Molality Calculator: Moles per Kilogram of Solvent

Molality counts moles of solute per kilogram of solvent. The solvent alone, not the finished solution. Because it rests on masses rather than volumes, a solution's molality stays the same when it warms or cools, which is why it is the unit behind freezing point and osmolality measurements.

Three modes

Pick one under "Solve for". The molar mass box is shared by all three, and the first two also ask for the solvent mass, in kg or g.

The hint under the solvent box points out that for water, 1 L is close to 1 kg. Near room temperature a liter of water weighs about 997 to 998 g, so weigh it when accuracy to a fraction of a percent matters.

The molality formula

b = n / m(solvent) = (m(solute) / MW) / m(solvent)

• b is the molality in mol/kg. Some textbooks write a lowercase m, which is easy to mix up with mass and with molarity's capital M.
• n is the amount of solute in moles.
• m(solute) is the solute mass in grams, and MW its molar mass in g/mol.
• m(solvent) is the solvent mass in kilograms.

Rearranged for the second mode: m(solute) = b × MW × m(solvent).

From molarity to molality

One liter of solution weighs ρ × 1000 grams, where ρ is the density in g/mL. Of that, c × MW grams are solute, and the rest is solvent. Dividing the moles by the solvent mass in kilograms gives the third mode's formula:

b = c / (ρ - c × MW / 1000)

Worked examples with the default values

Molality mode. 58.44 g of sodium chloride divided by its molar mass of 58.44 g/mol is exactly 1 mol. Dissolved in 1 kg of water, that is 1 mol/kg. The tool shows "Molality: 1 mol/kg", and the formula line under it repeats the sum, ending in "= 1 mol/kg".

Solute mass mode. For 0.5 mol/kg in 1 kg of water: 0.5 × 58.44 × 1 = 29.22 g. The tool shows "Solute to weigh: 29.22 g".

From molarity mode. Take one liter of 1 M NaCl with a density of 1.04 g/mL. It weighs 1,040 g, of which 58.44 g is salt, leaving 981.56 g (0.98156 kg) of water. Then 1 mol ÷ 0.98156 kg = 1.019 mol/kg, the value the tool displays. So a 1 M salt solution is a little over 1 mol/kg, and the gap grows as solutions get stronger.

Molarity vs molality

In dilute water solutions the two are close, because a liter of water weighs about a kilogram and a little solute takes up little room. Colligative properties follow molality: the freezing point drops by about i × Kf × b, where Kf for water is 1.86 °C·kg/mol and i is the number of particles per formula unit. The osmolarity calculator works with those particle counts.

Common mistakes

• Using the solution mass instead of the solvent mass. 58.44 g of salt plus 941.56 g of water is 1 kg of solution, but its molality is about 1.06 mol/kg, not 1.
• Unit picker slips. Typing 500 with the unit left on kg means 500 kilograms of solvent. Switch the menu to g first.
• Reusing 1.04 g/mL for every solution. That default suits about 1 M sodium chloride. Look up or measure the density of your own solution before converting.
• Forgetting hydrate water. With a hydrate, use the hydrate's molar mass for the moles. Its crystal water joins the solvent once it dissolves, so for precise work add that water to the solvent mass.

Limits

The conversion mode is only as good as the density you give it; the tool does not look densities up. Each mode handles one solute at a time, so work out mixtures solute by solute. Molality itself is an exact definition, but freezing point estimates built on it assume ideal behavior, which real salt solutions fall short of. For volume-based recipes, go back to the molarity calculator, and for formulas you do not know the weight of, the molar mass calculator.

FAQ

What is molality?

Molality is the number of moles of solute per kilogram of solvent, written mol/kg. A solution of 1 mol of sodium chloride (58.44 g) in 1 kg of water has a molality of 1 mol/kg.

What is the molality formula?

Molality b equals moles of solute divided by kilograms of solvent: b = (grams of solute ÷ molar mass) ÷ kg of solvent. To find the mass to weigh, rearrange it to grams = b × molar mass × kg of solvent.

What is the difference between molarity and molality?

Molarity divides moles by the liters of finished solution, while molality divides by the kilograms of solvent alone. Molarity is handier for volumetric recipes; molality stays constant with temperature and is the basis of freezing point and osmolality work.

Why does molality not change with temperature?

Molality is built only from masses, and mass does not change when a solution warms. Molarity uses volume, which expands slightly with temperature, so molarity drifts down a little as the solution heats up.

How do I convert molarity to molality?

You need the solution's density. Subtract the solute mass in one liter (molarity × molar mass) from the mass of that liter (density × 1000) to get grams of solvent, then divide the molarity by the solvent mass in kilograms. The "from molarity" mode does this; for 1 M NaCl at 1.04 g/mL it gives 1.019 mol/kg.