Osmotic Pressure

If a solution is separated from pure solvent by a semipermeable membrane that allows solvent, but not solute, molecules to pass through, solvent will move into the solution in an attempt to equalize the concentrations on the two sides of the membrane. This solvent transport process is called osmotic flow.

If there is no resisting force, solvent will continue to flow into the solution until the solvent reservoir is exhausted. However, if the solutions are arranged as shown in Figure 1.1, the incoming solvent will force the solution up the extension tube. The weight of this solution in the tube exerts a downward pressure that tends to oppose the flow of solvent. Eventually this pressure will exactly balance the force of solvent flow and equilibrium is attained. This equilibrium pressure is called the osmotic pressure.

The osmotic pressure P of a dilute solution of a nonelectrolyte is given by an equation formally equivalent to the ideal gas law:

    (1.1)

If C is the molar concentration of solute, T in K and R = 0.0821 L.atm/mol.K, P will have units of atm. Osmotic pressure measurements are particularly convenient for determination of the molar mass of macromolecules such as proteins.

Figure 1.1. Osmotic Pressure Apparatus

Example

A solution was prepared by dissolving 0.750 g of crab hemocyanin in 125 mL of water. At 4°C, the osmotic pressure corresponded to a rise of 2.6 mm of the solution (d = 1.00 g/mL). Determine the molar mass of the protein. We first convert the measured quantities to SI units and compute the osmotic pressure in pascals:

Then convert P to atm and compute the concentration using eq (1.1)

Finally compute the molar mass: