Calculate The Molality of The Following Aqueous Solutions

Molality is a measure of solution concentration that expresses the number of moles of solute per kilogram of solvent. Unlike molarity, which measures moles per liter of solution, molality is independent of temperature changes because it's based on the mass of the solvent rather than its volume.

What is Molality?

Molality (m) is defined as the number of moles of solute dissolved in one kilogram of solvent. It's particularly useful in cryoscopic and ebullioscopic measurements where temperature changes are involved, as it doesn't depend on solution volume which changes with temperature.

The key advantage of molality is that it remains constant during phase transitions (like freezing or boiling) because it's based on mass rather than volume. This makes it valuable in colligative properties studies.

Molality Formula

Molality (m) = (moles of solute) / (mass of solvent in kg)

Where:

moles of solute - the amount of solute in moles
mass of solvent - the mass of the solvent in kilograms

The result is expressed in units of moles per kilogram (mol/kg).

How to Calculate Molality

Determine the number of moles of solute using its molar mass
Measure the mass of the solvent in kilograms
Divide the moles of solute by the mass of solvent
Report the result in mol/kg units

Example Calculation

For a solution containing 5 grams of sodium chloride (NaCl) in 250 grams of water:

Molar mass of NaCl = 58.44 g/mol
Moles of NaCl = 5 g / 58.44 g/mol ≈ 0.0856 mol
Mass of water = 250 g = 0.250 kg
Molality = 0.0856 mol / 0.250 kg ≈ 0.3424 mol/kg

Units and Conversions

Molality is expressed in moles per kilogram (mol/kg). To convert between units:

1 mol/kg = 1000 mol/L (if solvent density is 1 g/mL)
For other solvents, use the actual density to convert

Note: Molality is not directly convertible to molarity without knowing the solution density, as volume changes with temperature.

Practical Applications

Molality is particularly useful in:

Cryoscopic measurements (freezing point depression)
Ebullioscopic measurements (boiling point elevation)
Osmotic pressure calculations
Solvent selection for specific applications

Property	Molality	Molarity
Temperature dependence	Independent	Dependent
Use in phase transitions	Preferred	Less suitable
Calculation complexity	Simpler	Requires density

FAQ

What is the difference between molality and molarity?: Molality is based on mass of solvent (kg), while molarity is based on volume of solution (L). Molality is constant during phase changes, while molarity changes with temperature.
When should I use molality instead of molarity?: Use molality for cryoscopic, ebullioscopic, or osmotic pressure calculations where temperature changes are involved. For most other applications, molarity is sufficient.
How does molality affect freezing point depression?: The freezing point depression (ΔTf) is directly proportional to molality: ΔTf = Kf × m, where Kf is the cryoscopic constant for the solvent.
Can molality be negative?: No, molality is always a positive value representing the concentration of solute in the solution.