Q.200 mL of an aqueous solution of a protein contains 1.26 g of protein. At 300 K, the osmotic pressure of this solution is found to be $2.52 \times 10^{-3}$ bar. The molar mass of protein will be (R = 0.083 L bar mol$^{-1}$ K$^{-1}$)

Osmosis and Osmotic Pressure

Imagine you have a glass of pure water and you drop a single raisin into it. After a few hours, the raisin swells up. Why? Water moved into the raisin. Now imagine you drop that same swollen raisin into a glass of concentrated sugar syrup. It shrivels. Water moved out of the raisin.

That movement of water — across a barrier that lets water through but not the bigger sugar molecules — is osmosis. The barrier is called a semipermeable membrane. Your raisin's skin acts like one: water passes, but the dissolved sugars and salts inside the raisin do not.

The Intuition: Water Wants to Equalise Concentration

Here is the core idea. Water molecules are in constant random motion. On one side of the membrane you have pure water (lots of water molecules). On the other side you have a solution (fewer water molecules because some space is taken up by solute particles). More water molecules hit the membrane from the pure side per second than from the solution side. The net result? Water flows from the region of higher water concentration (pure water) to the region of lower water concentration (the solution).

The Precise Statement

Osmosis is the net spontaneous movement of solvent molecules (usually water) from a region of lower solute concentration to a region of higher solute concentration, across a semipermeable membrane.

Now, what happens if you try to stop this flow? Suppose you have a U-shaped tube with a semipermeable membrane at the bottom. Left arm: pure water. Right arm: sugar solution. Water will rise in the right arm and fall in the left. Eventually the column of solution on the right gets so tall that its weight pushes water back through the membrane at the same rate it comes in. The system reaches equilibrium.

The extra pressure you would need to apply on the solution side to prevent any net movement of water is called the osmotic pressure ($\Pi$).