Colligative Properties for AP Chemistry (page 2)

By — McGraw-Hill Professional
Updated on Feb 9, 2011

Boiling-Point Elevation

Just as the freezing point of a solution of a nonvolatile solute is always lower than that of the pure solvent, the boiling point of a solution is always higher than the solvent's. Again, only the number of solute particles affects the boiling point. The mathematical relationship is similar to the one for the freezing-point depression above and is

ΔTb = iKb molality

where ΔTb is the number of degrees the boiling point has been elevated (the difference between the boiling point of the pure solvent and the solution); Kb is the boiling-point elevation constant; the molality is the molality of the solute; and i is the van't Hoff factor. You can calculate a solution's boiling point if you know the molality of the solution. If you know the amount of the boiling-point elevation and the molality of the solution, you can calculate the value of the van't Hoff factor, i.

For example, determine the boiling point of a solution prepared by adding 15.00 g of NaCl to 250.0 g water. (Kb = 0.512 K kg mol–1)

A 1.00 molal aqueous solution of trichloroacetic acid (CCl3COOH) is heated to the boiling point. The solution has a boiling point of 100.18°C.

Determine the van't Hoff factor for trichloroacetic acid (Kb for water = 0.512 K kg mol-1).

ΔT = (101.18 – 100.00) = 0.18°C = 0.18 K

i = ΔT/Kbm = 0.18 K/(0.512 K kg mol-1)(1.00 mol kg-1) = 0.35

A common mistake is the assumption that the van't Hoff factor must be a whole number. This is true only for strong electrolytes at very low concentrations.

Osmotic Pressure

If you were to place a solution and a pure solvent in the same container but separate them by a semipermeable membrane (which allows the passage of some molecules, but not all particles) you would observe that the level of the solvent side would decrease while the solution side would increase. This indicates that the solvent molecules are passing through the semipermeable membrane, a process called osmosis. Eventually the system would reach equilibrium, and the difference in levels would remain constant. The difference in the two levels is related to the osmotic pressure. In fact, one could exert a pressure on the solution side exceeding the osmotic pressure, and solvent molecules could be forced back through the semipermeable membrane into the solvent side. This process is called reverse osmosis and is the basis of the desalination of seawater for drinking purposes. These processes are shown in Figure 13.1.

Colligative Properties

The osmotic pressure is a colligative property and mathematically can be represented as π = (nRT/V ) i, where π is the osmotic pressure in atmospheres; n is the number of moles of solute; R is the ideal gas constant 0.0821 L. atm/K.mol; T is the Kelvin temperature; V is the volume of the solution; and i is the van't Hoff factor. Measurements of the osmotic pressure can be used to calculate the molar mass of a solute. This is especially useful in determining the molar mass of large molecules such as proteins.

For example, a solution prepared by dissolving 8.95 mg of a gene fragment in 35.0 mL of water has an osmotic pressure of 0.335 torr at 25.0°C. Assuming the fragment is a nonelectrolyte, determine the molar mass of the gene fragment.

Practice problems for these concepts can be found at:

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