Molar Mass by Freezing Point Calculator
Dissolving a solute lowers the freezing point of a solvent by an amount that depends only on how many particles are present, a colligative property. Because the depression is proportional to molality through the cryoscopic constant, a measured temperature drop reveals the moles of solute, and dividing the solute mass by those moles gives the molar mass. This calculator works back from the freezing point depression, the solvent's cryoscopic constant, the van 't Hoff factor, and the solute and solvent masses. Enter the cryoscopic constant for your solvent; for water it is about 1.86 degrees per molal.
Freezing point molar mass formula
delta T = i * Kf * molality
molality = delta T / (i * Kf)
moles of solute = molality * (solvent mass in kg)
molar mass = solute mass / moles of solute
The freezing point depression, cryoscopic constant, van 't Hoff factor, and both masses must all be greater than zero. Solvent mass is converted from grams to kilograms for the molality step.
Freezing point depression context
- Freezing point depression is colligative: it depends on particle count, not identity.
- The cryoscopic constant Kf is specific to each solvent.
- For water, Kf is about 1.86 degrees Celsius per molal.
- The van 't Hoff factor is 1 for non-electrolytes and larger for salts that dissociate.
- This method is a classic way to determine the molar mass of an unknown solute.
Freezing point molar mass: frequently asked questions
How does freezing point depression give molar mass?
Freezing point depression is proportional to molality: delta T = i x Kf x molality. From the measured temperature drop you find molality, then moles of solute from molality times solvent mass, and finally molar mass as solute mass divided by moles.
What is the cryoscopic constant Kf?
Kf is the freezing point depression constant of the solvent, the temperature drop per unit molality. For water it is about 1.86 degrees Celsius per molal. Each solvent has its own value, which you enter as a user-editable input.
What is the van 't Hoff factor i?
The van 't Hoff factor i is the number of particles a solute produces in solution per formula unit. It is 1 for a non-dissociating molecular solute like sugar, about 2 for sodium chloride, and 3 for calcium chloride. Enter 1 for non-electrolytes.
What units should I use?
Use a consistent set: solute mass and solvent mass in grams, Kf in degrees per molal, and the freezing point depression in the same degree unit as Kf. The calculator converts solvent mass to kilograms internally to compute molality.
Why is this a colligative property?
Freezing point depression depends on the number of dissolved particles, not their identity, which makes it a colligative property. That is why dividing by the van 't Hoff factor recovers the molality of formula units and lets you back out the molar mass.
Official sources
- IUPAC Gold Book: colligative properties and cryoscopic constant terminology.
- NIST Chemistry WebBook: solvent properties and reference data.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.