Vant Hoffs Law of Osmotic Pressure

As we indicated in Chapter 13, the requirement that all phases be at the same pressure at equilibrium does not apply in all situations, and in particular, it does not apply to two phases of different composition separated by a rigid membrane. If the membrane is permeable to only one component, we can show that the pressure on the two phases must be different if equilibrium is maintained at a. fixed temperature. 

If we add through the side arm A some solute to which the membrane is impermeable, then with adequate mixing, the solute will become distributed uniformly throughout the left chamber but will be absent from the right chamber. Solvent then will be observed to move from the right to the left side because 

The chemical potential and the escaping tendency of the pure solvent are always greater than the chemical potential and the escaping tendency of the solvent in the solution. 

The movement of solvent can be prevented and equilibrium can be restored if the pressure P is made sufficiently greater than Pq. In the new equilibrium state 

As Pi is a function of the pressure P and the mole fraction of solute Xx, we can express lipi(left) in Equation (15.34) as 

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