where is the number of moles of ith component. The equilibrium of a component between the liquid phases is expressed in terms of integral molar free energy. Integral molar free energy of solution

(2)

 represents free energy of solution and  is the free energy of pure components before entering into the solution. The quantity  is the partial molar free energy of mixing of component i and represent the change of energy or work which a mole of pure component i can make available.

Chemical potential is a useful concept to describe chemical equilibrium between liquid phases. At chemical equilibrium the chemical potential of any component is identical in all phases. Knowledge of chemical potential is important in steelmaking because an impurity can transfer in the gaseous or slag phase only when its chemical potential is lower than in hot metal.