2.2 Vapor-liquid equilibrium (VLE) and liquid-liquid equilibrium (LLE)

Phase equilibrium is crucial in separation processes, governing how components distribute between different phases. Understanding phase diagrams and equilibrium calculations helps predict and control separations in various systems, from simple binary mixtures to complex multicomponent systems.

Vapor-liquid equilibrium (VLE) is particularly important in distillation and other separation techniques. Mastering VLE calculations, including Raoult's law, Henry's law, and flash calculations, enables engineers to design and optimize separation processes for diverse applications in chemical and petroleum industries.

Fundamentals of Phase Equilibrium

Phase equilibrium and diagrams

Top images from around the web for Phase equilibrium and diagrams

• 

  Gibb’s Phase Rule – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

• 

  Phase Diagram – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

• 

  Phase Diagrams | Boundless Chemistry View original

  Is this image relevant?

• 

  Gibb’s Phase Rule – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

• 

  Phase Diagram – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

1 of 3

Top images from around the web for Phase equilibrium and diagrams

• 

  Gibb’s Phase Rule – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

• 

  Phase Diagram – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

• 

  Phase Diagrams | Boundless Chemistry View original

  Is this image relevant?

• 

  Gibb’s Phase Rule – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

• 

  Phase Diagram – Foundations of Chemical and Biological Engineering I View original

  Is this image relevant?

1 of 3

• Phase equilibrium occurs when two or more phases coexist in thermodynamic equilibrium requiring thermal, mechanical, and chemical potential equality (ice-water mixture at 0°C)
• Phase diagrams graphically represent equilibrium states showing relationships between pressure, temperature, and composition (water phase diagram)
• Pressure-temperature (P-T) diagrams display phase boundaries and triple points (carbon dioxide P-T diagram)
• Temperature-composition (T-x) and pressure-composition (P-x) diagrams illustrate phase behavior for binary mixtures (ethanol-water T-x diagram)
• Gibbs phase rule $F = C - P + 2$ determines degrees of freedom in a system (binary mixture in VLE has 2 degrees of freedom)
• Tie lines and lever rule determine compositions and amounts of coexisting phases (LLE of phenol-water system)

Vapor-liquid equilibrium calculations

• Raoult's law $P_i = x_i P_i^*$ applies to ideal solutions predicting partial pressures (benzene-toluene mixture)
• Henry's law $P_i = H_i x_i$ describes behavior of dilute solutions (oxygen dissolved in water)
• Dalton's law of partial pressures $P = \sum P_i$ relates total pressure to component partial pressures (air composition)
• VLE calculations involve:
  1. Total pressure calculation using component partial pressures
  2. Bubble point determination finding temperature or pressure at which first vapor bubble forms
  3. Dew point calculation identifying conditions for first liquid droplet formation
  4. Flash calculations to determine vapor and liquid compositions after partial vaporization

Advanced Phase Equilibrium Analysis

Binary and ternary phase diagrams

• Binary VLE diagrams:
  • T-x-y diagrams show boiling and condensation curves (ethanol-water system)
  • P-x-y diagrams illustrate pressure-composition relationships at constant temperature
  • Azeotropes appear as minimum or maximum boiling points (ethanol-water azeotrope at 95.6 wt% ethanol)
• Binary LLE diagrams display:
  • Upper and lower critical solution temperatures (triethylamine-water UCST at 18.5°C)
  • Partially miscible and immiscible systems (octanol-water immiscibility)
• Ternary LLE diagrams use triangular coordinate systems showing:
  • Tie lines connecting equilibrium compositions
  • Tie triangles for three-phase equilibria
  • Plait point where two-phase region ends (acetone-chloroform-water system)
• Interpreting phase diagrams involves:
  • Identifying present phases
  • Determining coexisting phase compositions
  • Calculating relative phase amounts using the lever rule

Factors affecting phase equilibria

• Temperature effects:
  • Increases vapor pressure following Antoine equation
  • Alters solubility in LLE systems (nicotine-water miscibility gap closes with increasing temperature)
• Pressure effects:
  • Shifts VLE according to Le Chatelier's principle
  • Enables formation of supercritical fluids (CO2 becomes supercritical above 31.1°C and 73.8 bar)
• Composition effects:
  • Induces non-ideal behavior in mixtures
  • Requires activity coefficients for accurate modeling (acetone-chloroform positive deviation from Raoult's law)
• Le Chatelier's principle predicts equilibrium shifts (pressure increase favors liquid phase in VLE)
• Clausius-Clapeyron equation $\ln(\frac{P_2}{P_1}) = \frac{\Delta H_{vap}}{R}(\frac{1}{T_1} - \frac{1}{T_2})$ relates vapor pressure to temperature
• Van 't Hoff equation describes temperature dependence of equilibrium constants
• Gibbs-Duhem equation relates chemical potentials in a mixture ensuring thermodynamic consistency