Molality is moles of solute divided by kilograms of solvent

Molality measures how many moles of a dissolved substance (the solute) are in one kilogram of the liquid that dissolves it (the solvent). The formula is straightforward: molality = moles of solute ÷ kilograms of solvent. Unlike molarity, which depends on the volume of the final solution and changes with temperature, molality stays constant because it uses mass instead. This makes it the preferred measure in chemistry when temperature shifts or when you need a measurement that does not change with conditions.

The unit for molality is mol/kg, often written as m. A 1 m solution contains 1 mole of solute dissolved in exactly 1 kilogram of solvent — not 1 kilogram of solution, but solvent alone. This distinction matters because the solute itself adds mass, so the total solution weighs more than the solvent by itself.

Key Takeaways

  • Molality equals moles of solute divided by kilograms of solvent, and the unit is mol/kg or m.
  • You must convert grams of solute to moles using its molar mass, and grams of solvent to kilograms by dividing by 1000.
  • Molality does not change with temperature because it is based on mass, not volume.
  • The solvent mass does not include the solute — if you dissolve 10 grams of salt in 100 grams of water, the solvent mass is 100 grams, not 110.

Step 1: Find the molar mass of the solute

The molar mass is the mass in grams of one mole of a substance. You find it by adding the atomic masses of all atoms in the chemical formula. Atomic masses are listed on the periodic table, usually to two decimal places.

For example, sodium chloride (NaCl) contains one sodium atom (atomic mass 23) and one chlorine atom (atomic mass 35.5). The molar mass is 23 + 35.5 = 58.5 g/mol. For glucose (C₆H₁₂O₆), you add: (6 × 12) + (12 × 1) + (6 × 16) = 72 + 12 + 96 = 180 g/mol.

Step 2: Convert grams of solute to moles

Once you know the molar mass, divide the mass of solute in grams by its molar mass in g/mol. The result is the number of moles.

If you have 29.25 grams of NaCl and its molar mass is 58.5 g/mol, then moles = 29.25 ÷ 58.5 = 0.5 moles. If you have 90 grams of glucose with a molar mass of 180 g/mol, then moles = 90 ÷ 180 = 0.5 moles. Always check that your units cancel: grams ÷ (grams/mole) = moles.

Step 3: Convert grams of solvent to kilograms

Molality uses kilograms of solvent, not grams. Divide the mass of solvent in grams by 1000 to convert to kilograms.

If your solvent is 500 grams of water, then kilograms of solvent = 500 ÷ 1000 = 0.5 kg. If you have 2000 grams of ethanol as your solvent, then kilograms = 2000 ÷ 1000 = 2 kg. Remember: this is the mass of solvent alone, not the total solution mass.

Step 4: Divide moles by kilograms of solvent

Now explore the molality formula: molality = moles of solute ÷ kilograms of solvent.

Using the NaCl example: 0.5 moles ÷ 0.5 kg = 1 m (one molar). Using the glucose example: 0.5 moles ÷ 0.5 kg = 1 m. If you had 0.5 moles of solute in 2 kg of solvent, the molality would be 0.5 ÷ 2 = 0.25 m.

A worked example from start to finish

Suppose you dissolve 34.2 grams of sucrose (table sugar) in 500 grams of water and need to find the molality. First, find the molar mass of sucrose (C₁₂H₂₂O₁₁): (12 × 12) + (22 × 1) + (11 × 16) = 144 + 22 + 176 = 342 g/mol.

Next, convert grams to moles: 34.2 grams ÷ 342 g/mol = 0.1 moles of sucrose. Then convert the solvent to kilograms: 500 grams ÷ 1000 = 0.5 kg of water. Finally, divide: 0.1 moles ÷ 0.5 kg = 0.2 m. The solution is 0.2 molar in sucrose.

Why molality matters more than molarity in some situations

Molarity (moles per liter of solution) is common in the lab because it is straightforward to measure volume with a graduated cylinder or volumetric flask. However, molarity changes when temperature changes because liquids expand and contract. If you prepare a 1 M solution at room temperature and then heat it, the volume increases and the molarity drops, even though the actual amount of solute has not changed.

Molality does not have this problem. Because it uses mass instead of volume, heating or cooling the solution does not change its molality. This makes molality essential in chemistry when you are studying how temperature affects reactions, or when you need a measurement that stays constant across different conditions. Molality is also the standard measure for colligative properties — properties that depend only on the number of solute particles, such as freezing point depression and boiling point elevation.

Frequently Asked Questions

What is the difference between molality and molarity?

Molarity is moles of solute per liter of total solution and changes with temperature. Molality is moles of solute per kilogram of solvent and does not change with temperature. Molarity is easier to measure in a lab with glassware, but molality is more useful when temperature varies or when studying colligative properties.

Do I include the solute mass in the solvent mass?

No. The solvent mass is the mass of the liquid before you add the solute. If you dissolve salt in water, the solvent mass is the water alone. The solute mass is separate. This is why molality calculations use only the solvent mass in the denominator.

Can molality be greater than molarity?

Yes, it often is. Because the denominator in molality (kilograms of solvent) is usually smaller than the denominator in molarity (liters of solution), molality values tend to be higher. A 1 M aqueous solution is typically around 0.98 m because 1 liter of solution contains slightly less than 1 kilogram of water.

What if the solute is a solid, not a liquid?

The calculation is the same. Convert the mass of solid solute to moles using its molar mass, then divide by kilograms of solvent. The solvent is still the liquid (usually water) in which you dissolve the solid.

How do I find the molar mass if I do not have a periodic table?

Most chemistry textbooks include a periodic table in the back or inside the cover. Online periodic tables are also available through a search. You need the atomic mass of each element in the compound, which you add together according to how many atoms of each element appear in the chemical formula.