Molality

The formula

• b = n / m_solvent

n is the amount of dissolved substance in moles and m_solvent the mass of the solvent alone, in kilograms. The unit is mol/kg, sometimes written molal.

A worked example

0.50 mol of sugar dissolved in 250 g of water: b = 0.50 / 0.250 = 2.0 mol/kg. Turned round, 2.0 mol/kg in 400 g of water holds 0.80 mol of sugar. The amount comes from the mass and the molar mass: 171 g of sucrose, molar mass 342 g/mol, is 0.50 mol.

Molality and molarity

Concentration, or molarity, divides by the volume of the whole solution in litres. Molality divides by the mass of the solvent alone. For dilute solutions in water the two numbers are close, since a litre of water weighs a kilogram and the solute adds little volume; for concentrated solutions, or solvents other than water, they part. A molarity changes when the solution is heated, because the volume expands; a molality does not, because nothing’s mass changes.

Where it is used

The boiling-point elevation and the freezing-point depression are proportional to the molality, which is why the formula is met in the chapter on colligative properties. The mole fraction is the other temperature-independent measure.

Common mistakes

• Dividing by the mass of the solution. The water alone goes in the denominator: 250 g of water, not 421 g of syrup.
• Grams instead of kilograms. 0.50 / 250 gives 0.002, a thousand times too small.
• Using the volume. That is molarity.

Frequently asked questions