Vapor-Liquid Equilibrium (VLE)

Vapor-Liquid Equilibrium (VLE) Introduction

• Phase equilibrium is the stable state where multiple phases coexist
• Vapor-liquid equilibrium (VLE) is a common concern in Chemical Engineering Thermodynamics, involving equilibrium between liquid and vapor phases

Equilibrium Criteria

• Temperature must be the same in all phases: $T^{\alpha} = T^{\beta} = T^{\gamma} =...$
• Pressure must be the same in all phases: $P^{\alpha} = P^{\beta} = P^{\gamma} =...$
• Chemical potential of each species must be the same 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

Phase Rule

• Developed by J. Willard Gibbs.
• Relates degrees of freedom, components, and phases in a system at equilibrium.
• Expressed as: $F = 2 - \pi + N$
  • $F$ is the number of degrees of freedom
  • $\pi$ is the number of phases in equilibrium
  • $N$ is the number of components in the system

Understanding the Phase Rule

• Degrees of Freedom (F): Number of intensive variables (e.g., temperature, pressure, composition) that can independently vary without changing 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, ice, liquid water, and steam coexist.
• $N = 1$ (water)
• $\pi = 3$ (ice, liquid water, steam)
• $F = 2 - 3 + 1 = 0$
• At the triple point, temperature and pressure are fixed with no degrees of freedom.

Binary System with Vapor and Liquid Phases

• Consider a mixture of ethanol and water 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 (e.g., temperature and composition of one phase).

Importance

• Crucial for designing and operating separation processes like distillation, extraction, and crystallization.
• Helps determine conditions to achieve desired separations and purifications.

Introduction to Vapor-Liquid Equilibrium (VLE) and phase equilibrium. Key concepts include equilibrium criteria (temperature, pressure, chemical potential) and the Phase Rule developed by J. Willard Gibbs. The Phase Rule relates degrees of freedom, components, and phases in a system at equilibrium.