Osmotic Pressure — Definition & Examples

What is Osmosis?

Osmosis is the diffusion of a solvent. The solvent moves from low solute concentration to high solute concentration. We observe osmosis by separating two solutions with a semipermeable membrane. A semipermeable membrane is a barrier that allows the solvent's movement. But, it blocks solute diffusion. The membrane's pores are large enough for the solvent but too small for the solute. So, the solvent flows but, the solute remains. Eventually, the system reaches equilibrium. On both sides of the membrane, the concentrations are equal.

What Causes Osmosis?

Like the other colligative properties, entropy causes osmosis. Remember, entropy is the dispersion of energy. More energy dispersion equals a more significant entropy change.

But, what's happening at the molecular scale? Let's say that we have two solutions of sodium chloride. They both start with the same volume. One is 2.0 molar and, the other is 1.0 molar. The 2.0 molar side has more solute-solvent interactions. More sodium and chlorine ions are interacting with water. As water diffuses, it dilutes the more concentrated side. So, there is more solvent. We have more solvent molecules to balance the ions' charges. So, our energy is more dispersed.

What is Osmotic Pressure?

How do we measure osmosis? We use osmotic pressure! The osmotic pressure is the pressure required to stop osmosis. Atmospheric pressure pushes down on the solution. For the solvent to flow across the semipermeable membrane, it must move against the atmosphere. So, we can calculate the pressure we would need to stop osmosis.

Osmotic Pressure Formula

The formula for atmospheric pressure is $\Pi=i\times\frac{n}{V}RT$ . Notice the similarity to the ideal gas law.

$\Pi$ is the osmotic pressure.
$i$ is the Van't Hoff factor. It is equal to the sum of the magnitude of the charges.
$\frac{n}{V}$ is the molar concentration.
$R$ is the universal gas constant. I recommend using $0.082057\frac{L \times atm}{mols \times K}$ .
$T$ is the temperature in kelvin.

Osmotic Pressure Example

The most common semipermeable membrane is the cell membrane. Your body is constantly using osmosis to balance the cells' osmotic pressures. Sometimes, doctors apply medicine directly into the bloodstream. They make sure the solution has the same osmotic pressure as your cells. A significant difference in osmotic pressure could cause your cells to burst.

Let's calculate the osmotic pressure of a blood cell. The concentration of sodium chloride in blood is $0.15\frac{mols}{L}$ . Calculate the osmotic pressure at $37^{o}C$ (the average body temperature).

$\Pi=i\frac{n}{V}RT\rightarrow 2\times0.15\frac{mols}{L}\times0.082057\frac{L \times atm}{mols \times K}\times 310.15K=7.6\, atm$

The Van't Hoff factor is two because sodium and chlorine each have a charge.