The physical properties of a solution are different from those of the pure solvent. Many differences in physical properties are predictable if the solute in the pure state is nonvolatile - that is, if it has a very low vapor pressure. Sugar, sodium chloride, and potassium nitrate are examples of nonvolatile solutes. Colligative properties are those physical properties of solutions of nonvolatile solutes that depend only on the number of particles present in a given amount of solution, not on the nature of those particles. We will consider four colligative properties: vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

A. Vapor Pressure Lowering
At any given temperature, the vapor pressure of a solution containing a nonvolatile solute is less than that of the pure solvent (see Section 10.3A for a discussion of vapor pressure). This effect is called vapor pressure lowering. The solid line in Figure 11.6 is a plot of the vapor pressure of pure water versus temperature. The break in the curve at 0°C is the intersection of the curve of the vapor pressure of the solid with the curve of the vapor pressure of the liquid. The dashed line in Figure 11.6 is a plot of the vapor pressure of an aqueous solution of sugar versis temperature. Notice that the vapor pressure of the solution is always less than that of the pure solvent. What causes this difference?

FIGURE 11.6 The vapor pressure of pure water is shown as a solid line; the vapor pressure of an aqueous solution is shown as a dashed line. Note the differences between the solution and the pure substance in melting point and boiling point.

The surface of a pure solvent (Figure 11.7a) is populated only by solvent molecules. Some of these molecules are escaping from the surface, and others are returning to the liquid state (see Section 10.3A). The surface of a solution is populated by two kinds of molecules; some are solvent molecules,

FIGURE 11.7 Vapor pressure lowering: (a) the vapor pressure of a pure liquid; (b) the vapor pressure of a solution. In (b), the number of solvent molecules on the surface of the liquid has been decreased by the presence of the solute molecules. Fewer solvent molecules can vaporize, and the vapor pressure is lower.

others are solute molecules. Only the solvent molecules are volatile. They alone can escape to build up the vapor pressure of the solution. There are fewer solvent molecules on the surface of the solution than on the surface of the pure liquid. Fewer will vaporize and, as a consequence, the vapor pressure of the solution will be less than that of the pure liquid at the same temperature (see Figure 11.7b).

B. Boiling Point Elevation
The boiling point of a substance is the temperature at which the vapor pressure of the substance equals atmospheric pressure. A solution containing a nonvolatile solute, having a lower vapor pressure than the pure solvent, must be at a higher temperature before its vapor pressure equals atmospheric pressure and it boils. Thus, the boiling point of a solution containing a nonvolatile solute is higher than that of the pure solvent (see Figure 11.6) This effect is called boiling point elevation.

C. Freezing Point Depression
Recall that freezing and melting point are two terms that describe the same temperature, the temperature at which the vapor pressure of the solid equals the vapor pressure of the liquid and at which the solid and the liquid are in equilibrium. Remember, too, that vapor pressure decreases as the temperature decreases. The vapor pressure of a solution is lower than that of the solvent, so the vapor pressure of a solution will equal that of the solid at a lower temperature than in the case of the pure solvent. Thus, the freezing point will be lower for a solution than for the pure solvent (see Figure 11.6). This effect is called freezing point depression. Remember that, just as it is the solvent that vaporizes when a solution boils, it is the solvent, not the solution, that becomes solid when a solution freezes. When a salt solution freezes, the ice is pure water (solid); the remaining solution contains all the salt.

Application of this principle leads us to add antifreeze (a nonvolatile solute) to the water in the radiators in our cars. We thus lower the freezing point of the solvent (water), and the solution remains a liquid even at subfreezing temperatures.

D. Osmosis and Osmotic Pressure
Osmosis and osmotic pressure depend on the ability of small molecules to pass through semipermeable membranes like a thin piece of rubber, a cell membrane, or a thin piece of plastic wrap. Think of the membrane as a sieve with very tiny holes. Solvent particles are small and can very easily pass through these holes; solute particles are larger and cannot pass through (Figure 11.8).

FIGURE 11.8 A semipermeable membrane allows small solvent molecules to pass through but prevents the passage of larger particles like those of a nonvolatile solute.

When a semipermeable membrane separates a solution from pure solvent, solvent molecules move back and forth through the membrane, but not in equal numbers. More move from the pure solvent into the solution than from the solution into the solvent.

The movement of solvent molecules will continue to be uneven until the number of solvent molecules is the same on both sides of the membrane. The process is called osmosis. Figure 11.9 illustates these points. In Figure 11.9a, different amounts of pure solvent (water) are separated by a semipermeable membrane. Water molecules from both sides move through the membrane until the pressure of solvent on both sides of the membrane is equal. This equality is indicated by the equal heights of the columns (Figure 11.9b).

In Figure 11.9c, solute molecules have been added on one side of the membrane, creating a solution. Now there are fewer solvent molecules next to this side of the membrane than there are on the side of the pure solvent. To overcome this difference, solvent molecules move more rapidly from the solvent side than from the solution side in an effort to equate these numbers. (Notice the bigger arrow meaning migration from the solvent side.) In Figure 11.9d, the height of the solution is greater than that of the solvent, but now the rate at which the solvent molecules pass through the membrane is the same from both sides. The difference in heights of the columns is proportional to the osmotic pressure of the original solution.

FIGURE 11.9 Osmosis and osmotic pressure. Differing amounts of pure solvent on either side of a semipermeable membrane (a) will, through osmosis, become equally divided on either side of the membrane (b). However, if solute molecules are added to one side (c), some of the solvent will migrate into the solution side, causing a difference in osmotic pressure (d). The difference in pressure can be counteracted by increased surface pressure on the solution side. (e)

Osmotic pressure is also being measured in Figure 11.9e. Here, pressure is being applied to the surface of the solution. The osmotic pressure of the solution is the pressure that must be applied to the solution to prevent migration of solvent molecules from the more dilute (or pure solvent) side into the solution.

E. Differences between Colligative Properties of Solutions of Ionic and Molecular Compounds
For any solution, the amount that the vapor pressure is lowered, the freezing point depressed, or the boiling point elevated with respect to the properties of the pure solvent depends on the number of solute particles in solution, not on the nature of those particles. Similarly, the osmotic pressure of a solution is dependent only on the number of solute particles, not on their nature. Table 11.6 shows the melting point (freezing point), boiling point, and osmotic pressure of several glucose solutions. The number of moles of glucose (therefore, the number of glucose molecules in a given amount of water) differs among these solutions. The greater the number of molecules of solute, the greater the difference between the properties of the pure solvent and those of the solution.

Table 11.6 shows the colligative properties of a solution of 0.1 mol sodium chloride in 1000 g water and of 0.1 mol sodium sulfate in 1000 g water. Notice that they differ from those of a solution with a molecular solute. One mole of glucose, a molecular compound, dissolves to yield one mole of particles; however, one mole of sodium chloride, an ionic compound, dissolves to yield two moles of particles - one mole of sodium ions and one mole of chloride ions. One mole of sodium sulfate (Na₂SO₄) dissolves to yield three moles of particles - two of sodium ions and one of sulfate ions. Because the number of particles determines the colligative properties of a solution, one mole of sodium chloride dissolves in a given amount of water causes approximately twice the change in colligative properties than does one mole of glucose dissolved in the same volume of water. One mole of sodium sulfate dissolved in the same amount of water causes approximately three times the change.