Vapor - Liquid Equilibrium (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?


