Chemistry - Use of osmosis to measure molecular weight of macromolecules
It has to do with the fact, that osmotic pressure of any solution is dependent only on the relative number of particles in the solution (in case of dilute solutions), irrespective of their nature. Hence osmotic pressure is called a colligative property.
Therefore, you take a certain known weight of the substance you want to calculate the molecular mass of, prepare a solution and measure the osmotic pressure. Then you compare this to the known osmotic pressure of standard solution which tells you the relative number of particles required to create such a pressure. From this and the knowledge of the weight you used to prepare the solution, you can get the required molecular weight (weight of Avogadro's number of particles). In practice, certain complications, like dissociation and association might complicate the matter a bit.
This method is widely used to calculate the molecular weight (especially) of polymers. See Berkeley and Hartley method.