Freezing Point Depression Calculator

The Freezing Point Depression Calculator works out how far a dissolved solute lowers a solvent's freezing point, using the colligative formula ΔT_f = i × K_f × m. Pick a solvent to pull in its real cryoscopic constant and freezing point, enter the molality (directly or from mass), set the van't Hoff factor for ionic solutes, and the tool returns the freezing point depression, the new freezing point of the solution, an animated thermometer, and a full step-by-step walkthrough.

What is Freezing Point Depression?

Freezing point depression is the drop in a solvent's freezing point that occurs when a solute is dissolved in it. It is one of the four colligative properties — properties that depend on the number of dissolved particles rather than what those particles are. Dissolved particles get in the way of the orderly crystal lattice the solvent needs to freeze, so the solution must be cooled further before it solidifies. This is why seawater freezes below 0 °C and why salt clears ice from winter roads.

Freezing Point Depression Formula

The calculation takes two short steps: find the depression, then subtract it from the pure solvent's freezing point.

Where:

• ΔT_f — the freezing point depression (°C)
• i — the van't Hoff factor, the number of particles each formula unit produces
• K_f — the cryoscopic (molal freezing point depression) constant of the solvent (°C·kg/mol)
• m — the molality of the solution (mol solute per kg solvent)
• T_f^° — the freezing point of the pure solvent (°C)

The van't Hoff Factor (i)

Because freezing point depression depends on the number of dissolved particles, an ionic compound that splits into several ions depresses the freezing point much more than the same molality of a non-electrolyte. The van't Hoff factor (i) captures this multiplier.

Cryoscopic Constants (Kf) of Common Solvents

Each solvent has its own K_f. The calculator's solvent menu fills these in automatically, but you can always enter your own.

Camphor's huge K_f made it the solvent of choice for the Rast method of molar mass determination: a large, easy-to-measure temperature drop from only a tiny amount of solute.

Worked Example

Dissolve 1 mol of NaCl in 1 kg of water (molality = 1 mol/kg). NaCl dissociates into Na⁺ and Cl⁻, so i = 2, and water's K_f = 1.86 °C·kg/mol:

The salt water now freezes at about −3.72 °C instead of 0 °C.

Molality vs Molarity

Colligative formulas use molality (moles of solute per kilogram of solvent), not molarity (moles per liter of solution). Mass does not change with temperature, but volume does — so molality keeps the result temperature-independent, which matters when you are deliberately cooling a solution to its freezing point.

How to Use This Calculator

1. Choose your solvent: Selecting one auto-fills its cryoscopic constant K_f and normal freezing point. Choose "Custom solvent" to enter your own.
2. Enter the molality: Type it directly, or switch to "Calculate molality from mass" and enter the solute mass, molar mass, and solvent mass.
3. Set the van't Hoff factor: Pick the solute type to set i automatically, or enter a measured value for real (non-ideal) solutions.
4. Click Calculate: Review the freezing point depression, the new freezing point, the animated thermometer, the dissociation diagram, and the step-by-step math.

Frequently Asked Questions

What is freezing point depression?

Freezing point depression is the lowering of a solvent's freezing point when a solute is dissolved in it. It is a colligative property, meaning it depends on the number of dissolved particles, not their chemical identity. Adding salt to water, for example, lowers water's freezing point below 0 °C.

What is the formula for freezing point depression?

The formula is ΔT_f = i × K_f × m, where i is the van't Hoff factor, K_f is the cryoscopic constant of the solvent, and m is the molality. The new freezing point is the pure solvent's freezing point minus ΔT_f.

What is the van't Hoff factor?

The van't Hoff factor (i) is the number of particles a solute produces when it dissolves. Non-electrolytes such as sugar give i = 1; NaCl gives i = 2; CaCl₂ gives i = 3; AlCl₃ gives i = 4. Real values are slightly lower than these ideals because of ion pairing.

What is the cryoscopic constant Kf?

K_f, the molal freezing point depression constant, is a property of the solvent that gives the freezing point drop per unit of molality. For water it is 1.86 °C·kg/mol; for benzene 5.12; for camphor about 37.7.

How is molality different from molarity?

Molality is moles of solute per kilogram of solvent, while molarity is moles per liter of solution. Colligative formulas use molality because mass — unlike volume — does not change with temperature.

Why does salt melt ice on roads?

Salt dissolves into ions and depresses water's freezing point. The resulting salt water freezes below 0 °C, so ice melts at temperatures where pure water would stay frozen — the everyday application of ΔT_f = i × K_f × m.

Additional Resources

• Freezing-point depression - Wikipedia
• Colligative properties - Wikipedia
• van't Hoff factor - Wikipedia