Molality Formula
Molality (m) equals moles of solute divided by kilograms of solvent.
Used for colligative properties like boiling point elevation.
The Formula
Molality measures the concentration of a solution by comparing moles of solute to the mass of solvent (not the total solution volume). Unlike molarity, molality does not change with temperature because mass does not expand or contract.
This makes molality especially useful for colligative property calculations like boiling point elevation and freezing point depression.
Variables
| Symbol | Meaning |
|---|---|
| m | Molality (in mol/kg, sometimes written as "molal") |
| moles of solute | Amount of dissolved substance (in mol) |
| kg of solvent | Mass of the solvent only, not the total solution (in kg) |
Molality vs Molarity
| Property | Molality (m) | Molarity (M) |
|---|---|---|
| Definition | mol solute / kg solvent | mol solute / L solution |
| Temperature dependent? | No | Yes |
| Uses mass or volume? | Mass of solvent | Volume of solution |
| Best for | Colligative properties | Volumetric analysis |
Example 1
You dissolve 58.44 g of NaCl (1 mole) in 500 g of water. What is the molality?
Moles of NaCl = 58.44 g / 58.44 g/mol = 1.00 mol
Mass of solvent = 500 g = 0.500 kg
m = 1.00 / 0.500
m = 2.00 mol/kg (2.00 molal)
Example 2
A solution of glucose (C₆H₁₂O₆, molar mass 180.16 g/mol) is prepared by dissolving 36 g of glucose in 400 g of water. What is the molality?
Moles of glucose = 36 / 180.16 = 0.200 mol
Mass of solvent = 400 g = 0.400 kg
m = 0.200 / 0.400
m = 0.500 mol/kg (0.500 molal)
When to Use It
Molality is preferred over molarity in several situations.
- Boiling point elevation calculations (ΔT_b = K_b × m)
- Freezing point depression calculations (ΔT_f = K_f × m)
- Osmotic pressure problems in some formulations
- Any experiment where temperature changes significantly (because molality is temperature-independent)
- Precise thermodynamic calculations
Key Notes
- Formula: m = moles solute / kg solvent: Molality is defined per kilogram of solvent (not solution). For dilute aqueous solutions, 1 kg water ≈ 1 L, so molality ≈ molarity numerically. At higher concentrations or temperatures, they diverge.
- Temperature independence is the key advantage: Because molality is based on mass (not volume), it doesn't change as temperature changes the volume of the solution. Molarity decreases slightly when heated (volume expands). For precision thermodynamic work, molality is preferred.
- Boiling point elevation: ΔTb = Kb × m: Kb is the ebullioscopic constant (water: 0.512°C/m). Adding 1 mol of solute per kg water raises the boiling point by 0.512°C. For the van't Hoff factor i > 1 (electrolytes): ΔTb = i × Kb × m.
- Freezing point depression: ΔTf = Kf × m: Kf for water = 1.86°C/m. Antifreeze (ethylene glycol) works by depressing the freezing point. A 50/50 mix by volume lowers the freezing point to about −37°C. Road salt (NaCl, i = 2) depresses freezing twice as effectively per mole as a non-electrolyte.
- Applications: Molality is used in colligative property calculations (boiling point elevation, freezing point depression, osmotic pressure for non-ideal solutions), antifreeze formulation, polymer solution analysis, chemical thermodynamics, and any application where temperature-independent concentration is required.