Colligative properties: the four that matter

Dissolve any non-volatile solute in a solvent and four measurable properties change: vapour pressure drops, boiling point rises, freezing point falls, and osmotic pressure appears. All four depend only on the number of solute particles, not on their identity — which is why they are called colligative (from Latin colligatus, “bound together”). This guide walks the four properties, the reason they share a common origin, and the van’t Hoff factor that extends them to electrolytes.

Prerequisites: concentrations decoded — colligative properties use molality, not molarity, and knowing why is half the battle.

Why they share an origin

At equilibrium between a pure solvent and its vapour, the chemical potentials match. Adding a non-volatile solute lowers the solvent’s mole fraction in the liquid phase, which lowers its chemical potential there. To restore equilibrium the vapour pressure over the solution must also drop — and by an amount set only by the mole fraction of solute, not its identity. Every colligative effect is a consequence of this one lowered chemical potential.

Formally, if μ*_A is the pure-solvent chemical potential and x_A is the solvent mole fraction:

$\mu_A(\text{solution}) = \mu_A^* + RT \ln x_A$

Because ln x_A < 0 when x_A < 1, the solvent’s chemical potential in solution is lower than in the pure liquid. All four colligative properties are consequences of that lowering.

Property 1 — Raoult’s law and vapour-pressure lowering

Raoult (1887) measured the vapour pressure of solutions and found:

$P_A = x_A P_A^*$

where P*_A is the vapour pressure of pure A and x_A is the mole fraction of A in the liquid. For a non-volatile solute (x_A = 1 − x_B), the drop is:

$\Delta P = P_A^* - P_A = x_B P_A^*$

The vapour-pressure depression is proportional to the mole fraction of solute. Concentration in mole fraction, not molarity — because the underlying variable is the mole ratio of solvent to solute in the liquid.

Property 2 — boiling-point elevation

The boiling point is the temperature at which vapour pressure equals atmospheric pressure. Lower the vapour pressure and you need a higher temperature to reach 1 atm; the boiling point rises. From the Clausius-Clapeyron equation applied at the boiling point, the elevation is:

$\Delta T_b = K_b m$

where m is molality (mol solute / kg solvent) and K_b is the ebullioscopic constant of the solvent (Zumdahl 10e §11.5). For water K_b = 0.512 K·kg/mol; for benzene 2.53; for camphor 5.61 (CRC 97e §8). Higher K_b means the same molality gives a bigger effect — hence camphor was the classic solvent for molecular-weight determination in the pre-mass-spec era.

Property 3 — freezing-point depression

By the same logic, the temperature at which a solvent freezes drops:

$\Delta T_f = K_f m$

For water K_f = 1.86 K·kg/mol; for benzene 5.12; for camphor 40.0 (Silberberg 8e §13.5). The larger K_f values explain why road salt (NaCl at ~1 m dissolved in the water film on roads) lowers the freezing point by roughly 6 K when both ions are counted — plenty to melt ice at −5 °C.

The mechanism is the same as boiling-point elevation: the liquid solvent has a lowered chemical potential, so the temperature at which its μ matches that of the pure solid is now lower.

Property 4 — osmotic pressure

Separate a solution from pure solvent by a semi-permeable membrane (permeable to solvent, not solute), and solvent flows into the solution until either the pressure difference or the concentration difference stops it. The equilibrium pressure difference is the osmotic pressure π. Van’t Hoff (1886) showed that for dilute solutions:

$\pi = c R T$

where c is molar concentration (moles solute per litre solution) and R is the gas constant. In SI, π comes out in Pa when c is in mol/m³; in bench units (M, atm) use R = 0.08206 L·atm/(K·mol).

Osmotic pressure looks like the ideal gas law, and for a good reason: at low concentration, solute particles in solution behave like independent molecules bouncing off a wall (the membrane), and their partial pressure of impact obeys the same combinatorial law as an ideal gas.

Osmotic pressure is by far the most sensitive of the four properties — a 1 mM solution gives π ≈ 0.024 atm ≈ 18 mmHg, which is easily measurable, while ΔT_f at the same concentration is only 0.002 K, below normal thermometer resolution. This is why osmometry is the standard technique for measuring molecular weights of proteins and polymers.

Worked example — freezing-point depression of a solution

The van’t Hoff factor — extending to electrolytes

An electrolyte dissociates into multiple ions per formula unit. NaCl gives Na⁺ + Cl⁻ (2 particles per formula unit); CaCl₂ gives Ca²⁺ + 2 Cl⁻ (3 particles); K₃PO₄ gives 3 K⁺ + PO₄³⁻ (4 particles). Colligative properties count particles, so all four formulas get multiplied by the van’t Hoff factor i:

$\Delta T_f = i K_f m; \quad \Delta T_b = i K_b m; \quad \pi = i c R T$

For a non-electrolyte, i = 1.

For a strong electrolyte in dilute solution, i approaches the theoretical value (2 for NaCl, 3 for CaCl₂, 4 for K₃PO₄). At real concentrations, i is systematically less than the theoretical value because of ion pairing (Debye-Hückel effect). For NaCl:

The gap between theoretical and measured i widens with concentration and with ionic charge (for 2:2 electrolytes like MgSO₄, i can be as low as 1.3 at 0.1 m — a substantial deviation from the theoretical 2).

For a weak electrolyte (partial dissociation), i is directly the fraction dissociated times the number of ions per formula unit, plus (1 − α) for the undissociated form. For an acid HA with degree of dissociation α: i = 1 + α.

Osmosis in biology

Isotonic saline is 0.9% NaCl w/w, which in molar terms is 0.154 M NaCl or (with i ≈ 1.9) about 0.29 osmol/L — matching human plasma. Hypotonic solutions (lower osmolarity) cause red blood cells to swell and lyse; hypertonic (higher) cause them to shrink and crenate. Osmotic pressure of plasma is about 7.5 atm at 310 K, an enormous mechanical force that shapes every cell-volume regulation mechanism.

Kidney concentrating gradients in the medulla can reach 1200 mOsm/L (nearly 30 atm of osmotic pressure) — an extreme physiological example of the same equation.

Worked example — osmotic pressure to estimate a protein’s MW

Common pitfalls

Using molarity instead of molality. Boiling-point elevation and freezing-point depression are defined via molality (which is temperature-independent). Molarity depends on solution volume, which itself depends on temperature — so at a boiling point, molarity has drifted from its room-temperature value. Molality is the same at every T because it counts moles per kg of solvent.

Forgetting the van’t Hoff factor. For any ionic compound, i > 1. For NaCl solutions, using i = 1 will systematically underestimate every colligative property by ~2×.

Assuming i = i_theoretical. In real solutions above ~0.01 m, ion pairing reduces i. Use a table of measured values (CRC 97e §8) rather than the stoichiometric prediction.

Applying colligative equations to volatile solutes. Raoult’s law extends to volatile solutes on both sides (giving Dalton-Raoult mixtures with two vapour components); the ΔT_b and ΔT_f equations assume the solute has negligible vapour pressure. Ethanol in water needs a different treatment.

Confusing osmolarity with osmolality. Both are used in biology; osmolarity = osmol per L solution, osmolality = osmol per kg solvent. In dilute biological fluids they are nearly equal; in concentrated protein solutions or glucose loads, they differ.

Practice

Where this leads

Colligative properties link solution structure to thermodynamics:

• Debye-Hückel theory — explains the systematic deviations of i from theoretical values via ion-atmosphere corrections.
• Cryoscopy in synthesis — molecular weight determination for insoluble organics via camphor freezing depression.
• Reverse osmosis — desalination pushes water against osmotic pressure via applied hydraulic force > π.
• Cell volume regulation — every biological membrane balances osmotic pressure via ion pumps and aquaporins.

Every one of them starts by counting particles in solution.