Vapor - Liquid Equilibrium Equation (VLE)

VLE and its applicability in closed systems. The equation states that the chemical potential of each component must be equal in both the liquid and vapor phases at equilibrium. This holds for vapor and liquid mixtures at thermodynamic equilibrium, and the derivation can be found in Chapter 10 of Introduction to Chemical Engineering Thermodynamics by Smith and Van Ness. The equation applies to both open and closed systems, even though it is typically derived for isolated systems.
  • #1
Dario56
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Most fundamental equation for VLE is $$ \mu_i^L = \mu_i^V $$
It states that for every component chemical potential must be equal in both liquid and vapor phase at equilibrium. However, in my thermo textbook, this equation is derived for isolated systems while usually when dealing with VLE, systems are closed since heat is usually exchanged with surroundings like in distillation for example. Does this equation hold also for closed systems and if so how can it be derived?
 
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  • #2
This equation holds for vapor mixtures and corresponding liquid mixtures at thermodynamic equilibrium with one another. The derivation of this fact is presented in Chapter 10 of Introduction to Chemical Engineering Thermodynamics, Smith and Van Ness.
 
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Likes Astronuc and Dario56
  • #3
It apply in open and closed systems

Horacio
 

FAQ: Vapor - Liquid Equilibrium Equation (VLE)

What is the Vapor-Liquid Equilibrium Equation (VLE)?

The Vapor-Liquid Equilibrium Equation (VLE) is a mathematical relationship that describes the equilibrium between a vapor phase and a liquid phase of a substance at a given temperature and pressure. It is used to determine the composition of the vapor and liquid phases in equilibrium with each other.

What factors affect the Vapor-Liquid Equilibrium Equation?

The factors that affect the Vapor-Liquid Equilibrium Equation include temperature, pressure, and the chemical properties of the substances involved. Changes in these factors can alter the equilibrium composition of the vapor and liquid phases.

How is the Vapor-Liquid Equilibrium Equation used in industry?

The Vapor-Liquid Equilibrium Equation is used in various industries, such as chemical engineering and petroleum refining, to design and optimize processes involving vapor-liquid separation. It is also used in the design of distillation columns and other separation equipment.

What are the limitations of the Vapor-Liquid Equilibrium Equation?

The Vapor-Liquid Equilibrium Equation is based on idealized assumptions and may not accurately predict the behavior of real systems. It also does not take into account factors such as non-ideal behavior, chemical reactions, and multi-component systems. Therefore, it should be used with caution and validated with experimental data.

How is the Vapor-Liquid Equilibrium Equation derived?

The Vapor-Liquid Equilibrium Equation is derived from the Gibbs-Duhem equation, which describes the relationship between the chemical potentials of the components in a mixture. It can also be derived from the Raoult's law, which states that the partial pressure of a component in a mixture is directly proportional to its mole fraction in the liquid phase.

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