Both terms tell you how much solute is present, and both count that solute in moles. They differ only in what the moles are divided by. Molarity divides by the volume of the whole solution. Molality divides by the mass of the solvent alone.
The comparison table
| Molarity | Molality | |
|---|---|---|
| Symbol | M | m |
| Definition | Moles of solute per litre of solution | Moles of solute per kilogram of solvent |
| Formula | M = moles of solute ÷ volume of solution in L | m = moles of solute ÷ mass of solvent in kg |
| Unit | mol/L | mol/kg |
| Denominator refers to | The solution, solute included | The solvent only |
| Affected by temperature | Yes, because volume changes | No, because mass does not |
| Measured using | A volumetric flask | A balance |
| Used mostly in | Titrations and everyday laboratory work | Colligative properties |
Two words carry the whole distinction: solution in one definition, solvent in the other. Read every question for which of them it gives you.
Both calculations begin by turning grams into moles. If that step is shaky, practise it with mole concept solved examples before going further.
Example 1 — molarity
4 g of sodium hydroxide is dissolved in water and the solution is made up to 250 mL. Find the molarity. (Molar mass of NaOH = 40 g/mol.)
- Moles of NaOH = 4 ÷ 40 = 0.1 mol
- Volume of solution = 250 mL = 0.25 L
- Molarity = 0.1 ÷ 0.25 = 0.4 mol/L
Notice the wording "made up to 250 mL". The 250 mL is the final volume of the solution, not the volume of water added.
Example 2 — molality
4 g of sodium hydroxide is dissolved in 250 g of water. Find the molality.
- Moles of NaOH = 0.1 mol, as before
- Mass of solvent = 250 g = 0.25 kg
- Molality = 0.1 ÷ 0.25 = 0.4 mol/kg
The two answers share a number here only because the question was built that way. The solutions are not the same: the second contains 250 g of water plus the solute, and its volume is not exactly 250 mL.
Example 3 — converting molarity to molality
A 2 mol/L solution of NaOH has a density of 1.10 g/mL. Find its molality.
Work with exactly one litre of solution.
- Mass of 1 L of solution = 1000 mL × 1.10 g/mL = 1100 g
- Moles of NaOH in it = 2 mol, so mass of NaOH = 2 × 40 = 80 g
- Mass of water = 1100 − 80 = 1020 g = 1.020 kg
- Molality = 2 ÷ 1.020 ≈ 1.96 mol/kg
The density is what makes the conversion possible. Without it you cannot get from a volume of solution to a mass of solvent, and a question that asks for the conversion will always supply it.
Why temperature separates them
Warm a solution and it expands. The moles of solute are unchanged, but they are now spread through a larger volume, so the molarity falls slightly. Cool it and the molarity rises.
Molality is built from two masses, and heating a sealed sample does not change the mass of anything in it. Its value stays fixed. This is the reason colligative properties, which are measured as temperature changes, are written in terms of molality.
Where marks are lost
- Using the volume of water for molarity. The denominator is the volume of the finished solution.
- Using the mass of the solution for molality. The denominator is the mass of the solvent only. Subtract the solute first when a question gives the total mass.
- Leaving millilitres or grams in the denominator. Convert to litres for molarity and kilograms for molality.
- Mixing up M and m. Capital M is molarity, small m is molality. In an answer, writing the unit out removes any doubt.
Quick check
18 g of glucose, of molar mass 180 g/mol, is dissolved in 500 g of water. What is the molality?
Moles of glucose = 18 ÷ 180 = 0.1 mol. The solvent is 0.5 kg. Molality = 0.1 ÷ 0.5 = 0.2 mol/kg.