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Finding Molality of an Aqueous Solution

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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 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

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

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

Finding Molality of an Aqueous Solution

Source: https://www.ausetute.com.au/molality.html