# Vapor - Liquid Equilibrium Equation (VLE)

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?

Chestermiller
Mentor
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.

Astronuc and Dario56
It apply in open and closed systems

Horacio