Crioscopia ΔT = Kf·m

Freezing-point depression: ΔT = Kf · m · i

Dissolve a solute and the solvent's freezing point drops. How far depends on three things: the molality (m), the solvent's cryoscopic constant (Kf), and the van't Hoff factor (i), which counts how many particles each formula unit breaks into. Water has Kf = 1.86 °C·kg/mol. NaCl splits into Na⁺ and Cl⁻, so i = 2; CaCl₂ releases 3 ions, so i = 3 and clears ice better. Run the numbers on 1 mol NaCl in 1 kg of water and you get ΔT = 1.86 · 1 · 2 = 3.72 °C, freezing at −3.72 °C. That's the reason cities salt their roads through winter (Toronto, the ranges around Curitiba) and the reason ice-cream makers pack rock salt around the bucket: the brine drops below 0 °C and freezes the cream. Automotive antifreeze takes a different route, using ethylene glycol (molecular, i = 1) at high molality to keep a radiator safe down to −40 °C.

Applications

Formulating automotive antifreeze, melting ice off city roads (NaCl, CaCl₂, MgCl₂), preserving cells in the cold (DMSO and glycerol lower intracellular freezing), making ice cream at home with salt and ice, de-icing aircraft, and working out a molar mass by cryoscopy in the chemistry lab.

FAQ

Why is CaCl₂ better than NaCl for ice? CaCl₂ breaks into 3 ions (i = 3) where NaCl gives 2, so at the same molality it pushes the freezing point down 1.5× as far. On top of that it gives off heat as it dissolves, so the ice goes faster.

What is i for sugar or glycol? Any molecular solute that stays in one piece has i = 1. Sucrose, ethylene glycol and urea all land there. You only get i above 1 from ionic compounds.

Why molality, not molarity? Molality counts mol of solute per kg of solvent, and that ratio holds steady as the temperature changes. Molarity doesn't, because the volume expands. Colligative properties need a concentration unit that the temperature can't shift.