Molality: Moles per Kilogram—Temperature-Independent Concentration
Molality (m) is the number of moles of solute per kilogram of solvent. Unlike molarity, it does not depend on temperature or pressure because it uses mass rather than volume. Molality is preferred for colligative property calculations and thermodynamic studies.
Why This Chemistry Calculation Matters
Why: Molality is used when temperature varies because volume changes with temperature but mass does not. Colligative properties (freezing point depression, boiling point elevation) depend on molality.
How: Divide moles of solute by kilograms of solvent. For colligative properties, use ΔT_f = i×K_f×m and ΔT_b = i×K_b×m, where i is the van't Hoff factor (particles per formula unit).
- ●For dilute aqueous solutions, molality ≈ molarity.
- ●Water: K_f = 1.86 °C/m, K_b = 0.512 °C/m.
- ●Ionic compounds have i > 1 (NaCl: i≈2, CaCl₂: i≈3).
Sample Examples
🧪 Basic Molality
Calculate molality: 0.5 mol NaCl in 1 kg water
🧂 Salt Solution
5.844 g NaCl in 500 g water - find molality
🍬 Sugar Solution
34.23 g sucrose in 1 kg water - calculate molality
🚗 Antifreeze Solution
Ethylene glycol antifreeze: 1.0 m solution
❄️ Freezing Point Depression
Calculate freezing point of 0.5 m NaCl solution
🌡️ Boiling Point Elevation
Calculate boiling point of 1.0 m glucose solution
🔄 Molarity to Molality
Convert 1.0 M NaCl solution (density 1.04 g/mL) to molality
📊 Mass Percent to Molality
Convert 10% by mass NaCl solution to molality
Enter Values
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
Antifreeze (ethylene glycol) lowers water freezing point via colligative properties.
— Physical chemistry
Molality is SI-preferred for amount-of-substance concentration in some contexts.
— IUPAC
van't Hoff factor i: non-electrolytes i=1; NaCl i≈2; CaCl₂ i≈3.
— IUPAC
Cryoscopy and ebullioscopy use colligative properties to determine molar mass.
— Physical chemistry
What is Molality?
Molality (m) is a concentration unit defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality is independent of temperature and pressure because it depends on mass rather than volume.
The formula for molality is:
m = n_solute / kg_solvent
where m = molality (mol/kg), n_solute = moles of solute, kg_solvent = mass of solvent (kg)
How to Calculate Molality
- Determine moles of solute: If given mass, divide by molar mass: n = mass / M_molar
- Measure mass of solvent: Convert to kilograms if necessary (1 kg = 1000 g)
- Calculate molality: Divide moles by kilograms of solvent: m = n / kg_solvent
Example:
Calculate molality of a solution with 0.5 mol NaCl dissolved in 1.0 kg water:
m = 0.5 mol / 1.0 kg = 0.5 m (mol/kg)
When to Use Molality
- Temperature-dependent studies: Molality doesn't change with temperature, making it ideal for thermodynamic calculations
- Colligative properties: Freezing point depression and boiling point elevation depend on molality
- Dilute solutions: For very dilute solutions, molality ≈ molarity
- Non-aqueous solvents: When working with solvents other than water
- Precise concentration measurements: When volume measurements are difficult or inaccurate
Key Formulas
Molality
m = n_solute / kg_solvent
Basic molality formula
Freezing Point Depression
ΔT_f = i × K_f × m
Where i = van't Hoff factor, K_f = cryoscopic constant, m = molality
For water: K_f = 1.86 °C/m
Boiling Point Elevation
ΔT_b = i × K_b × m
Where i = van't Hoff factor, K_b = ebullioscopic constant, m = molality
For water: K_b = 0.512 °C/m
Molarity to Molality Conversion
m ≈ M / (density - M × M_molar / 1000)
For dilute solutions: m ≈ M (molality ≈ molarity)
Mass Percent to Molality
m = (mass% / 100) × (1000 / M_molar) / (100 - mass%)
Convert mass percent to molality using molar mass
van't Hoff Factor
The van't Hoff factor (i) accounts for the number of particles a solute produces when dissolved:
- Non-electrolytes: i = 1 (glucose, sucrose, urea)
- Strong electrolytes: i ≈ number of ions (NaCl: i ≈ 2, CaCl₂: i ≈ 3)
- Weak electrolytes: i < number of ions (depends on dissociation)
Common Solvents and Constants
| Solvent | K_f (°C/m) | K_b (°C/m) | Freezing Point (°C) | Boiling Point (°C) |
|---|---|---|---|---|
| Water | 1.86 | 0.512 | 0 | 100 |
| Benzene | 5.12 | 2.53 | 5.5 | 80.1 |
| Camphor | 40 | 5.95 | 179 | 204 |
| Acetic acid | 3.9 | 3.07 | 16.6 | 118.1 |
| Naphthalene | 6.94 | 5.8 | 80.2 | 218 |
| Phenol | 7.27 | 3.56 | 40.9 | 181.7 |
Applications
Antifreeze
Ethylene glycol solutions lower freezing point of water in car radiators.
Laboratory Solutions
Precise molality measurements for temperature-independent concentration studies.
Food Preservation
Salt and sugar solutions used in food preservation rely on colligative properties.
Molecular Weight Determination
Cryoscopy and ebullioscopy use colligative properties to determine molar masses.