Freezing point and osmotic pressure

A solute also makes a solvent freeze at a lower temperature. This is why salt is spread on icy roads, and why ethylene glycol is added to the water in car radiators in cold countries:

ΔT_f = K_f × m

K_f is the freezing point depression constant of the solvent (for water, 1.86 K kg mol⁻¹). Again, use its units as given. ΔT_f is the fall, so subtract it from the solvent's freezing point.

To find the molecular formula of an element such as sulphur dissolved as S_x: first find the molar mass of the solute from ΔT_f, then divide by the mass of one atom. For sulphur in carbon disulphide this gives 256 ÷ 32 = 8, so the molecule is S₈.

Osmosis. Some membranes, such as the skin inside an egg or a cell wall, let solvent molecules pass but not solute particles. These are semipermeable membranes. Solvent flows through them from the dilute side to the concentrated side, as if trying to make the two sides equal.

The pressure needed to stop this flow is the osmotic pressure Π:

Π = CRT = (n ÷ V)RT

Even a small amount of a big molecule gives a pressure large enough to measure at room temperature, so osmotic pressure is the best way to find the molar masses of proteins and polymers.

Solutions with the same osmotic pressure are isotonic. A 0.9% salt solution is isotonic with blood, so it is safe in a drip. In a hypertonic (stronger) solution, water flows out of a cell and it shrinks; in a hypotonic (weaker) one, water flows in and the cell swells.

Push on the concentrated side with a pressure greater than Π and the flow runs backwards: pure water is squeezed out of salt water. This reverse osmosis is used to get drinking water from sea water.