Molality Calculator

A molality calculator finds the concentration of a solution in moles of solute per kilogram of solvent, a unit chemists call molality. It takes three inputs — the mass of the solute, the mass of the solvent, and the solute's molar mass — and returns the result in mol/kg.

What Is Molality?

Molality (symbol m) measures how many moles of a dissolved substance, the solute, sit inside one kilogram of the substance it is dissolved in, the solvent. It answers a simple question: for each kilogram of solvent, how many moles of solute are present?

$m = \frac{n_{solute}}{m_{solvent}}$

Here $n_{solute}$ is the number of moles of solute and $m_{solvent}$ is the mass of solvent in kilograms.

Molality only counts the solvent's mass, not the total mass of the finished solution. If 5.85 g of table salt (NaCl, molar mass 58.5 g/mol) dissolves in 100 g (0.1 kg) of water, the solution holds 0.1 mol of salt in 0.1 kg of water. That is a molality of 1.0 mol/kg, even though the combined solution weighs 105.85 g.

Molality does not change with temperature, because it is built from mass rather than volume. Liquids expand slightly when heated and shrink when cooled, so molarity (moles per liter of solution) drifts with temperature. Molality stays fixed, which is why it is the standard unit in freezing-point and boiling-point studies.

Molality Formula

Chemists rarely count moles directly; they weigh substances instead. Moles of solute equal the solute's mass divided by its molar mass, so the working formula becomes:

$m = \frac{m_{solute} / M_{solute}}{m_{solvent}}$

• $m_{solute}$ — mass of the solute that was weighed out, in grams
• $M_{solute}$ — molar mass of the solute, in g/mol, found from the periodic table
• $m_{solvent}$ — mass of the solvent, in kilograms

How to Calculate Molality

1. Weigh the solute. Record its mass in grams, kilograms, or milligrams.
2. Look up the solute's molar mass, in g/mol, from the periodic table. For a hydrate such as CuSO₄·5H₂O, include the mass of the water molecules in the total.
3. Weigh the solvent alone, before mixing, not the combined solution afterward.
4. Convert both masses to matching units: grams for the solute, kilograms for the solvent.
5. Divide the solute mass by its molar mass to get moles of solute.
6. Divide the moles of solute by the solvent mass in kilograms to get molality, in mol/kg.

Common mistakes

• Using the solution's mass instead of the solvent's. Weighing 100 g of water, then adding 10 g of salt, gives 110 g of solution — but the molality calculation still uses only the 100 g of water.
• Skipping water of hydration. CuSO₄·5H₂O has a molar mass of 249.7 g/mol, not the 159.6 g/mol of anhydrous CuSO₄ alone.
• Mixing up grams and kilograms. Entering solvent mass as 500 instead of 0.5 kg throws the answer off by a factor of 1000.
• Rounding too early. Carry extra digits through the moles-of-solute step before dividing, then round the final answer.

Example: Calculating Molality

Problem. Find the molality of a solution made from 10 g of sodium chloride (NaCl, molar mass 58.44 g/mol) dissolved in 500 g of water.

1. Convert the solvent mass to kilograms: 500 g = 0.5 kg.
2. Find moles of solute: 10 g ÷ 58.44 g/mol = 0.1711 mol.
3. Find molality: 0.1711 mol ÷ 0.5 kg = 0.3422 mol/kg.

Example: Working With Milligrams

Problem. Find the molality of a solution made from 25 mg of glucose (C₆H₁₂O₆, molar mass 180.16 g/mol) dissolved in 15 g of water.

1. Convert the solute mass to grams: 25 mg = 0.025 g.
2. Convert the solvent mass to kilograms: 15 g = 0.015 kg.
3. Find moles of solute: 0.025 g ÷ 180.16 g/mol ≈ 0.0001388 mol.
4. Find molality: 0.0001388 mol ÷ 0.015 kg ≈ 0.0093 mol/kg.

Molality vs. Molarity

Molality and molarity sound alike but measure different things. Molality divides moles of solute by kilograms of solvent. Molarity divides moles of solute by liters of the whole solution. Because liquid volume changes with temperature and molarity depends on volume, a solution's molarity shifts slightly as it warms or cools, while its molality stays the same. For dilute water-based solutions at room temperature, the two values are often close, but they are not identical and should not be swapped without checking.

An approximate way to convert between them, when the solution's density is known, is:

$Molarity = \frac{Molality \times \rho}{1 + (Molality \times M_{solute} / 1000)}$

where $\rho$ is the solution's density in g/mL.

Why Chemists Use Molality

Molality shows up wherever temperature changes during an experiment. In freezing-point depression, the drop in a solution's freezing point below that of the pure solvent, molality appears directly in the governing equation:

$\Delta T_f = K_f \times m \times i$

$\Delta T_f$ is the freezing-point depression, $K_f$ is a constant specific to the solvent, $m$ is molality, and $i$ is the number of particles each solute unit produces when it dissolves. Because molality does not drift as the sample cools toward its freezing point, it gives a stable number to plug into this equation. The same reasoning applies to boiling-point elevation and to pharmaceutical formulations that must hold a steady concentration across a range of storage temperatures.

Frequently Asked Questions

What is the difference between molality and molarity? Molality is moles of solute per kilogram of solvent. Molarity is moles of solute per liter of solution. Molality depends only on mass, so it does not change with temperature; molarity depends on volume, which does change with temperature.

Why do some experiments use molality instead of molarity? Any measurement taken across a range of temperatures, such as freezing-point depression, needs a concentration unit that will not shift as the sample warms or cools. Because molality is based on mass, it stays constant, while a molarity value would change slightly along with the solution's volume.

Can molality be negative or zero? No, molality cannot be negative, since it describes a physical amount of dissolved solute. It is zero only when no solute is present, meaning the sample is pure solvent rather than a solution.

Is there an upper limit to molality? Yes. Molality is capped by the solute's solubility in the solvent. Once the solvent holds as much solute as it can dissolve at that temperature and pressure, molality cannot rise further.

Does pure water have a molality? No. Molality describes a solute dissolved in a solvent. Pure water contains no solute, so molality does not apply to it.

How accurate is a molality calculator for concentrated or non-ideal solutions? The arithmetic is exact for any input. The molality figure itself is always correct; what can change in a concentrated or non-ideal solution is how that figure behaves in downstream equations, such as freezing-point depression, where ion-ion interactions can make real behavior deviate from the simple proportional formula.