Binary aqueous salt solution system:

In a binary aqueous salt solution system, let component, i represent water denoted through subscript w and let μi = μ* (chemical potential of water at a specified pressure and temperature). According to Eq., a chemical potential of water μ w in the solution at pressure P₁ is less than that of pure water.    *

μw  = μ*w+ RT ln a_w

where, a_w  is the thermodynamic activity of water in solution. The equilibrium could be restored through increasing the pressure on the solution side to P₂ such in which the chemical potential of water is raised to that of pure water, μw.  The increase in chemical potential of water in the solution as the pressure is increased from P₁ to P₂ is acquired from Eq.

Since this increase, added to μw    must restore the chemical potential of water and according to Eq.

 μ_w       +∫^P2_P1V_wd∫ P =μ*w

when V_w  is assumed constant.

The pressure difference (P₂ -P₁) is through definition the osmotic pressure of the solution, usually represented through Π. Thus,

V_w  Π   = - RT ln a_w