Vapor - Liquid Equilibrium Equation (VLE)

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The fundamental equation for vapor-liquid equilibrium (VLE) is expressed as μ_i^L = μ_i^V, indicating that the chemical potential of each component must be equal in both phases at equilibrium. This equation is typically derived for isolated systems, yet it also applies to closed systems where heat exchange occurs, such as in distillation processes. The equation is valid for both vapor and liquid mixtures at thermodynamic equilibrium. The derivation for this principle can be found in Chapter 10 of "Introduction to Chemical Engineering Thermodynamics" by Smith and Van Ness. Overall, the equation is applicable in both open and closed systems, confirming its versatility in thermodynamic analysis.
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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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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It apply in open and closed systems

Horacio
 

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