Molality Definition

Molality = moles of solute ÷ kilograms of solvent (mol/kg): a temperature-independent concentration used for colligative properties.

m = \frac{n_{\text{solute}}}{\text{kg of solvent}}

molality = moles of solute / kg of solvent

What it means

Molality counts moles of solute per kilogram of solvent. Because it is built from masses rather than volumes, it does not budge when a solution warms or cools — volumes expand and contract, masses do not. That stability is exactly why the colligative-property formulas (freezing point depression, boiling point elevation, osmotic pressure) are written in molality rather than molarity.

Variables

Symbol	Name	Unit	Meaning
$m$	Molality	mol/kg	Concentration of the solution: moles of solute per kilogram of solvent.
$n_solute$	Moles of solute	mol	The amount of solute dissolved, in moles.
$kg of solvent$	Mass of solvent	kg	The mass of the solvent alone, excluding the solute.

Assumptions

The denominator is the solvent mass only, never the whole solution mass.
Masses do not change with temperature, so molality is temperature-independent.
Lowercase m denotes molality; uppercase M is molarity — a different quantity.
The solute dissolves completely without reacting.

Worked example

Problem

A solution is made by dissolving 10.0 g of NaCl in 200.0 g of water. Calculate its molality.

Given:

Mass of NaCl = 10.0 g
Mass of water (solvent) = 200.0 g

Molar mass of NaCl = 58.44 g/mol.
Convert solute to moles: n = 10.0 g / 58.44 g/mol = 0.171 mol.
Convert solvent to kilograms: 200.0 g = 0.2000 kg.
m = n / kg solvent = 0.171 mol / 0.2000 kg = 0.856 mol/kg.

0.856 mol/kg (0.856 m)

There are about 0.86 moles of NaCl per kilogram of water — this is the concentration form that freezing-point and boiling-point calculations require.