Freezing Point Depression
Lowering a solvent's freezing point by adding solute
The Formula
Variables
- ΔTf = freezing point lowering (C)
- i = van't Hoff factor
- Kf = cryoscopic constant (C·kg/mol)
- m = molality (mol solute / kg solvent)
Typical Kf Values
- Water: 1.86 C·kg/mol
- Benzene: 5.12 C·kg/mol
- Acetic acid: 3.90 C·kg/mol
Step-by-Step Example
Problem:
What is the freezing point of a solution made by dissolving 0.500 mol NaCl in 1.00 kg water? (Assume i = 1.9, Kf water = 1.86 C·kg/mol)
1) Molality
m = 0.500 mol / 1.00 kg = 0.500 m
2) Calculate ΔTf
ΔTf = i Kf m = 1.9 × 1.86 × 0.500 = 1.77 C
3) New freezing point
Tf,solution = 0.00 C - 1.77 C = -1.77 C
Answer:
The solution freezes at -1.77 C (ideal assumption).
Common Mistakes to Avoid
Using molarity
Use molality (mol/kg solvent), not molarity.
Ignoring i
Electrolytes dissociate; include the van't Hoff factor.
Wrong units
Keep Kf in C·kg/mol and m in mol/kg.
Non-ideal behavior
At high concentration, i is lower than the ideal integer.
Related Calculators
Frequently Asked Questions
What is i for NaCl?
Ideal i = 2, but effective i is typically 1.8-1.9 at moderate concentration.
Why use molality?
Molality is temperature independent; molarity changes with thermal expansion.
Does this work for nonelectrolytes?
Yes, with i = 1 for nonelectrolytes like glucose.