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Molality Calculations

Key Concepts

The concentration of a solution can be given in moles of solute dissolved per kilogram of solvent.
This is known as molality.
(Not to be confused with molarity which is a different measure of concentration.)
Molality is given the symbol m.
molality = moles of solute ÷ mass of solvent in kilograms
m = n(solute) ÷ mass(solvent)
A solution containing 3 moles of solute per kilogram of solvent for example, is said to be 3-molal or 3m.

Example : Calculating Molality

What is the molality of a solution containing 5.0g NaCl dissolved in 25.0g water?

m = n(solute) ÷ mass(solvent)
Calculate moles of solute: n = mass ÷ molecular mass
mass = 5.0g
molecular mass = 22.99 + 35.45 = 58.44 g/mol
n(solute) = 5.0 ÷ 58.44 = 0.086 mol
Calculate molality: m = n(solute) ÷ mass(solvent)
n(NaCl) = 0.086 mol
mass(water) = 25.0g = 25.0 x 10^-3kg
m = 0.086 ÷ 25.0 x 10^-3 = 3.44 m

Calculating Mass of Solute

How many grams of sodium chloride per kilogram of water are present in a 2.7m aqueous solution?

Calculate moles of solute :
n(solute) = m x mass(solvent)
m = 2.7m
mass(solvent) = 1kg
n(NaCl) = 2.7 x 1 = 2.7mol
Calculate mass of solute :
mass(solute) = n(solute) x molecular mass
n(NaCl) = 2.7mol
MM(NaCl) = 22.99 + 35.45 = 58.44 g/mol
mass(NaCl) = 2.7 x 58.44 = 157.79g

Calculating Mass of Solvent

A sample of 1.3m aqueous solution of sodium chloride contains 6.4g of sodium chloride.
What mass of water is present?

Calculate moles of solute :
n(solute) = mass ÷ molecular mass
mass = 6.4g
molecular mass = 22.99 + 35.45 = 58.44 g/mol
n(NaCl) = 6.4 ÷ 58.44 = 0.11 mol
Calculate mass of water :
mass(solvent) = n(solute) ÷ m
n(NaCl) = 0.11 mol
m = 1.3m
mass(water) = 0.11 ÷ 1.3 = 0.085 kg = 85g

Practice Questions

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