Library / Solution chemistry, equilibria and kinetics / SCH-49
Solution chemistry, equilibria and kinetics
Freezing-point depression
Lowering of the freezing point of a dilute solution, from the solute molality b, the solvent’s cryoscopic constant Kf and the effective particle factor i.
- Ref
- SCH-49
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- ΔTf [K]
A dissolved non-volatile solute lowers the freezing point of the solvent by ΔTf = i Kf b, where b is the molality, Kf the solvent’s cryoscopic constant (1.86 K·kg/mol for water) and i the effective particle factor. The result is positive: subtract it from the pure-solvent freezing point. It applies to dilute solutions where the solute stays out of the solid. Use molality, not molarity, since it does not change with temperature.
Lowering of the freezing point of a dilute solution, from the solute molality b, the solvent’s cryoscopic constant Kf and the effective particle factor i. The result is positive, and is subtracted from the pure-solvent freezing point.
Calculator
- Freezing point if the solvent freezes at 273.15 K272.8 K
- Molality that gives a 1 K depression, 1/(i Kf)0.5376 mol/kg
- Depression per 0.1 mol/kg of solute0.186 K
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A solution at 0.2 mol/kg freezes 0.372 K below the pure solvent, so water would freeze at about −0.372 °C.
- To lower the freezing point by 10 K in water needs about 5.38 mol/kg of particles, which is why road salt is applied heavily in a hard frost.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (K) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Kf Cryoscopic constant of the solvent | 0.1 to 50 K·kg/mol | 0.02 | 10 | 9.98 | +10% | +10 % |
| b Solute molality | 0.001 to 5 mol/kg | 0.00186 | 9.3 | 9.298 | +10% | +10 % |
| i Effective particle factor | 1 to 5 | 0.372 | 1.86 | 1.488 | +10% | +10 % |
Sweep of Solute molality
| Solute molality (mol/kg) | Freezing-point depression (K) |
|---|---|
| 0.001 | 0.00186 |
| 0.0029 | 0.005394 |
| 0.008409 | 0.01564 |
| 0.02438 | 0.04536 |
| 0.07071 | 0.1315 |
| 0.205 | 0.3814 |
| 0.5946 | 1.106 |
| 1.724 | 3.207 |
| 5 | 9.3 |
Sweep one variable
Variables and how each one contributes
Freezing-point depression
What the equation gives you. Everything else feeds it.
Effective particle factor
The effective particle factor (about 1 for non-electrolytes, up to 2 or 3 for salts). Raises the depression in direct proportion. Raising it by 10 % (to 1.1) moves the result by +10 %, from 0.372 to 0.4092 K.
Cryoscopic constant of the solvent
The cryoscopic constant of the solvent, in K·kg/mol. Raises the depression in direct proportion. Raising it by 10 % (to 2.046) moves the result by +10 %, from 0.372 to 0.4092 K.
Solute molality
The solute molality, in mol/kg. Raises the depression in direct proportion. Raising it by 10 % (to 0.22) moves the result by +10 %, from 0.372 to 0.4092 K.
Worked example with the values above
- Particle molality: i b = 1 × 0.2 = 0.2 mol/kg.
- Multiply by Kf = 1.86 K·kg/mol.
- ΔTf = 0.372 K.
Assumptions and limits
- Dilute or ideal solutions with a non-volatile solute, unless a second volatile component is stated.
- Constant temperature (or constant pressure for boiling-point elevation) and a membrane that passes only the solvent for osmosis.
Common mistakes
- Using molarity in place of molality.
- Forgetting the factor i for an electrolyte.
- Adding the depression to the freezing point, instead of subtracting it.
Statistics and uncertainty
Colligative formulas assume ideal behaviour, which holds only for dilute solutions. The effective particle factor i of an electrolyte is below its ideal value, by 5 % to 30 % even at 0.1 mol/kg.
Where it is used
- Estimating antifreeze, de-icing and desalination behaviour.
- Finding molar masses and reading simple phase diagrams.
Maths you need
- Raoult’s law: partial pressure = mole fraction × pure vapour pressure
- Colligative properties: properties that depend on particle number
- Molality: moles of solute per kilogram of solvent