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Molality calculator: moles of solute per kilogram of solvent

Calculate the molality of a solution from the mass of solute, its molar mass and the mass of solvent, with the mass fraction and mole fraction.

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Results

Molality

0.2 mol/kg

Moles of solute
0.1 mol
Mass percent of solute
1.155 %
Mole fraction of solute
0.00359
Moles of solvent
27.75 mol

Molality in one sentence

Molality is the number of moles of solute dissolved per kilogram of solvent. Its unit is mol/kg, sometimes written m (a “1 molal” solution). Unlike molarity, it is based only on masses, so it does not change when the solution warms up or cools down and expands or contracts.

The formulas

  • Moles of solute n = mass of solute ÷ molar mass
  • Molality b = n ÷ mass of solvent in kg
  • Mass percent = mass of solute ÷ (mass of solute + mass of solvent) × 100
  • Mole fraction x = n ÷ (n + moles of solvent)

Worked example

Dissolve 5.844 g of sodium chloride (molar mass 58.44 g/mol) in 500 g of water.

  1. n = 5.844 ÷ 58.44 = 0.100 mol.
  2. Molality = 0.100 ÷ 0.500 kg = 0.200 mol/kg.
  3. Mass percent = 5.844 ÷ 505.844 × 100 = 1.155%.
  4. Moles of water = 500 ÷ 18.015 = 27.75 mol, so the mole fraction of NaCl = 0.100 ÷ 27.85 = 0.00359.

Molality versus molarity

Molality Molarity
Definition mol per kg of solvent mol per liter of solution
Unit mol/kg mol/L (M)
Depends on temperature No Yes, slightly
Easy to prepare Weigh solute and solvent Fill a volumetric flask
Main uses Colligative properties, physical chemistry Titrations, everyday lab work

For dilute aqueous solutions near room temperature, the two are almost equal, since one liter of water weighs about one kilogram. They diverge in concentrated solutions and for solvents that are much denser or lighter than water.

Where molality matters

Freezing point depression, boiling point elevation and osmotic effects depend on the number of solute particles per mass of solvent, which is why their formulas use molality. It is also the concentration unit of choice for thermodynamic tables and for any work over a range of temperatures, such as studying solubility from 0 to 100 °C.

Practical tips

  • Weigh the solvent, not the final solution.
  • For hydrated salts such as CuSO₄·5H₂O, use the molar mass of the hydrate for n, and add the water of crystallization to the solvent mass.
  • Use an analytical balance: masses are easier to measure precisely than volumes, which is another advantage of molality.

Frequently asked questions

What is molality?

The number of moles of solute per kilogram of solvent, in mol/kg. Dissolving 5.844 g of NaCl (0.1 mol) in 500 g of water gives 0.2 mol/kg.

What is the difference between molality and molarity?

Molarity divides by the volume of solution in liters, molality by the mass of solvent in kilograms. Molality does not change with temperature, because masses do not expand.

When is molality used?

For colligative properties such as freezing point depression and boiling point elevation, and in physical chemistry when temperature varies.

Are molality and molarity ever equal?

Approximately, for dilute aqueous solutions near room temperature, since 1 L of water weighs about 1 kg.

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Results are estimates provided for information purposes. They do not replace professional advice.

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