Osmotic Pressure – Definition, Formula, Examples

Osmotic pressure is the minimum pressure that prevents solvent molecules (water) from flowing through a semipermeable membrane. In other words, it is the pressure of a solvent against a semipermeable membrane that seeks to equalize the concentration of a solution on both sides of the membrane. Osmotic pressure is a colligative property of matter, so it depends on the number of solute particles and not their chemical identity.

What Is Osmotic Pressure? How It Works

Osmotic pressure is an example of diffusion and osmosis. In diffusion, molecules move from regions of high concentration to those of low concentration until both solute and solvent are evenly dispersed. In osmosis, there is a semipermeable membrane that allows solvent molecule movement, but prohibits transfer of larger solute molecules.

When you separate a pure solvent or dilute solution and a concentrated solution using a semipermeable membrane, water flows across the membrane. The movement of the solvent continues until the concentration is the same on both sides. So, you can look at osmotic pressure as either the force of the solvent molecules pushing across the membrane into the concentrated solution or as the pressure you need to apply to that solution to prevent the water from crossing the membrane.

Osmotic Pressure Examples

Red blood cells in various solutions are a great osmotic pressure example. The cell membrane is a semipermeable membrane.

• If you place red blood cells in water, the water is hypotonic or less concentrated compared with the cell contents. Water from outside the cells pushes through the cell membrane. The cells swell and burst.
• Placing red blood cells in an isotonic solution (such as physiological saline) causes no change in the size or appearance of the cells. Water enters and exits cells at the same rate.
• If you place red blood cells in a concentrate solution, the liquid is hypertonic or more concentrated than the cell cytoplasm. Water exits the cells, giving them a shrunken, crumpled appearance (crenation).

You can demonstrate the effect of osmotic pressure using an egg. First, soak a raw egg in vinegar or weak acetic acid and dissolve the shell. This leaves a semipermeable membrane surrounds the yolk and egg white.

• Place the egg in corn syrup. The syrup contains a lot of sugar but very little water so it is hypertonic with respect to the egg contents. Water flows across the membrane from the egg into the syrup. The egg becomes shrunken, leaving only the visible yolk.
• Place the egg in pure water. The water is hypotonic with respect to the egg contents, so water crosses the membrane into the egg and makes it swell.

Osmotic Pressure Formula

Credit for the osmotic pressure formula goes to Jacobus van’t Hoff. The formula relates osmotic pressure to solute concentration:

Π = iMRT

Here, Π is the osmotic pressure, i is the van’t Hoff factor, M is the solute molar concentration, R is the ideal gas constant, and T is the absolute temperature.

Example Problem

For example, how much glucose (C₆H₁₂O₆) per liter of water do you need for an intravenous solution that is isotonic to blood (7.64 atm at 37 °C)?

1. The first step is determining the van’t Hoff factor. Glucose dissolves in water, but it does not dissociate into ions. So, the van’t Hoff factor is 1.
2. Next, convert the Celsius temperature to absolute temperature (Kelvin). The absolute temperature is 37 + 273 = 310 Kelvin.
3. Now, calculate the concentration of glucose.

This involves rearranging the osmotic pressure formula:

Π = iMRT
M = Π/iRT =  7.65 atm/(1)(0.08206 L·atm/mol·K)(310) = 0.301 mol/L

For each liter of solution, there are 0.301 moles of sucrose.

Find the molar mass of glucose. From the periodic table:

C = 12 g/mol
H = 1 g/mol
O = 16 g/mol

Using the glucose formula (C₆H₁₂O₆), the molar mass is:

molar mass glucose = 6(12) + 12(1) + 6(16) = 72 + 12 + 96 = 180 g/mol

The mass of glucose you need to make the solution is the molar mass multiplied by the the mass of glucose:

mass of glucose = 0.301 mol x 180 g/mol = 54.1 grams

Keep in mind, other solutes in a solution also affect osmotic pressure. In this example, the solution likely is likely glucose in physiological saline rather than glucose in pure water.

References

• Atkins, Peter W.; de Paula, Julio (2010). “Section 5.5 (e)”. Physical Chemistry (9th ed.). Oxford University Press. ISBN 978-0-19-954337-3.
• Lewis, Gilbert Newton (1908). “The Osmotic Pressure of Concentrated Solutions and the Laws of the Perfect Solution”. Journal of the American Chemical Society. 30 (5): 668–683. doi:10.1021/ja01947a002
• Voet, Donald; Judith Aadil; Charlotte W. Pratt (2001). Fundamentals of Biochemistry (Rev. ed.). New York: Wiley. ISBN 978-0-471-41759-0.