Vapor-Liquid Equilibrium (VLE)

Vapor-Liquid Equilibrium (VLE) Introduction

• Phase equilibrium occurs when multiple phases exist together in a stable state.
• Vapor-liquid equilibrium (VLE) involves a liquid and a vapor phase coexisting in equilibrium.

Equilibrium Criteria

• Temperature equilibrium requires all phases to have the same temperature: $T^{\alpha} = T^{\beta} = T^{\gamma} =...$.
• Pressure equilibrium requires all phases to have the same pressure: $P^{\alpha} = P^{\beta} = P^{\gamma} =...$.
• Chemical potential equilibrium requires each species to have the same chemical potential in all phases: $\mu_{i}^{\alpha} = \mu_{i}^{\beta} = \mu_{i}^{\gamma} =...$.
• $\alpha, \beta, \gamma$ represent different phases.
• (i) represents a specific species in the mixture.

The Phase Rule

• The phase rule, developed by J. Willard Gibbs, relates degrees of freedom, components, and phases in a system at equilibrium.
• The phase rule equation is: $F = 2 - \pi + N$.
• (F) is the number of degrees of freedom.
• (\pi) is the number of phases in equilibrium.
• (N) is the number of components in the system.
• Components are the independent chemical species needed to define the composition of all phases in the system.

Understanding the Phase Rule

• Degrees of Freedom ((F)): Number of intensive variables that can be independently changed without altering the number of phases.
• Phases ((\pi)): Number of physically distinct and homogeneous parts of the system.
• Components ((N)): Minimum number of independent chemical constituents required to specify the composition of each phase.

Examples

• Single Component System (e.g., Water):
  • At the triple point of water:
    • (N = 1) (water)
    • (\pi = 3) (ice, liquid water, steam)
    • (F = 2 - 3 + 1 = 0) (no degrees of freedom, temperature and pressure are fixed).
• Binary System with Vapor and Liquid Phases (e.g., ethanol and water mixture):
  • In vapor-liquid equilibrium:
    • (N = 2) (ethanol and water)
    • (\pi = 2) (vapor and liquid)
    • (F = 2 - 2 + 2 = 2) (two intensive properties can be independently varied).

Importance

• The phase rule is crucial for designing and operating separation processes like distillation, extraction, and crystallization.
• It helps determine the conditions needed to achieve desired separations and purifications.

Understand Vapor-Liquid Equilibrium (VLE) with phase equilibrium where liquid and vapor phases coexist. Key conditions include temperature, pressure, and chemical potential equilibrium across phases. The phase rule, (F = 2 - \pi + N), relates degrees of freedom, components, and phases.