Explain Solubility of one liquid in another -Liquid–Liquid Equilibria

Suppose substances A and B are both liquids when pure. In discussing the solubility of liquid B in liquid A, we can treat B as either a solute or as a constituent of a liquid mixture. The difference lies in the choice of the standard state or reference state of B.

We can define the solubility of B in A as the maximum amount of B that can dissolve without phase separation in a given amount of A at the given temperature and pressure. Treating B as a solute, we can express its solubility as the mole fraction of B in the phase at the point of phase separation. The addition of any more B to the system will result in two coexisting liquid phases of fixed composition, one of which will have mole fraction x_B equal to its solubility.

Consider a system with two coexisting liquid phases α and β containing components A and B. Let α be the A-rich phase and β be the B-rich phase. For example, A could be water and B could be benzene, a hydrophobic substance. Phase α would then be an aqueous phase polluted with a low concentration of dissolved benzene, and phase β would be wet benzene. x^α_B would be the solubility of the benzene in water, expressed as a mole fraction. Below, relations are derived for this kind of system using both choices of standard state or reference state.