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