Molality: concentration per kilogram of solvent

What molality measures

Molality answers the same question molarity does — how concentrated is this solution? — but it measures the solvent in kilograms instead of the solution in liters. The definition is:

$$m = \frac{n}{\text{kilograms of solvent}}$$

where $n$ is the moles of solute. The symbol is a lowercase m, read as molal, and the unit is mol/kg.

The denominator is the key difference: kilograms of solvent, not liters of solution and not kilograms of solution. Weigh the water (or other solvent) by itself, dissolve the solute in it, and divide.

Worked example: 1.00 m sodium chloride

A straightforward example: stir 1.00 mol of NaCl into exactly 1.00 kg of water. The molar mass of NaCl is 58.44 g/mol, so you weigh out 58.44 g of salt.

$$m = \frac{1.00\ \text{mol}}{1.00\ \text{kg water}} = 1.00\ \text{m}$$

No volumetric flask is needed and no final-volume reading matters, because the mass of the water is fixed at 1.00 kg regardless of how much space the dissolved salt occupies. For a less trivial case: 0.250 mol of glucose dissolved in 500 g (0.500 kg) of water gives $0.250 / 0.500 = 0.500$ m.

Why molality ignores temperature

Liquids expand when heated, so a liter of solution at 20 °C becomes slightly more than a liter at 40 °C. Molarity, which divides by that volume, therefore drifts downward as temperature rises. Molality divides by kilograms of solvent, and a kilogram of water is a kilogram of water at any temperature.

This stability is why every colligative-property formula — freezing-point depression, boiling-point elevation — is written with molality rather than molarity. Those effects are measured across temperature changes, so a concentration unit that shifts with temperature would corrupt the calculation.

Molality versus molarity in practice

In dilute water solutions, 1.00 M and 1.00 m are nearly the same number, because 1 L of water weighs about 1 kg. The approximation fails in three situations: concentrated solutions where the solute adds real volume, hot solutions where thermal expansion has stretched the volume, and non-aqueous solvents whose densities differ from 1 g/mL.

Exact conversion needs the solution density. For example, a solution with density 1.10 g/mL contains 1.10 kg of solution per liter; subtract the solute mass to get the solvent mass, then divide moles by that solvent mass. When a problem gives density alongside molarity, it is asking you to perform exactly this conversion.

Molality and colligative properties

Colligative properties depend on the number of dissolved particles, and molality counts those particles on a temperature-proof basis. The freezing-point depression formula is:

$$\Delta T_f = i \cdot K_f \cdot m$$

with $m$ the molality, $K_f$ the solvent's freezing-point constant, and $i$ the van't Hoff factor for dissociation. Plug in a molarity here and the units still seem to work, but the answer quietly inherits the temperature dependence you were trying to avoid. Textbooks, exam rubrics, and the worked antifreeze examples all use molality for this reason.

Preparing and reading molal solutions

To prepare a molal solution, weigh the solvent on a balance — do not measure it by volume. Add the weighed solute, stir until fully dissolved, and you are done; there is no final mark to hit. This makes molality convenient for field work and for solvents where volumetric glassware is impractical.

Keep the solute and solvent roles straight: the solvent is the component present in the greatest amount, and its mass alone goes in the denominator. If a problem states that 10.0 g of urea is dissolved in 200 g of water, the water is the solvent and the molality is $(10.0/60.06)/0.200 = 0.833$ m, using urea's molar mass of 60.06 g/mol.

Variables and units

Common mistakes

Real-world applications

• Computing freezing-point depression and boiling-point elevation, which require molality

• Studying reaction rates in solution, where temperature changes alter volumes but not masses

• Comparing the colligative effects of different solvents on an equal footing

• Antifreeze and de-icing formulations, where effectiveness is quoted per kilogram of water

• Food science: controlling freezing points and osmotic behavior in brines and syrups

• Geochemistry: describing concentrated natural brines whose density makes molarity awkward