Molarity vs molality
Molarity (M) is moles of solute per liter of solution. Molality (m) is moles of solute per kilogram of solvent.
For dilute aqueous solutions, the two values are almost equal. One liter of a dilute solution contains close to one kilogram of water.
| Property | Molarity (M) | Molality (m) |
|---|---|---|
| Definition | Moles of solute per liter of solution | Moles of solute per kilogram of solvent |
| Formula | M = n / V solution | m = n / mass solvent |
| Unit | mol/L | mol/kg |
| Effect of temperature | Changes, because volume changes | No change, because mass does not change |
| Measured with | Volumetric flask | Balance |
| Common use | Titrations and lab solutions | Boiling point elevation and freezing point depression |
How to convert molarity to molality
You need the solution density, ρ, in g/mL and the solute molar mass, Mw, in g/mol.
Molarity to molality: m = M ÷ (ρ − M × Mw ÷ 1000)
Molality to molarity: M = 1000 × m × ρ ÷ (1000 + m × Mw)
Molarity and molality problems
Problem 1
58.44 g of NaCl dissolves in 1.000 kg of water. The solution density is 1.038 g/mL. Find the molality and the molarity.
- Moles of NaCl = 58.44 g ÷ 58.44 g/mol = 1.000 mol.
- Molality = 1.000 mol ÷ 1.000 kg = 1.000 mol/kg.
- Solution mass = 1000 g + 58.44 g = 1058.44 g.
- Solution volume = 1058.44 g ÷ 1.038 g/mL = 1019.7 mL = 1.0197 L.
- Molarity = 1.000 mol ÷ 1.0197 L = 0.981 mol/L.
Answer: 1.000 m and 0.981 M
Problem 2
A 2.00 M glucose solution has a density of 1.12 g/mL. The molar mass of glucose is 180.16 g/mol. Find the molality.
- Use m = M ÷ (ρ − M × Mw ÷ 1000).
- m = 2.00 ÷ (1.12 − 2.00 × 180.16 ÷ 1000) = 2.00 ÷ 0.760 = 2.63 mol/kg.
Answer: 2.63 m
Problem 3
0.500 mol of KCl dissolves in 250 g of water. Find the molality.
- Convert the solvent mass: 250 g = 0.250 kg.
- Molality = 0.500 mol ÷ 0.250 kg = 2.00 mol/kg.
Answer: 2.00 m
How to use this calculator
- Select Mass and formula, then enter the solute mass and formula.
- Enter the solvent mass and select its unit.
- Enter the solution density to calculate molarity as well as molality.
- Calculate and compare mol/L of solution with mol/kg of solvent.
Formula and variables
M = n / L solution; m = n / kg solvent
| Symbol | Meaning | Unit |
|---|---|---|
| M | molarity | mol/L |
| m | molality | mol/kg |
| n | solute amount | mol |
| ρ | solution density | g/mL |
Worked example
58.44 g NaCl in 1.000 kg water gives 1.000 mol/kg. At 1.038 g/mL, the 1.0197 L solution is 0.981 mol/L.
Interpretation
Molarity divides by solution volume. Molality divides by solvent mass. Density links the two because it converts solution mass to volume.
Common mistakes
- Use the solvent mass for molality, not the total solution mass.
- Use the solution volume for molarity, not the solvent volume.
- Do not use M and m as the same symbol.
Frequently asked questions
What is the difference between molality and molarity?
Molality uses solvent mass. Molarity uses final solution volume.
Which is larger, molarity or molality?
For most aqueous solutions, molality is slightly larger. One liter of solution usually contains less than one kilogram of water.
How does the calculator find molarity?
It adds the solute and solvent masses. Then it divides the total by the density to get the solution volume.
Can I enter solute mass instead of moles?
Yes. Enter the solute formula so the calculator can derive its molar mass.
Does temperature change molality?
Temperature does not directly change molality because the denominator is mass, not volume.
Can I use scientific notation?
Yes. Enter values such as 6.022e23 or 1.0e-6 in a numeric field.
How should I round the result?
Keep extra digits during the calculation. Round the final result to the precision required by your data.