H](C(O1)O)O)O)O)O
c1ccc2ccccc2c1
OCCO
OCC(O)CO

Fractional Distillation & Azeotropes

Fractional Distillation

Procedure for separating liquid components based on different boiling points.

  • Distillate (receiving flask): lower boiling point component
  • Residue (distilling flask): higher boiling point component

Azeotrope

A mixture that distills at constant composition; cannot be separated by simple fractional distillation.

Positive Deviation Azeotropes (Minimum Boiling Point)

System Azeotrope Composition Boiling Point
Ethanol–Benzene 32.4% ethanol Lower than both pure components
Ethanol–Water 95.6% ethanol, 4.4% water 78.2°C
  • Starting < azeotrope % → distillate = azeotrope, residue = higher bp component
  • Starting > azeotrope % → distillate = azeotrope, residue = higher bp component
  • Starting = azeotrope → only azeotrope distills over

Negative Deviation Azeotropes (Maximum Boiling Point)

System Azeotrope Composition Boiling Point
HCl–Water 20.2% HCl Higher than both pure components
HNO₃–Water 68% HNO₃, 32% water 120.5°C
  • Starting < azeotrope % → distillate = lower bp pure component, residue = azeotrope
  • Starting > azeotrope % → distillate = higher bp pure component, residue = azeotrope
CCO
CCCCO
Cl
O=[N+]([O-])O

Related Topics

Sources