Depression (decrease) of the freezing point

• The freezing point of an aqueous solution is always lower than that of pure water under normal atmospheric pressure.
• The reason is that the attractions between water molecules and solute particles hinder the water molecules from bonding together into the ordered hydrogen-bonded lattice of ice; the solution has to be cooled further before ice crystals can form.

ΔT_f = i · K_f · m with K_f (water) = 1.86 °C·kg/mol.

Applications and examples:

• Salt on icy roads. In cold countries, when the temperature falls to about 0 °C, salt is spread on roads. The salt dissolves in the thin film of water and lowers its freezing point, so the water does not freeze, which reduces car skidding and accidents. (It works down to about −9 °C for ordinary salt; below that, other chemicals are used.)
• Sea water freezes below 0 °C (about −1.9 °C for 35 g/kg salinity), so polar seas can stay liquid when the air is cold; when sea ice forms, the salt is mostly left behind in the water below, making the underlying water saltier and denser, which then sinks and drives deep ocean currents (link to Module 3).
• Antifreeze (ethylene glycol) added to a car radiator lowers the freezing point and raises the boiling point of the coolant.
• Organisms use the same idea: some fish and insects make sugars or "antifreeze proteins" so that their body fluids do not freeze (Module 11).

Worked example 2. Problem. (a) 58.5 g of NaCl is dissolved in 1.00 kg of water. Calculate the freezing point and the boiling point of the solution (assume complete dissociation and ideal behaviour). (b) Calculate the same for 342 g of sucrose (M = 342) in 1.00 kg of water.

Solution. (a) n(NaCl) = 1.00 mol; m = 1.00 mol/kg; i = 2. ΔT_f = 2 × 1.86 × 1.00 = 3.72 °C → freezing point −3.72 °C. ΔT_b = 2 × 0.512 × 1.00 = 1.02 °C → boiling point 101.02 °C. (b) Sucrose does not ionise (i = 1); m = 1.00. ΔT_f = 1.86 °C → −1.86 °C; ΔT_b = 0.512 → 100.51 °C. Same moles, but the salt produces twice the effect because it gives twice the number of particles; this is exactly what "depends on the number of particles, not on the type of solute" means.