Colligative Properties

Colligative properties: Definition Those properties that depend on the number of particles (molecules or ions) of the solute rather than on their physical and chemical properties.

1. vapor pressure lowering
2. boiling point elevation
3. freezing point depression
4. osmotic pressure

Osmotic pressure and vapor pressure are difficult to measure, so other colligative properties are determined and then related to osmotic pressure, or vapor pressure since all colligative properties are interrelated.

2. Boiling Point Elevation

The boiling point of a liquid is the temperature at which the vapor pressure of the liquid is equal to the external atmospheric pressure.

Since the vapor pressure of a solvent is lowered when a nonvolatile solute is added, the result is that the solution must be heated to a higher temperature than the pure solvent to reach the same vapor pressure. The boiling point of a solution is thus elevated in comparison to the boiling point of the pure solvent.

The extent of the lowering of the vapor pressure depends on the mole fraction of solute present. The freezing point depression and boiling point elevation also depend on the mole fraction of solute present, but since in dilute solutions the molality of solute is proportional to its mole fraction we can write

T_b = K_b x m

Example
An aqueous solution of solute (MW = 342) is prepared by dissolving 0.500 g solute in 0.100 kg water. Calculate the boiling point elevation of this solution (T_b). K_b = 0.515 deg. kg/mole

mol solute = 0.500 g/ 342 g/mol = 0.00146 mol

molality = 0.00146 mol / 0.100 kg = 0.0146 m

T_b = 0.515 ^oC/m x 0.0146 m = 0.00752 ^oC

Freezing Point Depression

The freezing point of a liquid is the temperature at which the solid and the liquid phases are in equilibrium at one atmosphere.

In a manner similar to that used for boiling point elevation we can write for freezing point depression

T_f = -K_f x m

where T_f is the lowering of the freezing point of a solvent in a solution, m is the molality of the solute and K_f is the molal lowering of the freezing point. The K_f value for water is 1.858 ^oC/m.
Example

What is the freezing point of a solution containing 3.42 g of solute and 0.500 kg of water? MW of the solute = 342. K_f in dilute solution = 1.86 deg. kg/mol = 1.86 ^oC/m.

mol solute = 3.42 g/ 342 g/mol = 0.0100 mol

molality = 0.0100 mol / 0.500 kg = 0.0200 m

T_f = -1.86 ^oC/m x 0.0200 m = -0.0372 ^oC
T_{f =} 0.000 ^oC + (-0.0372 ^oC) = - 0.0372 ^oC