Freezing Point Depression Calculator
Calculate freezing point depression with ΔTf = i × Kf × m. Enter a solvent's Kf value, the solution's molality, and its van't Hoff factor for instant results.
Freezing Point Depression Calculator
The molal freezing point depression constant is specific to the solvent. Common values: Water (1.86), Benzene (5.12), Acetic Acid (3.90).
The pure solvent's normal freezing point. It is 0°C for water, but 5.5°C for benzene, 16.6°C for acetic acid and 6.55°C for cyclohexane. Set automatically when you pick a solvent below.
The concentration of solute in moles per kilogram of solvent.
The number of particles a solute forms when dissolved. For non-electrolytes like sugar, i = 1. For strong electrolytes, i equals the number of ions formed.
Calculation Formula
ΔTf = i × Kf × m
Where ΔTf is the freezing point depression, i is the van't Hoff factor, Kf is the molal freezing point depression constant, and m is the molality.
ΔTf = 1 × 1.86 × 1.00 = 1.86 °C
Visualization
Visual representation of freezing point depression (not to scale)
Freezing Point Depression
This is how much the freezing point of the solvent will decrease due to the dissolved solute.
Common Kf Values
| Solvent | Kf (°C·kg/mol) |
|---|---|
| Water | 1.86 °C·kg/mol |
| Benzene | 5.12 °C·kg/mol |
| Acetic Acid | 3.90 °C·kg/mol |
| Cyclohexane | 20.0 °C·kg/mol |
Documentation
What is freezing point depression?
Freezing point depression is the drop in a liquid's freezing temperature that happens when another substance is dissolved in it. Pure water freezes at 0°C, but salt water freezes below that because the dissolved salt gets in the way of ice forming. This calculator finds how many degrees a solution's freezing point drops for a given solvent, solute, and concentration.
The effect is a colligative property. That means it depends on how many dissolved particles are in the liquid, not on what those particles are. One mole of dissolved sugar molecules and one mole of dissolved sodium ions lower the freezing point by about the same amount, because particle count is what matters, not chemical identity.
Why dissolved particles lower the freezing point
A liquid freezes when its molecules lock into an ordered crystal. Dissolved solute particles sit between solvent molecules and get in the way of that ordering, so the liquid has to cool further before enough order can form. The dissolved particles also raise the solution's entropy, or disorder, which makes staying liquid more favorable at a given temperature. Both effects push the freezing point down.
Freezing point depression formula
The freezing point depression, ΔTf, is calculated with:
- ΔTf: the freezing point depression, in °C
- i: the van't Hoff factor, the number of particles one unit of solute produces when it dissolves
- Kf: the molal freezing point depression constant, specific to the solvent, in °C·kg/mol
- m: molality, moles of solute per kilogram of solvent
The solution's new freezing point is the solvent's own normal freezing point minus ΔTf:
Water's normal freezing point is 0°C, so ΔTf can be subtracted directly from 0 for water solutions. Other solvents freeze at different temperatures, so this step matters for them. Benzene normally freezes at 5.5°C, acetic acid at 16.6°C, and cyclohexane at 6.55°C.
The three variables explained
Molal freezing point depression constant (Kf)
Kf is a fixed property of each solvent. It is the freezing point drop produced by a 1-molal solution of a solute that does not split into ions (i = 1).
| Solvent | Kf (°C·kg/mol) | Normal freezing point |
|---|---|---|
| Water | 1.86 | 0 °C |
| Benzene | 5.12 | 5.5 °C |
| Acetic acid | 3.90 | 16.6 °C |
| Cyclohexane | 20.0 | 6.55 °C |
Molality (m)
Molality is the amount of solute, in moles, divided by the mass of solvent, in kilograms:
Chemists use molality rather than molarity (moles per liter of solution) in this formula because molality does not change with temperature. A solution's volume expands as it warms, which changes molarity, but the mass of solvent stays fixed.
Van't Hoff factor (i)
The van't Hoff factor is the number of particles one formula unit of solute produces in solution. Molecules that stay intact, such as sugar, have i = 1. Table salt (NaCl) splits into a sodium ion and a chloride ion, giving i = 2. Calcium chloride (CaCl₂) splits into three ions, giving i = 3.
| Solute type | Example | Theoretical i |
|---|---|---|
| Non-electrolyte | Sucrose, glucose | 1 |
| Binary electrolyte | NaCl, KBr | 2 |
| Ternary electrolyte | CaCl₂, Na₂SO₄ | 3 |
| Quaternary electrolyte | AlCl₃, Na₃PO₄ | 4 |
Real solutions often fall short of the theoretical value, especially at higher concentration. In a concentrated solution, oppositely charged ions can pair up and behave like a single particle, which lowers the effective i below its theoretical value.
How to calculate freezing point depression: worked example
A road crew dissolves NaCl in water to reach a molality of 1.0 mol/kg.
- Kf (water) = 1.86 °C·kg/mol
- m = 1.0 mol/kg
- i (NaCl) = 2
ΔTf = 2 × 1.86 × 1.0 = 3.72 °C
New freezing point = 0 °C − 3.72 °C = −3.72 °C
The salted water stays liquid down to about −3.7°C, roughly four degrees below plain water's freezing point.
For a solvent that does not freeze at 0°C, the same subtraction applies to that solvent's own freezing point. A solute dissolved in acetic acid (normal freezing point 16.6°C) that produces a ΔTf of 2°C gives a new freezing point of 16.6 − 2 = 14.6°C, not −2°C.
How to use this calculator
- Pick a solvent, or enter its Kf value and normal freezing point directly.
- Enter the molality of the solution.
- Enter the van't Hoff factor for the solute: 1 for non-electrolytes, higher for salts that split into ions.
- Read the freezing point depression and the new freezing point.
Where freezing point depression is used
Road de-icing. Rock salt (NaCl, i = 2) works down to about −9°C. Calcium chloride (i = 3) works at lower temperatures and releases heat as it dissolves, but costs more per ton.
Automotive antifreeze. Ethylene glycol mixed with water lowers a coolant's freezing point well below 0°C, commonly protecting an engine to below about −30°C depending on the mix ratio, while also raising the coolant's boiling point.
Ice cream. Sugar, milk proteins, and fat dissolved in the mix depress its freezing point to roughly −3°C to −5°C. At freezer temperature the mix is only partly frozen, which is what keeps it scoopable.
Seawater. Seawater freezes at about −1.9°C rather than 0°C. Its average salinity, about 35 grams of dissolved salt per kilogram of water, corresponds to a molality near 0.6 mol/kg. Putting m = 0.6 mol/kg and the theoretical i = 2 for NaCl into the formula gives ΔTf = 2 × 1.86 × 0.6 ≈ 2.2°C, higher than the measured 1.9°C. The gap exists because seawater is concentrated enough that some sodium and chloride ions pair up instead of acting as separate particles, so the effective van't Hoff factor is closer to 1.7 than to the theoretical 2.
Limits of the formula
The formula assumes an ideal, dilute solution and works well below about 0.1 mol/kg. At higher concentrations, ion pairing and other solute-solvent interactions make the real depression smaller than the theoretical prediction, as the seawater example shows. Kf itself is defined near the solvent's normal freezing point, so the formula becomes less reliable far from that temperature.
Frequently asked questions
What is freezing point depression? It is the decrease in a liquid's freezing temperature caused by a dissolved substance. It is a colligative property, meaning it depends on the number of dissolved particles rather than their identity.
Why does salt melt ice on roads? Salt does not melt ice directly. It dissolves into the thin film of liquid water that exists on an ice surface even below 0°C, and the resulting salt solution has a lower freezing point than plain water. Because that solution's freezing point is now below the surrounding ice's temperature, more ice keeps dissolving into it until the salt runs out or the temperature drops too far. Below about −9°C, NaCl solutions stop working because the solution itself starts to freeze.
Why does seawater freeze at a lower temperature than fresh water? Dissolved salts, mostly sodium chloride, lower seawater's freezing point to about −1.9°C. The formula's idealized prediction, using a molality of 0.6 mol/kg and i = 2, gives about 2.2°C, somewhat higher than the measured value, because at seawater's concentration some ions pair up rather than acting independently.
What is the difference between freezing point depression and boiling point elevation? Both depend on the number of dissolved particles. Freezing point depression lowers the temperature at which a solution freezes; boiling point elevation raises the temperature at which it boils. The formulas share the same shape, ΔT = i × K × m, but use different constants, Kf versus Kb.
Can freezing point depression measure an unknown solute's molar mass? Yes. If the masses of solute and solvent are known, measuring ΔTf and solving the formula for molality, then for moles, gives the solute's molar mass.
Does a higher van't Hoff factor always mean a lower freezing point? At the same molality and Kf, yes: a higher i produces a larger ΔTf. Increasing molality by adding more solute has a similar effect, so the two should not be confused. A dilute CaCl₂ solution can produce less depression than a more concentrated NaCl solution even though CaCl₂ has the higher van't Hoff factor.