Difficulty: Intermediate | Prerequisites: Solutions and solubility, concentration units (especially molality and molarity)
Colligative properties are physical properties of solutions that depend only on how many solute particles are present, not on what those particles are. This is the section where concentration units pay off: you will use molality for boiling point and freezing point calculations, molarity for osmotic pressure, and mole fraction for Raoult's Law. If you are not solid on the difference between molarity and molality, review the concentration notes first.
Colligative properties are physical behaviours of solutions that change depending on how many solute particles are dissolved, regardless of what those particles are. The four key colligative properties are vapour pressure depression (Raoult's Law), boiling point elevation, freezing point depression, and osmotic pressure. Each has its own formula, and all of them use the van't Hoff factor to account for ionic compounds that dissociate into multiple particles.
Colligative properties
Physical properties of solutions that depend on the concentration of dissolved particles but not on their chemical identity.
In simple terms, it does not matter what the solute is, only how many particles of it are floating around in the solvent.
Vapour pressure depression
The decrease in vapour pressure of a solvent when a nonvolatile solute is added.
Think of it as solute molecules sitting on the surface of the liquid and physically blocking some solvent molecules from evaporating.
Raoult's Law
The vapour pressure of a solvent above a solution equals the mole fraction of the solvent multiplied by the vapour pressure of the pure solvent: P_A = X_A P°_A.
In simple terms, the more solute you add, the lower the vapour pressure of the solvent becomes, in direct proportion.
Boiling point elevation
The increase in a solution's boiling point relative to the pure solvent, caused by the addition of a nonvolatile solute.
Think of it as: lower vapour pressure means the liquid needs more heat to boil.
Freezing point depression
The decrease in a solution's freezing point relative to the pure solvent, caused by solute particles interfering with the formation of the solid lattice.
Think of it as: solute particles get in the way of the solvent molecules arranging themselves into a crystal, so you need colder temperatures to freeze the solution.
Van't Hoff factor (i)
The number of particles a compound dissociates into when dissolved. For NaCl, i = 2 (Na⁺ and Cl⁻). For covalent molecules that do not dissociate, i = 1.
In simple terms, it is a multiplier that accounts for ionic compounds breaking into separate ions.
Osmotic pressure
The pressure that must be applied to a solution to prevent the net flow of solvent into it through a semipermeable membrane.
Think of it as the "sucking" pressure a concentrated solution exerts, drawing pure solvent toward it.
Osmolarity
The number of individual particles in solution per litre. For a 1 M NaCl solution, the osmolarity is 2 osmol/L because NaCl dissociates completely into two ions.
In simple terms, it is molarity multiplied by the van't Hoff factor.
Adding a nonvolatile solute to a solvent lowers the solvent's vapour pressure
Solute molecules on the liquid surface block solvent molecules from evaporating, but do not block condensation
The vapour pressure of the solvent above a solution: P_A = X_A P°_A
P_A is the vapour pressure of the solvent above the solution
X_A is the mole fraction of the solvent
P°_A is the vapour pressure of the pure solvent
Lower vapour pressure means a higher boiling point
Raoult's Law holds exactly only for ideal solutions, where the intermolecular attractions between unlike molecules equal those between like molecules
Non-ideal solutions show deviations
The vapour pressure of water at 100 °C is 1 atm
A nonvolatile solute raises the boiling point of the solution above that of the pure solvent
The formula gives the change in boiling point, not the final boiling point itself:
ΔT_b = i K_b m
i = van't Hoff factor (number of particles the compound dissociates into)
K_b = ebullioscopic constant (boiling point elevation constant) of the solvent
m = molality of the solution
K_b of water is 0.512 K kg/mol
NaCl has a van't Hoff factor of 2 (dissociates into Na⁺ and Cl⁻)
Covalent molecules that do not dissociate have a van't Hoff factor of 1
Depends only on the number of particles, not their identity
Solute particles interfere with the formation of the crystal lattice that the solvent molecules need to solidify
The solution requires more energy removal (lower temperature) to freeze
The formula gives the change in freezing point from the pure solvent:
ΔT_f = i K_f m
K_f of water is 1.86 K kg/mol
Same variables as boiling point elevation: i, K_f, and molality
Depends only on concentration of particles, not their identity
This is why roads are salted in winter: the salt depresses the freezing point of water, preventing ice from forming at 0 °C
The pressure generated by a solution that draws solvent into it through a semipermeable membrane
Formula: Π = iMRT
Π is osmotic pressure
i = van't Hoff factor
M = molarity of the solute
R = ideal gas constant
T = temperature in Kelvin
Uses molarity (not molality), unlike the other colligative property equations
The total number of individual particles per litre of solution
For a 1 M NaCl solution: NaCl dissociates completely, so osmolarity = 2 osmol/L
Osmolarity = molarity x van't Hoff factor
Raoult's Law (vapour pressure depression):
P_A = X_A \cdot P^\circ_AP_A = vapour pressure of solvent above solution, X_A = mole fraction of solvent, P°_A = vapour pressure of pure solvent.
Boiling point elevation:
\Delta T_b = i \cdot K_b \cdot mi = van't Hoff factor, K_b = ebullioscopic constant (water: 0.512 K kg/mol), m = molality.
Freezing point depression:
\Delta T_f = i \cdot K_f \cdot mi = van't Hoff factor, K_f = cryoscopic constant (water: 1.86 K kg/mol), m = molality.
Osmotic pressure:
\Pi = i \cdot M \cdot R \cdot Ti = van't Hoff factor, M = molarity, R = ideal gas constant, T = temperature in Kelvin.
Summary of key constants for water:
Property | Constant | Value |
|---|---|---|
Boiling point elevation | K_b | 0.512 K kg/mol |
Freezing point depression | K_f | 1.86 K kg/mol |
Normal boiling point | T_b | 100 °C (373.15 K) |
Normal freezing point | T_f | 0 °C (273.15 K) |
Vapour pressure at 100 °C | P° | 1 atm |
Freezing point depression is why we salt roads and pavements in winter. The dissolved salt lowers the freezing point of water, so ice melts (or fails to form) at temperatures below 0 °C.
Osmotic pressure is critical in biology and medicine. Intravenous fluids must be isotonic (matching the osmolarity of blood) to prevent cells from swelling or shrinking. This is why saline drips use 0.9% NaCl rather than pure water.
Students often forget the van't Hoff factor for ionic compounds. NaCl dissociates into two particles (i = 2), so its effect on boiling point, freezing point, and osmotic pressure is double that of a covalent solute at the same molality.
Students often think ΔT_b or ΔT_f gives the actual boiling or freezing point. It does not. It gives the change from the pure solvent's boiling or freezing point. You must add ΔT_b to the normal boiling point, or subtract ΔT_f from the normal freezing point.
Students often confuse which concentration unit to use. Boiling point elevation and freezing point depression use molality. Osmotic pressure uses molarity. Raoult's Law uses mole fraction.
Students often assume Raoult's Law applies to all solutions. It applies exactly only to ideal solutions. Real solutions can show positive or negative deviations.
⚠️ Know each formula and which concentration unit it uses. This is commonly tested as a straightforward calculation.
⚠️ Always account for the van't Hoff factor. A common exam trap is giving you an ionic solute and expecting you to multiply by i.
⚠️ Be clear that ΔT_b and ΔT_f are changes, not final values. The exam may ask for the actual boiling or freezing point of the solution.
⚠️ Know the constants for water: K_b = 0.512 K kg/mol, K_f = 1.86 K kg/mol. These are frequently provided, but understanding what they represent helps you reason through problems.
⚠️ Understand Raoult's Law qualitatively: why vapour pressure drops, why boiling point rises, and the connection between them.
True or false: Colligative properties depend on the identity of the solute.
Answer: False. They depend only on the number of dissolved particles.
Fill in the blank: The van't Hoff factor for glucose (a covalent molecule) is ______.
Answer: 1 (it does not dissociate).
True or false: ΔT_b = i K_b m gives you the actual boiling point of the solution.
Answer: False. It gives the change in boiling point from the pure solvent.
Fill in the blank: Osmotic pressure uses ______ as its concentration unit, not molality.
Answer: Molarity.
True or false: Adding NaCl to water raises its freezing point.
Answer: False. It depresses (lowers) the freezing point.
Q: Calculate the boiling point of a solution made by dissolving 0.50 mol of NaCl in 1.00 kg of water. (K_b = 0.512 K kg/mol)
A: NaCl has i = 2. ΔT_b = i K_b m = (2)(0.512)(0.50) = 0.512 K. The boiling point of the solution is 100.00 + 0.512 = 100.512 °C.
Q: What is the freezing point of a 0.25 m glucose solution in water? (K_f = 1.86 K kg/mol)
A: Glucose is covalent, so i = 1. ΔT_f = (1)(1.86)(0.25) = 0.465 K. The freezing point is 0.00 - 0.465 = -0.465 °C.
Q: A solution has a mole fraction of solvent equal to 0.95. If the vapour pressure of the pure solvent is 100 mmHg, what is the vapour pressure above the solution?
A: P = X P° = (0.95)(100) = 95 mmHg.
Q: Calculate the osmotic pressure of a 0.10 M NaCl solution at 25 °C. (R = 0.0821 L atm / mol K)
A: i = 2, M = 0.10, T = 298 K. Π = iMRT = (2)(0.10)(0.0821)(298) = 4.89 atm.
Q: Two solutions are prepared: 0.10 m NaCl and 0.10 m CaCl₂. Which has the lower freezing point? Explain.
A: CaCl₂ has i = 3 (one Ca²⁺ and two Cl⁻), while NaCl has i = 2. Since ΔT_f = i K_f m, CaCl₂ produces a larger freezing point depression at the same molality, so the CaCl₂ solution has the lower freezing point.
Colligative properties build directly on concentration units from the previous notes. You cannot calculate boiling point elevation without understanding molality, or osmotic pressure without understanding molarity.
Vapour pressure depression connects to phase diagrams: adding a solute shifts the liquid-vapour equilibrium curve, which is why the boiling point rises and the freezing point drops.
Osmotic pressure is foundational in biology, particularly for understanding how cells regulate water balance (osmosis, tonicity, and the behaviour of red blood cells in hypertonic or hypotonic solutions).
Colligative properties, Raoult's Law, vapour pressure depression, boiling point elevation, freezing point depression, osmotic pressure, osmolarity, van't Hoff factor, ebullioscopic constant, cryoscopic constant, K_b, K_f, molality, molarity, mole fraction, ideal solution, nonvolatile solute, semipermeable membrane, osmosis, tonicity, CHEM 101, general chemistry