Relative Molecular Masses in Solution · Chemistry

Colligative properties

Some properties of a solution depend only on the number of particles of solute dissolved, not on what the particles are. These are the colligative properties: lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure. They can be used to find the relative molecular mass of a solute.

The more particles, the lower the freezing point: salts give two or three particles per formula unit.

Property	Effect of dissolving a non-volatile solute	Use
Vapour pressure	Lowered	Raoult’s law
Boiling point	Raised: ΔT_b = K_b m	Finding Mr
Freezing point	Lowered: ΔT_f = K_f m	Antifreeze, salting roads, finding Mr
Osmotic pressure	Appears when a solution is separated from water by a semipermeable membrane: π = cRT	Finding Mr of proteins and polymers

K is the molal constant of the solvent (for water K_f = 1.86 K kg/mol and K_b = 0.52 K kg/mol), m is the molality and i is the van’t Hoff factor.

The van’t Hoff factor i shows how many particles each formula unit gives in solution: i = 1 for sugar, about 2 for NaCl (Na⁺ and Cl⁻), about 3 for CaCl₂. Association and dissociation change i.

Worked exampleMr from freezing point depression

5.0 g of a non-electrolyte dissolved in 100 g of water lowers the freezing point by 0.93 K. Find its relative molecular mass. (K_f = 1.86 K kg/mol)

Molality from ΔT = K_f m.
Moles in 0.100 kg of water: 0.50 × 0.100 = 0.050 mol.
Mr = mass ÷ moles.

Answer: The relative molecular mass is 100.

Try itFreezing point of a solution

Choose the mass of solute, its molar mass and the van’t Hoff factor, dissolved in 1 kg of water. Find the freezing point depression.

Open the dilution lab
Prepare solutions of known concentration, as you would for colligative measurements.

Osmosis and osmotic pressure

Osmosis is the net movement of solvent through a semipermeable membrane from a dilute solution to a more concentrated one. The osmotic pressure π is the pressure needed to stop it. Because π = cRT, a small amount of a large molecule gives a measurable pressure, which makes osmotic pressure ideal for finding the molar mass of proteins.

Check yourself Which solution has the lowest freezing point? (equal molality)

Check yourself Which is NOT a colligative property?

Check yourself What does a van’t Hoff factor of about 2 for NaCl show?

Key terms

Colligative property: A property that depends on the number of solute particles, not their identity.
Molality: Moles of solute per kilogram of solvent.
Osmotic pressure: The pressure that must be applied to stop osmosis.
Isotonic: Having the same osmotic pressure.

Summary

Colligative properties depend on the number of particles: vapour pressure, boiling point, freezing point and osmotic pressure.
ΔT = K m i; osmotic pressure π = cRT.
Use them to find relative molecular mass.
Salts have i > 1 because they dissociate.