Hong Life CalculatorsUnderstanding the molality calculator — concept and principle
This calculator finds the molality of a solution, the moles of solute per kilogram of solvent, from the masses and molar masses. It also gives the solute amount, solution mass, mass percent, mole fraction and the solute mass needed for 1 mol/kg. It is used in chemistry labs and for colligative-property calculations such as freezing-point depression.
How it is calculated
n_solute = solute mass ÷ molar mass
Molality b = n_solute ÷ solvent mass (kg)
Mass percent = solute ÷ (solute + solvent) × 100
Mole fraction = n_solute ÷ (n_solute + n_solvent), with n_solvent = solvent mass ÷ solvent molar mass
- Masses in grams; molar masses in g/mol.
The principle
Molality counts solute particles relative to the mass of solvent, not the volume of solution. Masses do not change with temperature, while volumes do, so molality stays the same when a solution warms or cools. That makes it the natural concentration unit for freezing-point and boiling-point formulas, where temperature changes. For dilute aqueous solutions molality and molarity are close, but they differ more as concentration rises.
Worked example
Default inputs: 29.22 g NaCl (58.44 g/mol) in 500 g water (18.015 g/mol).
- n = 29.22 ÷ 58.44 = 0.5 mol.
- b = 0.5 ÷ 0.500 kg = 1 mol/kg.
- Solution mass = 29.22 + 500 = 529.22 g; mass percent = 29.22 ÷ 529.22 = 5.52%.
- Water = 500 ÷ 18.015 = 27.755 mol, so mole fraction of NaCl = 0.5 ÷ 28.255 = 0.0177.
- Solute for 1 mol/kg in 500 g = 29.22 g.
| Solute molar mass (g/mol) | Molality (mol/kg) |
|---|---|
| 14.6 | 4 |
| 29.2 | 2 |
| 43.8 | 1.3333 |
| 58.4 | 1 |
| 73 | 0.8 |
| 87.7 | 0.6667 |
| 117 | 0.5 |
How to read the result
A 1 mol/kg solution has one mole of solute for every kilogram of solvent. For colligative effects, remember that NaCl splits into two ions, so the particle molality is about twice the formula molality (the van 't Hoff factor). Seawater, for comparison, is roughly 3.5% salt by mass.
Common mistakes
- Dividing by the solution mass instead of the solvent mass.
- Forgetting to convert grams of solvent to kilograms.
- Confusing molality (mol/kg) with molarity (mol/L).
- Ignoring dissociation when using molality for colligative properties.
Frequently asked questions
What is the difference between molality and molarity?
Molality uses kilograms of solvent; molarity uses litres of solution.
Why use molality for freezing-point depression?
It does not change with temperature.
Is 1 mol/kg the same as 1 mol/L?
Only approximately for dilute aqueous solutions.
What is the mole fraction used for?
Raoult's law and other vapour-pressure calculations.
Sources: OpenStax, Chemistry: Atoms First 2e, section 11.4 "Colligative Properties"