This freezing point depression calculator finds how far a solute drags a solvent’s freezing point down (ΔTf = i · Kf · m) — and its mirror, boiling point elevation — for common solvents and electrolytes.
Colligative means it counts particles, not identity: 1 molal of anything (times i) shifts water’s freezing point by the same 1.86 °C. Real electrolytes come in under their ideal i (ion pairing) — NaCl behaves at ~1.9 in dilute solution. Molality, not molarity, because mass-based concentration survives temperature swings (see the Molality Calculator).
ΔT = i · K · m — Counting Particles Again
Freezing is an ordering act; dissolved particles obstruct crystal formation proportionally to their number density per kilogram of solvent. The van’t Hoff factor i upgrades molecules to particles (NaCl → ~2, CaCl₂ → ~3, glucose stays 1). This is the winter-roads and ice-cream physics: salt doesn’t “melt” ice by heat, it lowers the temperature at which water can freeze — the brine stays liquid and equilibrium does the rest. Part of our Chemistry Calculators collection.
Worked Examples (Verified)
- 1 m NaCl in water (defaults): ΔTf = 2 × 1.86 × 1 = 3.72 °C → freezes at −3.72 °C — one line of arithmetic behind every salted road (real brine, concentrated and non-ideal, reaches ≈ −21 °C at the eutectic)
- 2 m glucose (i=1): same 3.72 °C via twice the molality — particle counting verified by two different routes
- Boiling side: 2 m in water elevates boiling by 2 × 0.512 × 1 = 1.02 °C — why “salt raises pasta water’s boiling point” is technically true and practically negligible (a chef’s pinch is ~0.05 m → 0.03 °C)
- Molar-mass archaeology: an unknown at 0.5 m depressing camphor (Kf 40) by 10 °C → the Rast method’s historical route to molecular weights from a melting-point apparatus
Real-World Calibration
- Antifreeze (ethylene glycol in water) exploits the same law to ≈ −37 °C at 50/50 — plus boiling elevation for summer, one additive, both shifts.
- Seawater (≈ 1.1 m total particles) freezes at ≈ −1.9 °C — matching the formula and explaining sea-ice brine rejection.
- i is empirical at real concentrations: ion pairing pulls NaCl’s effective i below 2 as concentration climbs; textbook i is the dilute limit.
- Supercooling can delay freezing below the computed point kinetically — thermodynamics sets the boundary, nucleation decides when it’s honored.
Related Tools
- Molality Calculator — the m in the formula
- Osmotic Pressure Calculator — the fourth colligative property
- Chemistry Calculators — the full collection
Frequently Asked Questions
How do you calculate freezing point depression?
ΔTf = i × Kf × m: van’t Hoff factor × solvent’s cryoscopic constant × molality. For 1 molal NaCl in water: 2 × 1.86 × 1 = 3.72 °C, so the solution freezes at −3.72 °C. Kf is a property of the solvent alone (water 1.86, benzene 5.12, camphor 40 °C/m).
What is the van’t Hoff factor?
The number of dissolved particles per formula unit: 1 for non-electrolytes (glucose), ideally 2 for NaCl (Na⁺ + Cl⁻), 3 for CaCl₂. Measured values run slightly lower from ion pairing, converging to the integers only in dilute solution.
Why molality instead of molarity here?
Freezing and boiling happen across temperatures, and molarity (per liter) shifts as the solution expands or contracts. Molality (per kilogram of solvent) is temperature-invariant — colligative formulas are written in the unit that doesn’t move. Our Molality Calculator converts from masses.
Does salt melt ice or prevent freezing?
Prevents refreezing, technically: salt dissolves into the liquid film on ice, depressing its freezing point, so ice melts into the brine faster than it can refreeze — net melting while temperature sits below 0 °C. It stops working near the eutectic (−21 °C for NaCl brine), which is why colder climates switch to CaCl₂ or sand.
How is boiling point elevation different?
Same law, different constant and direction: ΔTb = i × Kb × m raises the boiling point (Kb for water 0.512 °C/m). Both are colligative — particle-counting — alongside vapor-pressure lowering (Raoult) and osmotic pressure, the four properties that defined solution physical chemistry.
Is this freezing point depression calculator free?
Yes — free, instant, no sign-up.