Molality:
moles of solute per kilogram of solvent

The molality formula

Molality tells you how many moles of a dissolved substance sit in each kilogram of the solvent. Dissolve 0.5 mol of a solute in 2 kg of water and the solution is 0.25 molal, written 0.25 mol/kg or 0.25 m.

The key detail is the denominator. It is the mass of the solvent only, not the combined mass of solvent and solute, and not the volume of the solution. Because mass does not change when a solution warms up or cools down, a molality value is the same at 5 °C and at 80 °C.

That temperature independence is why molality is the preferred unit in physical chemistry whenever properties such as freezing and boiling points are being studied.

If you start with grams of solute, first convert to moles by dividing by the molar mass, then divide by the solvent mass in kilograms. If the solvent mass comes in grams, divide by 1,000 to reach kilograms. A common slip is to leave it in grams, which makes the answer 1,000 times too small.

Worked example: table salt in water

Suppose 18 g of sodium chloride is dissolved in 250 g of water. Sodium chloride has a molar mass of 58.44 g/mol (22.990 for sodium plus 35.45 for chlorine).

Note that the solution weighs 268 g in total, but only the 250 g of water is used in the calculation.

Molality versus molarity

The two are easy to mix up because their names differ by one letter. Both count moles of solute, but they divide by different things.

For dilute aqueous solutions the two numbers are close, because 1 kg of water occupies about 1 litre near room temperature. In concentrated or non-aqueous solutions they can differ widely.

Where molality earns its place

Colligative properties depend on how many solute particles are present per kilogram of solvent. The best-known are freezing-point depression and boiling-point elevation, given by ΔT = i × K × m, where i is the number of particles each formula unit produces and K is a constant for the solvent.

For water, the freezing-point constant is about 1.86 °C·kg/mol. For the 1.232 mol/kg salt solution above, sodium chloride splits into two ions, so the ideal estimate is 2 × 1.86 × 1.232 ≈ 4.58 °C of lowering. Real solutions deviate because ions interact, so treat that as a first estimate.

• Antifreeze and road-salt planning rely on freezing-point depression.
• Boiling-point elevation explains why salted pasta water boils very slightly hotter.
• Osmotic pressure and vapour-pressure lowering use the same particle-count idea.

Finding the solvent mass when the recipe hides it

Often a problem or a label gives the mass of the whole solution and the percentage of solute, not the solvent mass directly. The route is always the same: take the solution mass, find the solute mass from the percentage, subtract it to get the solvent mass, and convert the solute to moles.

Take 100 g of a 10% by mass glucose solution. The solute is 10 g, which at 180.16 g/mol is 0.0555 mol. The solvent is 90 g, or 0.090 kg. Divide: 0.0555 ÷ 0.090 = 0.617 mol/kg. Note that treating the full 100 g as solvent would give 0.555, an error of about 10%, which is exactly the mistake the definition is designed to prevent.

For dilute solutions the error from this mistake is small; for concentrated syrups and brines it can be large.

Moving between molality and molarity

You can convert from one unit to the other if you know the density of the solution. Take a 1.00 molal solution as the basis: it holds 1 mol of solute in 1 kg of solvent, so the total mass is 1 kg plus the solute mass. Divide that total mass by the density to get the volume in litres, and the moles over that volume is the molarity.

For a 1.00 molal sodium chloride solution, the total mass is 1,000 + 58.44 = 1,058.44 g. If the density were 1.037 g/mL, the volume would be 1,058.44 ÷ 1.037 = 1,020.7 mL, so the molarity is 1 ÷ 1.0207 = 0.98 mol/L. The two units differ by only 2% here, which is why the distinction is easy to overlook in dilute work.

Choosing between the concentration units

No single unit suits every job, and knowing which one a formula expects is half the work. Molality earns its place when temperature changes or when you want to add up solute and solvent by weighing alone. Molarity suits titration and volumetric work where reagents are poured, not weighed. Mole fraction suits gas mixtures and vapour-pressure calculations. Mass percent is the everyday label unit.

A useful sanity check: for a dilute water solution, molality and molarity are nearly equal numbers, so if your two figures differ by a factor of two or more, one of the inputs has probably been entered in the wrong units or the solvent mass has been confused with the solution mass.

Common slips to avoid

• Using the mass of the whole solution instead of the solvent alone.
• Leaving the solvent mass in grams.
• Forgetting that a salt that dissociates counts as several particles in colligative formulas, even though molality itself counts formula units.
• Mixing up the symbol: a lowercase m means molality, while a capital M means molarity.