Freezing Point Depression Calculator
How it Works
01Enter Molality
Moles of solute per kg of solvent — the colligative concentration unit (does NOT depend on temperature)
02Pick a Solvent Preset
Auto-fills K_f and pure-solvent T_f for water, benzene, ethanol, chloroform, and 6 other common solvents
03Set Van't Hoff Factor
i = 1 for non-electrolytes; i = 2 for NaCl; i = 3 for CaCl₂ (number of dissolved ions per formula unit)
04ΔT_f = K_f · m · i
Get the depression magnitude and the new solution freezing point in your chosen unit (°C / °F / K)
What is a Freezing Point Depression Calculator?
Just enter the molality (moles solute per kg solvent), select a solvent (or enter custom values), and the calculator instantly returns the depression magnitude ΔTf and the new solution freezing point Tf(solution) = Tf(pure) − ΔTf. Our cryoscopic-constant database uses standard CRC Handbook values: water Kf = 1.86 K·kg/mol, benzene 5.12, ethanol 1.99, chloroform 4.68, camphor 39.7 (the highest among common solvents — the historical reason camphor was used by Beckmann for cryoscopic molar-mass determination). The van't Hoff factor i lets you correctly model dissolved ionic compounds: i ≈ 1 for non-electrolytes (sugar, urea, ethylene glycol), i ≈ 2 for 1:1 salts (NaCl, KBr), i ≈ 3 for 2:1 or 1:2 salts (CaCl₂, K₂SO₄, MgCl₂).
Designed for general chemistry students learning colligative properties, biochemistry students working with cryoprotection of cells (DMSO, glycerol), automotive engineers formulating coolants, food scientists controlling ice crystal formation in frozen desserts, environmental chemists studying brine de-icing of roads, and pharmaceutical scientists using cryoscopy to verify drug molecular weights, the tool runs entirely in your browser — no data is stored or transmitted.
Pro Tip: Pair this with our Molar Mass Calculator to convert grams to moles for the molality calculation, or our Molarity Calculator if you need to convert between molarity and molality for dilute aqueous solutions.
How to Use the Freezing Point Depression Calculator?
How is freezing point depression calculated?
Freezing point depression is one of four colligative properties (the others: boiling point elevation, vapor pressure lowering, osmotic pressure) that all share the same fundamental physics — solute particles disrupt the ideal solid-liquid equilibrium of a pure solvent. Here's the complete derivation:
In 1882 François-Marie Raoult discovered that a wide variety of solutes lowered the freezing point of water by an amount proportional to molality, with the proportionality constant being a property of the solvent alone. This result earned him the Davy Medal of the Royal Society and laid the foundation of cryoscopy.
The Formula
For dilute solutions:
ΔTf = Kf × m × i
where ΔTf is the magnitude of freezing-point depression (always positive — depression means the new Tf is LOWER), Kf is the cryoscopic constant (also called molal freezing point depression constant) of the solvent, m is molality of the solute (mol/kg), and i is the van't Hoff factor (effective number of dissolved particles per formula unit).
The Cryoscopic Constant Kf
Kf is a thermodynamic property of the SOLVENT (not the solute) given by:
Kf = R · Tf² · M / (1000 · ΔHfus)
where R is the gas constant, Tf is the pure-solvent freezing point in K, M is solvent molar mass in g/mol, and ΔHfus is solvent enthalpy of fusion in J/mol. For water: Tf = 273.15 K, M = 18.015, ΔHfus = 6010 J/mol → Kf = 8.314 × 273.15² × 18.015 / (1000 × 6010) = 1.86 K·kg/mol ✓.
The Van't Hoff Factor i
For non-electrolytes that dissolve as intact molecules: i = 1. For strong electrolytes that fully dissociate:
- NaCl → Na⁺ + Cl⁻: i = 2 (ideal); ~1.87 measured at 0.1 M (some ion pairing)
- CaCl₂ → Ca²⁺ + 2 Cl⁻: i = 3 ideal; ~2.7 measured at 0.1 M
- K₂SO₄ → 2 K⁺ + SO₄²⁻: i = 3 ideal; ~2.3 measured
- Sugar, urea, ethylene glycol: i = 1 (non-electrolytes)
- Acetic acid (weak): i ≈ 1.01-1.05 (only ~1% dissociation in water)
Why Solute Lowers the Freezing Point
At equilibrium between solid and liquid solvent, the chemical potentials must match: μ(solid) = μ(liquid in solution). Adding solute lowers μ(liquid) (it dilutes the solvent) but doesn't change μ(solid) (the solid is pure crystalline solvent — solute is excluded). To restore equilibrium, the system must lower temperature, which raises μ(liquid) more than μ(solid) (because liquid has more entropy). The new equilibrium temperature is below Tf(pure) by ΔTf.
Solution Freezing Point
Tf(solution) = Tf(pure) − ΔTf
Cryoscopic Molar Mass Determination
Rearranging to solve for solute molar mass M:
M = (1000 · Kf · wsolute) / (ΔTf · wsolvent · i)
where wsolute is grams of solute and wsolvent is grams of solvent. This was THE classical method for determining unknown molar masses before mass spectrometry — Ernst Beckmann's apparatus (1888) using camphor as the solvent (high Kf = 39.7) was the gold standard for organic-compound analysis through ~1960.
Limits of the Equation
- Dilute regime only. Strictly valid for m → 0; works well for m < 0.5 mol/kg in most solvents.
- Solute insolubility in solid solvent. Assumes solute does not enter the crystal lattice (true for most cases — pure ice forms even from salty seawater).
- Ideal-solution behavior. No specific solute-solvent interactions, no ion pairing, no association.
- Constant pressure (1 atm). The formula doesn't account for pressure effects on Tf.
Freezing Point Depression Calculator – Worked Examples
- Step 1 — Compute molality: moles ethylene glycol = 100 / 62.07 = 1.611 mol. Molality = 1.611 / 0.500 = 3.222 mol/kg.
- Step 2 — Apply the formula: ΔTf = Kf × m × i = 1.86 × 3.222 × 1 = 5.99 K = 5.99 °C.
- Step 3 — New freezing point: Tf(solution) = 0 − 5.99 = −5.99 °C = 21.2 °F.
- Comparison: Real automotive coolant is 50:50 ethylene glycol:water by volume — about 8 mol/kg — giving ~36 °C depression and freezing around −36 °C, which is why your car radiator stays liquid in winter. Pure water would freeze at 0 °C and burst the engine.
Now consider road de-icing with NaCl: 100 g of salt in 500 g of water. M(NaCl) = 58.44 g/mol. Inputs: m = (100/58.44)/0.500 = 3.422 mol/kg, Kf = 1.86, i = 2 (NaCl → Na⁺ + Cl⁻).
- ΔTf = 1.86 × 3.422 × 2 = 12.73 K.
- Tf(solution) = 0 − 12.73 = −12.73 °C.
- Note that using twice as much salt by mass as ethylene glycol gives only twice the depression — but salt is much cheaper. That's why road salt (NaCl, MgCl₂, CaCl₂) is the universal de-icer on highways.
- CaCl₂ for the same mass: 100 g / 110.98 = 0.901 mol → m = 1.802; with i = 3, ΔTf = 1.86 × 1.802 × 3 = 10.06 K. CaCl₂ is preferred for very cold conditions because it's still effective at lower T (its eutectic is −51 °C vs −21 °C for NaCl).
Cryoscopic molar mass example: dissolve 1.50 g of an unknown organic compound in 25 g of camphor (Kf = 39.7, Tf = 178.4 °C). Measured Tf(solution) = 174.0 °C. Find M.
- ΔTf = 178.4 − 174.0 = 4.4 °C.
- m = ΔTf / Kf = 4.4 / 39.7 = 0.1108 mol/kg.
- moles solute = m × kg solvent = 0.1108 × 0.025 = 0.00277 mol.
- M = 1.50 g / 0.00277 mol = 541 g/mol. Likely a small natural product or polypeptide. This is exactly how Beckmann's apparatus was used pre-MS to characterize organic compounds.
Who Should Use the Freezing Point Depression Calculator?
Technical Reference
Raoult's Original Work: F.-M. Raoult, "Loi de congélation des solutions aqueuses" (Law of freezing of aqueous solutions), Comptes Rendus Acad. Sci. Paris 94, 1517 (1882). Raoult systematically measured ΔTf for hundreds of organic and inorganic solutes in water and discovered the now-famous proportionality. He won the Davy Medal in 1892 and the Faraday Medal in 1899 for this and related work on vapor pressure (Raoult's law).
Beckmann's Apparatus (1888). Ernst Beckmann developed the high-precision differential thermometer (Beckmann thermometer, ±0.001 K) and the cryoscopic apparatus for molar-mass determination. Camphor (Kf = 39.7) was preferred because its huge Kf means even very small molality gives easily measurable ΔTf — perfect for high-molar-mass natural products. The Beckmann method dominated organic-compound molecular weight determination from 1888 until reliable mass spectrometry emerged in the 1950s-60s.
Cryoscopic Constants Kf for Common Solvents (CRC Handbook, K·kg/mol):
- Water: 1.86 (Tf = 0.00 °C)
- Benzene: 5.12 (Tf = 5.50 °C)
- Ethanol: 1.99 (Tf = −114.6 °C)
- Chloroform: 4.68 (Tf = −63.5 °C)
- Diethyl ether: 1.79 (Tf = −116.3 °C)
- Nitrobenzene: 7.00 (Tf = 5.7 °C)
- Acetic acid: 3.90 (Tf = 16.6 °C)
- Cyclohexane: 20.0 (Tf = 6.5 °C)
- Naphthalene: 6.94 (Tf = 80.2 °C)
- Camphor: 39.7 (Tf = 178.4 °C — highest among common solvents)
Connection to Other Colligative Properties. Freezing point depression is mathematically parallel to boiling point elevation (ΔTb = Kb·m·i) and osmotic pressure (Π = MRTi). All three quantify the same underlying effect: solute lowers the chemical potential of the solvent. Vapor pressure lowering (Raoult's law: ΔP = P°·xsolute·i) is the underlying cause. For water at 1 m solute (i = 1): ΔTf ≈ 1.86 K, ΔTb ≈ 0.51 K, Π ≈ 24 atm — the osmotic pressure is enormous compared to the temperature shifts, which is why osmometry is the most sensitive cryometric technique.
Real-World Applications:
- Automotive coolant (50/50 ethylene glycol/water): ΔTf ≈ 36 °C → freezes at −36 °C; protects engine to about −20 °C in routine use.
- Road salt (NaCl): Effective to about −10 °C; below that, CaCl₂ or MgCl₂ are used (eutectic of CaCl₂ + water = −51 °C).
- Sea ice: Seawater (~3.5% salt by mass) freezes at −1.9 °C; sea ice itself is much fresher than seawater because salt is excluded from the ice lattice.
- Ice cream: Sugar (sucrose ~30% by mass) and milk solids depress freezing to ~−2.5 °C, keeping the dessert soft and scoopable in a typical home freezer (−18 °C).
- Cryopreservation: 10% DMSO in cell culture medium → ΔTf ≈ 2.4 K, which slows ice nucleation enough to prevent intracellular crystallization during freezing.
Sources of Error. (1) Ion pairing — real i is less than ideal i for concentrated electrolytes (NaCl 0.1 M: i_observed ≈ 1.87 vs ideal 2.00). (2) Activity coefficients — molality should strictly be replaced with molal activity for non-ideal solutions. (3) Solvent purity — trace impurities can shift Tf(pure) by 0.1-1 °C. (4) Solute insolubility in solid solvent — most solutes don't enter the crystal lattice (good), but if they do (solid solution), the formula breaks down. (5) Volatile solute — the formula assumes the solute stays dissolved; volatile solutes that partially evaporate will show smaller ΔTf.
Key Takeaways
Frequently Asked Questions
What is the Freezing Point Depression Calculator?
Output: ΔTf in your chosen unit (°C, °F, or K), the new solution freezing point Tf(solution) = Tf(pure) − ΔTf, a 5-band magnitude classification (negligible → extreme), full step-by-step calculation breakdown, and a comparison table of cryoscopic constants for common solvents. Designed for general chemistry students, automotive engineers, food scientists, cryobiologists, and pharmaceutical scientists. Runs entirely in your browser — no data stored.
Pro Tip: Use our Molar Mass Calculator to convert grams to moles for the molality calculation.
What's the formula for freezing point depression?
What is the cryoscopic constant K_f and where do values come from?
What's the van't Hoff factor and why does it matter?
Why molality and not molarity?
Can I use this calculator for ice melting or de-icing?
How is this used to determine an unknown molar mass?
Why does adding solute lower the freezing point at all?
Does the type of solute matter?
What are the limits of this formula?
Can the calculator handle weak electrolytes like acetic acid?
Disclaimer
The equation ΔT_f = K_f · m · i strictly applies only to dilute, ideal solutions. For concentrated solutions, real depression can deviate 10-30% (need Debye-Hückel corrections). Real van't Hoff factors for strong electrolytes are slightly less than ideal due to ion pairing (NaCl 0.1 M: i_observed ≈ 1.87 vs 2.00). Cryoscopic constants are CRC Handbook reference values; real solvents may show small variation due to purity. The formula assumes solute is excluded from the solid solvent lattice and solvent doesn't participate in chemical reactions with solute.