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.
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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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