# 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 in kg)
• A solution containing 3 moles of solute per kilogram of solvent for example, is said to be 3-molal or 3m.

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## Example : Calculating Molality

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

Solution:

1. Write the equation for calculating molality:
molality = moles(solute) ÷ mass(solvent in kg)
2. Identify the solute and solvent that make up the solution:
solute = NaCl
solvent = water

3. Calculate moles of solute: moles = mass ÷ molar mass
mass = 5.0 g (given in question)
molar mass = 22.99 + 35.45 = 58.44 g mol-1
moles(solute) = 5.0 ÷ 58.44 = 0.086 mol
4. Calculate mass of solvent in kilograms:
mass(water) = 25.0 g (given in question)
Convert mass in grams (g) to mass in kilograms (kg) by dividing by 1000
mass(water) = 25.0 g ÷ 1000 g/kg = 25.0 × 10-3 = 0.0250 kg
5. Calculate molality = moles(solute) ÷ mass(solvent)
moles(NaCl) = 0.086 mol
mass(water) = 0.0250 kg
molality = 0.086 ÷ 0.0250 = 3.44 m

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## Calculating Mass of Solute using Molality

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

Solution:

1. Write the equation for calculating molality:
molality = moles(solute) ÷ mass(solvent in kg)
2. Rearrange equation to find moles(solute):
 molality = moles(solute)   mass(solvent in kg)

 molality × mass(solvent in kg) = moles(solute) ×   mass(solvent)mass(solvent)

 moles(solute) = molality × mass(solvent in kg)
3. Identify the solute and solvent that make up the solution:
solute = sodium chloride = NaCl
solvent = water
4. Calculate moles of solute :
moles(solute) = molality × mass(solvent in kg)
molality = 2.7 m
mass(solvent in kg) = 1 kg
moles(NaCl) = 2.7 × 1 = 2.7 mol
5. Calculate mass of solute :

moles(solute) = mass(solute in g) ÷ molar mass(solute in g mol-1)
Rearrange equation to find mass:
mass(solute) = moles(solute) × molar mass

moles(NaCl) = 2.7 mol
molar mass(NaCl) = 22.99 + 35.45 = 58.44 g mol-1
mass(NaCl) = 2.7 × 58.44 = 157.79 g

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## Calculating Mass of Solvent using Molality

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

Solution:

1. Write the equation for calculating molality:
molality = moles(solute) ÷ mass(solvent in kg)
2. Rearrange equation to find mass(solvent in kg):
 molality = moles(solute)   mass(solvent in kg)

 molality × mass(solvent in kg) = moles(solute) ×   mass(solvent)mass(solvent)

 molality × mass(solvent in kg) = moles(solute)

 molality × mass(solvent in kg)molality = moles(solute)molality

 mass(solvent in kg) = moles(solute)molality
3. Identify the solute and solvent that make up the solution:
solute = sodium chloride = NaCl
solvent = water (because this is an aqueous solution)
4. Calculate moles of solute :
moles(solute) = mass ÷ molar mass

mass(NaCl) = 6.4 g
molar mass(NaCl) = 22.99 + 35.45 = 58.44 g mol-1
moles(NaCl) = 6.4 ÷ 58.44 = 0.11 mol

5. Calculate mass of water :

mass(solvent) = moles(solute) ÷ molality

moles(NaCl) = 0.11 mol
molality = 1.3 m
mass(water) = 0.11 ÷ 1.3 = 0.085 kg = 85 g

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