Glossary

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

3 min read•july 24, 2024

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.

(VLE) is particularly important in and other separation techniques. Mastering VLE calculations, including , , 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

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  • 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 )
  • 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 )
  • Gibbs phase rule F=C−P+2F = 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 Pi=xiPi∗P_i = x_i P_i^* applies to ideal solutions predicting partial pressures (benzene-toluene mixture)
  • Henry's law Pi=HixiP_i = H_i x_i describes behavior of dilute solutions (oxygen dissolved in water)
  • Dalton's law of partial pressures P=∑PiP = \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 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 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 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⁡(P2P1)=ΔHvapR(1T1−1T2)\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

Key Terms to Review (18)

Activity Coefficient: The activity coefficient is a numerical value that quantifies how the behavior of a component in a mixture deviates from ideal behavior, particularly in non-ideal solutions. It reflects the effective concentration of a species compared to its ideal state, where interactions between molecules are negligible. Understanding activity coefficients is crucial for analyzing phase equilibria and calculating thermodynamic properties in separation processes.
Azeotrope: An azeotrope is a mixture of two or more liquids that maintains a constant boiling point and composition during distillation, behaving like a single substance. This occurs when the vapor phase has the same composition as the liquid phase at certain proportions, which complicates separation processes. Azeotropes can be minimum boiling or maximum boiling, affecting how mixtures can be separated through techniques like distillation.
Daniel Gabriel Fahrenheit: Daniel Gabriel Fahrenheit was a German physicist and engineer who is best known for inventing the mercury-in-glass thermometer and the Fahrenheit temperature scale. His contributions significantly advanced the fields of thermometry and temperature measurement, which are crucial in understanding various separation processes that involve vapor-liquid and liquid-liquid equilibria.
Distillation: Distillation is a separation process that involves heating a liquid mixture to create vapor and then cooling the vapor to recover the liquid, effectively separating components based on their boiling points. This technique plays a crucial role in various industries, enabling the purification and concentration of valuable substances while also providing insight into phase behavior and thermodynamic properties.
Enthalpy of mixing: Enthalpy of mixing is the change in enthalpy that occurs when two or more substances are mixed together, reflecting the energy absorbed or released during the process. This concept is crucial in understanding how mixtures behave during phase changes and equilibrium states, particularly in vapor-liquid and liquid-liquid scenarios. It provides insight into the interactions between different components and can influence properties such as volatility, solubility, and overall mixture stability.
Equilibrium constant: The equilibrium constant is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium in a reversible chemical reaction. This constant provides insight into the extent to which a reaction favors the formation of products over reactants and is influenced by temperature, pressure, and other conditions. Understanding the equilibrium constant is essential for analyzing processes like adsorption, ion exchange, vapor-liquid equilibrium, and liquid-liquid equilibrium.
Extraction: Extraction is a separation process used to isolate a specific substance from a mixture by dissolving it in a suitable solvent. This method is crucial for obtaining desired components from complex mixtures, allowing for the purification and concentration of valuable materials.
Gibbs Free Energy: Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. It helps determine whether a reaction or process is spontaneous by analyzing the change in Gibbs Free Energy (ΔG). When ΔG is negative, the process can occur spontaneously, which is essential for understanding various physical and chemical behaviors, including phase equilibria and separation techniques.
Henry's Law: Henry's Law states that at a constant temperature, the amount of a gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid. This principle is essential in understanding how gases interact with liquids in various separation processes, particularly in absorption and stripping operations, as well as in the analysis of vapor-liquid and liquid-liquid equilibria.
Ideal solution: An ideal solution is a mixture where the interactions between different components are similar to those between the molecules of each pure component, resulting in predictable behavior regarding properties such as vapor-liquid equilibrium and liquid-liquid equilibrium. In an ideal solution, Raoult's Law applies perfectly, meaning that the partial vapor pressures of each component can be calculated as a function of their mole fractions in the mixture. This results in linear relationships and consistent thermodynamic properties.
Liquid-liquid equilibrium: Liquid-liquid equilibrium refers to the state in which two immiscible liquids coexist in a system, maintaining distinct phases while reaching a balance in their chemical potentials. This concept is crucial in understanding how substances partition between different liquid phases, which is essential for various separation processes like extraction and distillation. It plays a significant role in mass transfer operations where the interaction between liquids influences the efficiency of separation techniques.
Miscibility: Miscibility refers to the ability of two substances to mix together in any proportion without separating into two phases. This property is essential in understanding how different substances behave in both vapor-liquid and liquid-liquid interactions, impacting factors like solubility, phase behavior, and separation processes.
Non-ideal behavior: Non-ideal behavior refers to the deviations from ideal predictions in physical and chemical processes, particularly in relation to vapor-liquid and liquid-liquid equilibria. This behavior occurs when real mixtures exhibit interactions that differ from those predicted by ideal models, leading to discrepancies in phase compositions, vapor pressures, and other thermodynamic properties. Understanding non-ideal behavior is crucial for accurately modeling and designing separation processes involving different phases.
Phase Diagram: A phase diagram is a graphical representation that shows the relationship between temperature, pressure, and the phases of a substance (solid, liquid, gas). It helps to visualize how different phases coexist at varying conditions and is crucial for understanding vapor-liquid equilibrium and liquid-liquid equilibrium.
Raoult's Law: Raoult's Law states that the partial vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. This law is fundamental in understanding how mixtures behave during processes like distillation and absorption, providing insight into vapor-liquid equilibrium and helping in the design of separation processes.
T-x diagram: A t-x diagram is a graphical representation that illustrates the relationship between temperature (t) and composition (x) of a mixture, particularly in the context of phase behavior during vapor-liquid equilibrium and liquid-liquid equilibrium. This diagram helps in visualizing how the phases of a system change with varying temperature and composition, which is crucial for understanding separation processes and thermodynamic principles.
Vapor-Liquid Equilibrium: Vapor-liquid equilibrium (VLE) is a state where the rates of evaporation and condensation of a liquid are equal, resulting in a stable balance between its vapor and liquid phases. This concept is essential in various separation processes, as it helps to understand how mixtures behave and how components can be separated based on their volatilities.
William H. Miller: William H. Miller is a prominent figure in the field of chemical engineering, particularly known for his contributions to the understanding of vapor-liquid equilibrium (VLE) and liquid-liquid equilibrium (LLE). His work has helped to refine models and equations that describe these equilibria, which are crucial for the design and operation of separation processes in various industries. By focusing on thermodynamics and phase behavior, Miller's research aids engineers in predicting how mixtures will behave under different conditions, enhancing efficiency in processes like distillation and extraction.
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