13.10: Osmosis

 Learning Objectives

• Explain the following laws within the Ideal Gas Law

Before we introduce the final colligative property, we need to present a new concept. A semipermeable membrane is a thin membrane that will pass certain small molecules, but not others. A thin sheet of cellophane, for example, acts as a semipermeable membrane. Consider the system in Figure \(\PageIndex{1}\).

Figure \(\PageIndex{1}\): Osmosis. (a) Two solutions of differing concentrations are placed on either side of a semipermeable membrane. (b) When osmosis occurs, solvent molecules selectively pass through the membrane from the dilute solution to the concentrated solution, diluting it until the two concentrations are the same. The pressure exerted by the different height of the solution on the right is called the osmotic pressure. (CC BY-SA-NC 3.0; anonymous)

1. A semipermeable membrane separates two solutions having the different concentrations marked. Curiously, this situation is not stable; there is a tendency for water molecules to move from the dilute side (on the left) to the concentrated side (on the right) until the concentrations are equalized, as in Figure \(\PageIndex{1b}\).
2. This tendency is called osmosis. In osmosis, the solute remains in its original side of the system; only solvent molecules move through the semipermeable membrane. In the end, the two sides of the system will have different volumes. Because a column of liquid exerts a pressure, there is a pressure difference (Π) on the two sides of the system that is proportional to the height of the taller column. This pressure difference is called the osmotic pressure, which is a colligative property.

The osmotic pressure of a solution is easy to calculate:

\[\Pi = MRT \nonumber \]

where \(Π\) is the osmotic pressure of a solution, M is the molarity of the solution, R is the ideal gas law constant, and T is the absolute temperature. This equation is reminiscent of the ideal gas law we considered in Chapter 6.

Example \(\PageIndex{5}\): Osmotic Pressure

What is the osmotic pressure of a 0.333 M solution of C₆H₁₂O₆ at 25°C?

Solution

First we need to convert our temperature to kelvins:

T = 25 + 273 = 298 K

Now we can substitute into the equation for osmotic pressure, recalling the value for R:

\[Π =(0.333M)\left (0.08205\dfrac{L.atm}{mol.K} \right )(298K) \nonumber \]

The units may not make sense until we realize that molarity is defined as moles per liter:

\[Π =\left ( 0.333\dfrac{mol}{L} \right )\left (0.08205\dfrac{L.atm}{mol.K} \right )(298K) \nonumber \]

Now we see that the moles, liters, and kelvins cancel, leaving atmospheres, which is a unit of pressure. Solving,

\[Π = 8.14 \,atm \nonumber \]

This is a substantial pressure! It is the equivalent of a column of water 84 m tall.

Exercise \(\PageIndex{5}\)

What is the osmotic pressure of a 0.0522 M solution of C₁₂H₂₂O₁₁ at 55°C?

Answer

1.40 atm

Osmotic pressure is important in biological systems because cell walls are semipermeable membranes. In particular, when a person is receiving intravenous (IV) fluids, the osmotic pressure of the fluid needs to be approximately the same as blood serum to avoid any negative consequences. Figure \(\PageIndex{3}\) shows three red blood cells:

• A healthy red blood cell.
• A red blood cell that has been exposed to a lower concentration than normal blood serum (a hypotonic solution); the cell has plumped up as solvent moves into the cell to dilute the solutes inside.
• A red blood cell exposed to a higher concentration than normal blood serum (hypertonic); water leaves the red blood cell, so it collapses onto itself. Only when the solutions inside and outside the cell are the same (isotonic) will the red blood cell be able to do its job.

Figure \(\PageIndex{3}\): Osmotic Pressure and Red Blood Cells. (a) This is what a normal red blood cell looks like. (b) When a red blood cell is exposed to a hypotonic solution, solvent goes through the cell membrane and dilutes the inside of the cell. (c) When a red blood cell is exposed to a hypertonic solution, solvent goes from the cell to the surrounding solution, diluting the hypertonic solution and collapsing the cell. Neither of these last two cases is desirable, so IV solutions must be isotonic with blood serum to not cause deleterious effects. (Public Domain; Mariana Ruiz Villareal)

Osmotic pressure is also the reason you should not drink seawater if you’re stranded on a lifeboat in the ocean; seawater has a higher osmotic pressure than most of the fluids in your body. You can drink the water, but ingesting it will pull water out of your cells as osmosis works to dilute the seawater. Ironically, your cells will die of thirst, and you will also die. (It is okay to drink the water if you are stranded on a body of freshwater, at least from an osmotic pressure perspective.) Osmotic pressure is also thought to be important—in addition to capillary action—in getting water to the tops of tall trees.

Summary

• Osmotic pressure is caused by concentration differences between solutions separated by a semipermeable membrane, and is an important biological consideration.