Freezing Point Depression Calculator

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:

$\Delta T_f = i \times K_f \times m$

For a solute that stays as whole molecules, i = 1 and the formula reduces to the textbook form ΔTf = Kf × m.

• 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:

$T_f(\text{solution}) = T_f(\text{solvent}) - \Delta T_f$

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). The water, benzene and acetic acid values below match the OpenStax constants table. The cyclohexane value of 20.0 matches the HyperPhysics table.

Molality (m)

Molality is the amount of solute, in moles, divided by the mass of solvent, in kilograms:

$m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}$

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.

Real solutions often fall short of the theoretical value, especially at higher concentration. Oppositely charged ions can pair up and behave like a single particle, which lowers the effective i. Even at 0.05 mol/kg, measured i for NaCl is 1.9 rather than 2.

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

1. Pick a solvent, or enter its Kf value and normal freezing point directly.
2. Enter the molality of the solution.
3. Enter the van't Hoff factor for the solute: 1 for non-electrolytes, higher for salts that split into ions.
4. Read the freezing point depression and the new freezing point.

Where freezing point depression is used

Road de-icing. Rock salt (NaCl, i = 2) is practical down to a pavement temperature of about 15 to 20°F, roughly −9 to −7°C. Road crews add calcium chloride (i = 3) or magnesium chloride at lower temperatures because they lower the freezing point further.

Automotive antifreeze. Ethylene glycol mixed with water lowers a coolant's freezing point well below 0°C, while also raising the coolant's boiling point. How far it drops depends on the mix ratio.

Ice cream. Sugar and milk salts dissolved in the mix depress its freezing point below 0°C. At freezer temperature the mix is only partly frozen, which is what keeps it scoopable.

Seawater. Seawater freezes at about 28.4°F, roughly −2°C, rather than 0°C. Ocean salinity typically ranges from 32 to 37 PSU, or grams of salt per kilogram of seawater. At 35 g/kg, treating the salt as NaCl gives a molality near 0.6 mol/kg. Putting m = 0.6 mol/kg and the theoretical i = 2 into the formula gives ΔTf = 2 × 1.86 × 0.6 ≈ 2.2°C, a little more than the real drop of about 2°C. The gap exists because some sodium and chloride ions pair up instead of acting as separate particles, so the effective van't Hoff factor is below 2.

Limits of the formula

The formula assumes an ideal, dilute solution and works best at low molality. 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. Road agencies treat about 15 to 20°F (−9 to −7°C) as the lowest practical pavement temperature for salting, although salt still melts some ice down to about −6°F (−21°C).

Why does seawater freeze at a lower temperature than fresh water? Dissolved salts, mostly sodium chloride, lower seawater's freezing point to about −2°C. The formula's idealized prediction, using a molality of 0.6 mol/kg and i = 2, gives a drop of about 2.2°C. The real drop is a little smaller because 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.

References

1. OpenStax. Chemistry 2e, 11.4 Colligative Properties. Chemistry 2e: Colligative Properties — ΔTf = Kf m; Kf and freezing points for water (1.86, 0.0 °C), acetic acid (3.9, 16.6 °C) and benzene (5.12, 5.5 °C); the van't Hoff factor, ion pairs, and measured i = 1.9 for 0.05 m NaCl.
2. HyperPhysics, Georgia State University. Freezing Point Depression and Boiling Point Elevation. HyperPhysics constants table — cyclohexane melting point 6.55 °C and Kf 20.0.
3. Minnesota Department of Transportation. Maintenance FAQ. MnDOT maintenance FAQ — salt's practical range is a pavement temperature of 15–20 °F and above; it melts ice down to −6 °F; chlorides such as calcium chloride are added at lower temperatures.
4. NOAA National Ocean Service. Can the ocean freeze?. Can the ocean freeze? — seawater freezes at about 28.4 °F because of its salt.
5. National Snow and Ice Data Center. Science of Sea Ice. Science of Sea Ice — ocean salinity typically varies from 32 to 37 PSU, and sodium chloride is the most abundant salt.