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:
- Write the equation for calculating molality:
molality = moles(solute) ÷ mass(solvent in kg)
- Identify the solute and solvent that make up the solution:
solute = NaCl
solvent = water - 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 - 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 - 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:
- Write the equation for calculating molality:
molality = moles(solute) ÷ mass(solvent in kg)
- 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) - Identify the solute and solvent that make up the solution:
solute = sodium chloride = NaCl
solvent = water - 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 - 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:
- Write the equation for calculating molality:
molality = moles(solute) ÷ mass(solvent in kg)
- 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 - Identify the solute and solvent that make up the solution:
solute = sodium chloride = NaCl
solvent = water (because this is an aqueous solution) - 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 - 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
How molality is calculated?
The formula for molality is m = moles of solute / kilograms of solvent. In problem solving involving molality, we sometimes need to use additional formulas to get to the final answer. One formula we need to be aware of is the formula for density, which is d = m / v, where d is density, m is mass and v is volume.
Why do we calculate molality?
Concentrations expressed in molality are used when studying properties of solutions related to vapor pressure and temperature changes. Molality is used because its value does not change with changes in temperature. The volume of a solution, on the other hand, is slightly dependent upon temperature.