Vapor-Liquid Equilibrium (VLE)

Vapor-Liquid Equilibrium (VLE)

• Phase equilibrium occurs when multiple phases coexist in a stable condition.
• Vapor-liquid equilibrium (VLE) involves a liquid and vapor phase in equilibrium.
• In equilibrium, the temperature of all phases is the same: $T^{\alpha} = T^{\beta} = T^{\gamma} =...$
• In equilibrium, the pressure of all phases is the same: $P^{\alpha} = P^{\beta} = P^{\gamma} =...$
• The chemical potential of each species must be the same in all phases: $\mu_{i}^{\alpha} = \mu_{i}^{\beta} = \mu_{i}^{\gamma} =...$

The Phase Rule

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

Understanding the Phase Rule

• Degrees of Freedom (F) indicates how many intensive variables can be changed without altering the number of phases.
• Phases ($\pi$) indicates the number of physically distinct and homogeneous parts of the system.
• Components (N) indicates the minimum number of independent chemical constituents to specify the composition of each phase.

Examples of the Phase Rule

• Single Component (Water):
  • At the triple point of water, ice, liquid, and steam coexist.
  • $N = 1$, $\pi = 3$, $F = 2 - 3 + 1 = 0$
  • At the triple point, there are no degrees of freedom, thus the temperature and pressure are fixed.
• Binary System (Ethanol and Water):
  • Ethanol and water are in vapor-liquid equilibrium.
  • $N = 2$, $\pi = 2$, $F = 2 - 2 + 2 = 2$
  • Two intensive properties can be independently varied, such as temperature and composition of one phase.

Importance of the Phase Rule

• The phase rule is useful in designing and operating chemical engineering separation processes.
• The phase rule aids in determining the conditions needed for separations and purifications.

Understanding vapor-liquid equilibrium (VLE) is crucial in chemical engineering. Phase equilibrium occurs when multiple phases coexist stably. The phase rule, developed by J. Willard Gibbs, relates degrees of freedom, components, and phases in a system at equilibrium.