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Molality Calculator

Calculate molality from the masses of solute and solvent, or the mass of either one for a target molality. Add the solution's density to convert to molarity.

Formula

b=mMW×msolventb = \dfrac{m}{\mathrm{MW}\times m_{\text{solvent}}}
m=b×MW×msolventm = b \times \mathrm{MW} \times m_{\text{solvent}}
M=1000 ρ b1000+b MWM = \dfrac{1000\,\rho\, b}{1000 + b\,\mathrm{MW}}
bb
molality, in mol of solute per kg of solvent
mm
mass of solute, in grams
msolventm_{\text{solvent}}
mass of the solvent alone, in kilograms
MW\mathrm{MW}
molecular weight of the solute, in g/mol
ρ\rho
density of the finished solution, in g/mL
MM
molarity, in mol per litre of solution

How it works

Molality counts moles of solute against the mass of the solvent, not the volume of the solution. Because masses do not change with temperature, a molal concentration stays the same when the solution warms or cools. That is why it is the unit used for freezing-point depression, boiling-point elevation and osmotic calculations.

Converting molality to molarity needs the density of the finished solution: one kilogram of solvent plus its solute weighs 1000 + b × MW grams, and dividing that mass by the density gives the volume those moles occupy.

Worked example

5.844 g of sodium chloride (58.44 g/mol) is dissolved in 500 g of water.

  1. Amount of NaCl = 5.844 g / 58.44 g/mol = 0.1 mol.
  2. b = 0.1 mol / 0.5 kg = 0.2 mol/kg.

The solution is 0.2 mol/kg, or 200 mmol/kg. It weighs 505.844 g in total and is 1.155% sodium chloride by mass.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • The solvent mass is the solvent alone, before the solute is added.
  • The solute is 100% pure and the molecular weight matches the reagent in the bottle.
  • The molarity conversion uses the density you enter; it is not estimated.

Common mistakes

  • Dividing by the mass of the solution instead of the mass of the solvent.
  • Treating molality and molarity as interchangeable. They are close only in dilute aqueous solutions.
  • Weighing a hydrate and ignoring its water, which ends up as extra solvent.

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