Thermodynamic Explanation
Consider the system at the point it has reached equilibrium. The condition for this is that the chemical potential of the solvent (since only it is free to flow toward equilibrium) on both sides of the membrane is equal. The compartment containing the pure solvent has a chemical potential of . On the other side, the compartment containing the solute has an additional contribution from the solute (factored as the mole fraction of the solvent, < 1) but there also appears an addition in pressure. The balance is therefore:
where denotes the external pressure, the solvent, the mole fraction of the solvent and the osmotic pressure exerted by the solutes. The addition of solute decreases the chemical potential (an entropic effect), while the pressure increases the chemical potential, and thus a balance is reached. Note that the presence of the solute decreases the potential due to being smaller than 1.
Read more about this topic: Osmotic Pressure
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