Colligative Properties: Boiling Point Elevation, Freezing Point Depression, and Osmotic Pressure

Colligative properties are solution properties that depend only on the number of dissolved solute particles, not on their identity. The four colligative properties are: boiling point elevation (solutions boil at higher temperatures than the pure solvent), freezing point depression (solutions freeze at lower temperatures), vapor pressure lowering (solutions have lower vapor pressure), and osmotic pressure (solutions separated from pure solvent by a semipermeable membrane draw solvent through the membrane). The magnitude of each effect is proportional to the molality of particles in solution. For electrolytes that dissociate (like NaCl splitting into Na+ and Cl-), you multiply by the van't Hoff factor (i) — the number of particles the solute produces per formula unit.

The underlying mechanism is the same for all colligative properties: dissolved solute particles interfere with solvent molecules' ability to escape the liquid phase. At the surface of a solution, some of the positions that would normally be occupied by solvent molecules are instead occupied by solute particles. Fewer solvent molecules at the surface means fewer can evaporate per unit time, which means lower vapor pressure.

Lower vapor pressure has cascading effects. Boiling occurs when vapor pressure equals atmospheric pressure — if the vapor pressure is lower, you need a higher temperature to reach the boiling point. Freezing occurs when the vapor pressure of the liquid equals the vapor pressure of the solid — lower liquid vapor pressure means you need a lower temperature for this equality. The solute literally makes it harder for the solvent to change phase.

Here is the key insight that makes colligative properties colligative: the solute particles do not need to interact with the solvent in any special way. A glucose molecule and a urea molecule have completely different structures and chemistries, but if you dissolve the same number of moles of each in water, the boiling point elevation, freezing point depression, and osmotic pressure are identical. The effect depends on particle count, not particle identity. This is why the property is called colligative — from the Latin colligatus, meaning bound together.

Boiling point elevation: deltaT_b = i x K_b x m. The boiling point increases by deltaT_b degrees. K_b is the ebullioscopic constant for the solvent (for water, K_b = 0.512 °C/m). m is the molality (moles of solute per kilogram of solvent). i is the van't Hoff factor.

Freezing point depression: deltaT_f = i x K_f x m. The freezing point decreases by deltaT_f degrees. K_f is the cryoscopic constant (for water, K_f = 1.86 °C/m). Note that K_f for water is about 3.6 times larger than K_b — which is why salting roads works so well. A 1 molal NaCl solution (i = 2) depresses the freezing point by 2 x 1.86 x 1 = 3.72°C, bringing it down to about -3.72°C.

Worked example: You dissolve 58.5 g of NaCl (1 mole, MW = 58.5) in 1 kg of water. NaCl dissociates into Na+ and Cl-, so i = 2. Molality = 1 mol / 1 kg = 1 m. Boiling point: 100 + (2)(0.512)(1) = 101.02°C. Freezing point: 0 - (2)(1.86)(1) = -3.72°C. Cooking pasta in salted water does technically raise the boiling point, but the typical amount of salt used (a tablespoon in several liters) raises it by less than 0.5°C — not enough to make a practical difference in cooking time. It is for flavor, not physics.

Osmotic pressure: pi = iMRT, where M is molarity (not molality), R is the gas constant (0.0821 L·atm/mol·K), and T is temperature in Kelvin. Osmotic pressure is used extensively in biology (cell membrane osmolarity) and in industrial applications (reverse osmosis water purification, where you apply pressure greater than the osmotic pressure to force water through a membrane against the concentration gradient).

The van't Hoff factor (i) is the number of particles a solute produces in solution. For molecular (non-electrolyte) solutes like glucose or sucrose, i = 1 — the molecule dissolves intact. For strong electrolytes that fully dissociate: NaCl has i = 2 (Na+ and Cl-), CaCl2 has i = 3 (Ca²+ and 2 Cl-), and Al2(SO4)3 has i = 5 (2 Al³+ and 3 SO4²-).

In practice, the measured van't Hoff factor for strong electrolytes is slightly less than the theoretical value because of ion pairing — some of the ions in solution momentarily associate with each other, temporarily reducing the effective particle count. A 1 molal NaCl solution has an effective i of about 1.87 rather than 2.00. For most gen chem problems, you use the theoretical value unless the problem specifically states otherwise.

Weak electrolytes (like acetic acid, which only partially dissociates) have i values between 1 and their theoretical maximum. A weak acid with 5% dissociation has an effective i of about 1.05. Calculating the exact i requires knowing the degree of dissociation, which depends on concentration.

The van't Hoff factor is the reason CaCl2 is a better road de-icer than NaCl per gram, despite costing more. CaCl2 produces 3 particles per formula unit versus 2 for NaCl, giving 50% more freezing point depression at the same molality. It also releases heat when it dissolves (exothermic dissolution), giving it an additional ice-melting mechanism that NaCl lacks. ChemistryIQ includes practice problems that require you to determine the van't Hoff factor from a chemical formula and apply it correctly in colligative property calculations.

Antifreeze (ethylene glycol in car radiators) works by both depressing the freezing point and elevating the boiling point of water. A 50/50 mixture of ethylene glycol and water freezes at approximately -37°C and boils at approximately 106°C, compared to 0°C and 100°C for pure water. This protects the engine cooling system in both winter and summer. Ethylene glycol is a molecular compound (i = 1), so its colligative effects come purely from high molality — you add a lot of it (about 6.4 moles per kg of water in a 50/50 mix).

Osmolarity in IV fluids is a direct application of colligative properties. Normal saline (0.9% NaCl, approximately 0.154 M) has an osmolarity of about 308 mOsm/L — matching the osmolarity of blood plasma. This is why it is called isotonic. An IV fluid with higher osmolarity (hypertonic) draws water out of cells. Lower osmolarity (hypotonic) causes cells to swell. Getting this wrong in a clinical setting can be fatal — hemolysis (red blood cell lysis) occurs if blood cells are placed in significantly hypotonic solution.

Molecular weight determination is a classic application. If you dissolve a known mass of an unknown compound in a known mass of solvent and measure the freezing point depression, you can calculate the molality, then the moles of solute, then the molar mass (molar mass = mass / moles). This was historically one of the primary methods for determining molecular weights before mass spectrometry became widespread.