Molar Mass from Freezing Point Calculator
Determine an unknown solute’s molar mass from freezing-point depression — the classic colligative method — using the solvent’s cryoscopic constant.
How it works
ΔTf = i · Kf · molality → molality = ΔTf / (i·Kf) → molar mass = grams / (molality × kg solvent)
Dissolving a solute lowers a solvent’s freezing point in proportion to the number of dissolved particles, a colligative property that does not depend on what the solute is. Measuring how far the freezing point drops therefore reveals how many moles of particles are present; dividing the known mass of solute by that mole count gives its molar mass. The van’t Hoff factor accounts for solutes such as salts that split into several ions per formula unit.
Worked example
Dissolving 62 g of a non-electrolyte (i = 1) in 1.00 kg of water (Kf = 1.86 °C·kg/mol) lowers the freezing point by 1.86 °C. Molality = 1.86 / (1 × 1.86) = 1.00 mol/kg, so moles = 1.00 mol and molar mass = 62 / 1.00 = 62 g/mol — consistent with ethylene glycol.
Frequently asked questions
What is the van’t Hoff factor?
It is the number of particles a solute yields per formula unit in solution. Non-electrolytes like sugar give i = 1; NaCl gives about 2 and CaCl₂ about 3, since they dissociate into ions.
Why does freezing-point depression measure molar mass?
The depression depends only on the concentration of particles, so it counts moles regardless of identity. Knowing the mass that produced those moles lets you back out the mass per mole — the molar mass.
What is the cryoscopic constant Kf?
It is a property of the solvent that sets how many degrees the freezing point drops per unit molality. For water it is 1.86 °C·kg/mol; benzene, camphor and other solvents have their own, often larger, values.
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This calculator is for educational purposes. Double-check important results before acting on them.