Molality Calculator

How Molality Is Calculated

Molality is a concentration unit that expresses the number of moles of solute per kilogram of solvent (not solution).
Unlike molarity, molality does not change with temperature, which is why colligative property calculations are written in it.

Molality Formula: m = n_solute / m_solvent(kg)

Where:

• m = molality in mol/kg (molal, symbol m)
• n_solute = moles of solute
• m_solvent = mass of solvent in kilograms (NOT total solution mass)

Moles of Solute: n = mass(g) / molar mass(g/mol)

Worked Example: Dissolve 58.44 g of NaCl (molar mass = 58.44 g/mol) in 750 g of water:

• n(NaCl) = 58.44 / 58.44 = 1.0 mol
• m_solvent = 750 g = 0.750 kg
• Molality = 1.0 / 0.750 = 1.333 mol/kg (1.333 m)

Colligative Property Applications:

• Boiling point elevation: ΔT_b = K_b × m (K_b for water = 0.512 °C/m)
• Freezing point depression: ΔT_f = K_f × m (K_f for water = 1.86 °C/m)

For the NaCl example above (dissociates into 2 ions, i = 2):

• Freezing point depression = 1.86 × 1.333 × 2 = 4.96°C → water freezes at −4.96°C

Molality vs Molarity:

• Molarity (M): mol per litre of solution, and it changes with temperature
• Molality (m): mol per kg of solvent, and it does not
• For dilute aqueous solutions, M ≈ m (since 1L water ≈ 1 kg)

Mole fraction, and why the solvent’s molar mass is asked for

The result panel reports mole fraction alongside molality, because the two answer different questions. Mole fraction is χᵢ = nᵢ / n_total: the share of all the molecules present that are the species you care about. Computing it needs the moles of solvent as well as solute, which is why the solvent’s molar mass is an input even though molality itself does not use it.

For dilute aqueous solutions the numbers look strikingly different. A 1 molal solution has one mole of solute per kilogram of water, and a kilogram of water is 55.5 moles, so the solute’s mole fraction is only 0.0177. Even a fairly concentrated solution is overwhelmingly solvent by particle count.

Molality or molarity?

Use molality when temperature will change. Molarity is moles per litre of solution, and the volume of that solution expands as it warms, so the molarity of a sample drifts even though nothing has been added or removed. Molality is defined against the mass of solvent, which does not care about temperature at all.

That is why every colligative-property formula, boiling point elevation and freezing point depression included, is written in molality rather than molarity.