Colligative properties

freezing point depressionboiling point elevationosmotic pressureRaoult's lawantifreeze calculation

Boiling-point elevation, freezing-point depression, osmotic pressure and Raoult's law — the four effects that count particles, not identity.

Boiling-Point Elevation

ΔTb=Kbb\Delta T_b = K_b \, b

Gives how far a dissolved solute raises a solvent's boiling point from the molality and the solvent's ebullioscopic constant.

Freezing-Point Depression

ΔTf=Kfb\Delta T_f = K_f \, b

Gives how far a dissolved solute lowers a solvent's freezing point from the molality and the solvent's cryoscopic constant.

Osmotic Pressure (Π = MRT)

Π=MRT\Pi = M R T

Gives the osmotic pressure of a dilute solution from its molar concentration and absolute temperature using the van 't Hoff equation.

Raoult's Law

P=xP0P = x \, P^{0}

Gives the vapor pressure of a solvent above an ideal solution as its mole fraction times the pure solvent's vapor pressure.

How they fit together

Colligative means the solute's identity does not matter — only how many particles it contributes. Dissolved particles lower the solvent's escaping tendency, and every one of these four is a consequence: vapour pressure drops (Raoult), so the boiling point has to rise and the freezing point has to fall, and a membrane that lets solvent through but not solute develops an osmotic pressure. Sugar and salt at the same particle count do the same thing to a radiator.

Choose by the phase boundary you care about: freezing for antifreeze and road salt, boiling for a raised cooking point, osmotic pressure for anything crossing a membrane, Raoult for the vapour above the liquid. The near-universal mistake is forgetting that the particle count is not the formula-unit count. These equations as written assume one particle per formula unit, so for an electrolyte you must first multiply the molality by the van 't Hoff factor: NaCl gives roughly two particles, CaCl₂ roughly three, and skipping that step halves or thirds your answer. Note also that boiling and freezing take molality, not molarity — the constants Kb and Kf are defined per kilogram of solvent.