Osmosis: Two samples of water are separated by a semipermeable membrane. Water flows back and forth, but no solute molecules can flow through the membrane.

If one side contains solute particles then on that side there are fewer water molecules next to the membrane, which means that there are fewer water molecules to go through the membrane. The solvent on the side without solute particles diffuses through the membrane more quickly than the side with solute particles present.

In the drawing to the left, water molecules can pass freely through the membrane. Since the same number of molecules move in each direction the volumes do not change.

Now that there are solute particles next to the membrane there are fewer water molecules to pass through the membrane. Since the more water moves from the right to the left than from the left to the right the volume increases on the left hand side. The volume keeps increasing until the pressure caused be the height of the column of water is large enough to counterbalance the influx of water from the right side.

The relationship between osmotic pressure and concentration is

Where is the osmotic pressure, the pressure required to prevent the flow of solvent from one side of the membrane to the other, in atm, M is the concentration of the solution in moles per liter, R is the universal gas constant 0.08206 L•atm•mol^-1•K^-1, and T is the absolute temperature of the solution.

For example

35.0 g of hemoglobin are dissolved in water to make a 1 L solution. (I do not know anyone who would do this experiment on such a large scale. It would make more sense to make ca. 1 mL, or less, of the solution.) At 25 °C the osmotic pressure was found to be 10.0 torr. What is the molecular mass of hemoglobin?

 

The 1 L solution contains 0.000537799 mol or 35.0 g so...

Our least precise measurement has three significant figures (35.0 g, 10.0 torr and 273+25 = 298 K) so our answer can have three significant figures.

Because we used a more sensitive property, osmotic pressure, we arrived at a more precise molar mass determination than BP elevation or MP depression could provide. In fact, BP elevation and MP depression would not work for hemoglobin. The temperature change would be to small.

What kind of freezing point depression would one see? Because the solution is so dilute the molality is almost the same as the molarity. So, let us assume that m = M, or m = 0.0005378 m.

Essentially, freezing point depression or boiling point elevation would not be measureable.