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General Chemistry II · Properties of Solutions

Colligative Properties

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On this page 8 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Study tools
  8. Sources & references

In 30 seconds

Colligative properties depend only on the number of solute particles in a solution, not on their identity. Dissolving a solute lowers the vapor pressure (Raoult's law), which in turn raises the boiling point and lowers the freezing point, and it creates an osmotic pressure across a semipermeable membrane. For electrolytes, each formula unit contributes i particles (the van't Hoff factor), so ionic solutes have a proportionally larger effect.

Why this matters

  • Antifreeze & de-icing: ethylene glycol and road salt lower the freezing point of water.
  • Cooking: adding salt raises the boiling point of water.
  • Biology/medicine: osmotic pressure drives water balance across cell membranes; IV fluids must be isotonic (matched osmotic pressure) to avoid bursting or shrinking cells.
  • Osmosis: reverse osmosis desalinates seawater by applying pressure against the osmotic gradient.

The college version

Core Concept

Colligative properties depend only on the number of solute particles in a solution, not on their identity. Dissolving a solute lowers the vapor pressure (Raoult's law), which in turn raises the boiling point and lowers the freezing point, and it creates an osmotic pressure across a semipermeable membrane. For electrolytes, each formula unit contributes i particles (the van't Hoff factor), so ionic solutes have a proportionally larger effect.

Key Ideas

The four colligative properties

  1. Vapor-pressure lowering (Raoult's law): P_solution = X_solvent · P°_solvent.
  2. Boiling-point elevation: ΔT_b = i·K_b·m.
  3. Freezing-point depression: ΔT_f = i·K_f·m.
  4. Osmotic pressure: Π = i·M·R·T.

Why they depend on particle number

  • A solute particle blocks solvent from the surface (lowers vapor pressure) and interferes with freezing; the effect scales with how many particles are present, not what they are.

Constants

  • Water: K_b = 0.512 °C·kg/mol, K_f = 1.86 °C·kg/mol.

Osmosis

  • Solvent flows through a semipermeable membrane from low to high solute concentration (toward higher osmotic pressure).

Equations and Variables

  • Raoult's law: P_solution = X_solvent · P°_solvent; vapor-pressure lowering ΔP = X_solute · P°.
  • Boiling-point elevation: ΔT_b = i·K_b·m.
  • Freezing-point depression: ΔT_f = i·K_f·m.
  • Osmotic pressure: Π = i·M·R·T, with R = 0.08206 L·atm/(mol·K), T in kelvin.
    • i = van't Hoff factor, K_b/K_f = ebullioscopic/cryoscopic constants, m = molality, M = molarity.

How It Works

  1. A solute lowers the solvent's vapor pressure because fewer solvent molecules occupy the surface to escape.
  2. Lowered vapor pressure shifts the phase equilibria: the boiling point rises (more heat needed to reach P_vapor = P_external) and the freezing point falls (the liquid is stabilized relative to the solid).
  3. The magnitudes scale with particle concentration — molality (for ΔTb, ΔTf) or molarity (for Π) times i.
  4. For electrolytes, multiply by i (e.g., i = 2 for NaCl, 3 for CaCl₂) because each formula unit produces multiple particles.
  5. Osmosis drives solvent across a membrane toward the more concentrated side, generating osmotic pressure Π = iMRT.

Worked Example

(a) Calculate the freezing point of a solution of 25.0 g of ethylene glycol (C₂H₆O₂, 62.07 g/mol, a nonelectrolyte) in 250 g of water. (b) Calculate the osmotic pressure of 0.0100 M sucrose at 25 °C.

  1. (a) Molality. n = 25.0 / 62.07 = 0.4027 mol; m = 0.4027 / 0.250 kg = 1.611 m.
  2. (a) Freezing-point depression. ΔT_f = i·K_f·m = (1)(1.86 °C/m)(1.611 m) = 2.996 °C → T_f = 0 − 2.996 = −3.00 °C.
  3. (b) Osmotic pressure. Π = i·M·R·T = (1)(0.0100 mol/L)(0.08206 L·atm/mol·K)(298.15 K) = 0.245 atm.

How it works

  1. A solute lowers the solvent's vapor pressure because fewer solvent molecules occupy the surface to escape.
  2. Lowered vapor pressure shifts the phase equilibria: the boiling point rises (more heat needed to reach P_vapor = P_external) and the freezing point falls (the liquid is stabilized relative to the solid).
  3. The magnitudes scale with particle concentration — molality (for ΔTb, ΔTf) or molarity (for Π) times i.
  4. For electrolytes, multiply by i (e.g., i = 2 for NaCl, 3 for CaCl₂) because each formula unit produces multiple particles.
  5. Osmosis drives solvent across a membrane toward the more concentrated side, generating osmotic pressure Π = iMRT.

Common confusions

  • "Colligative properties depend on the solute's identity." — Wrong. They depend only on the number of dissolved particles.
  • "ΔTf and Π both use molarity." — Wrong. ΔTf and ΔTb use molality; osmotic pressure uses molarity.
  • "Raoult's law uses the solute's mole fraction." — Wrong. P = X_solvent·P° uses the solvent's mole fraction (the solute lowers it).
  • "Adding solute raises the freezing point." — Wrong. Solutes lower the freezing point and raise the boiling point.
  • "A nonelectrolyte and an electrolyte at the same molarity have the same effect." — Wrong. The electrolyte's effect is multiplied by i.

Quick review

  • Four colligative properties: vapor-pressure lowering, bp elevation, fp depression, osmotic pressure.
  • P = X_solvent·P°; ΔT_b = i K_b m; ΔT_f = i K_f m; Π = i M R T.
  • Water K_b = 0.512, K_f = 1.86 °C·kg/mol.
  • Worked: ethylene glycol → ΔTf = 3.00 °C; 0.0100 M sucrose → Π = 0.245 atm.
  • Osmosis: solvent flows toward higher solute concentration.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Colligative properties are a "head count" effect: it doesn't matter who you add to the swimming pool — salt, sugar, or antifreeze — it only matters how many particles you add. Every particle is like a little kid getting in the way, making it harder for the water to freeze (so the freezing point drops) and harder to boil (so the boiling point rises), and pulling water across a membrane to dilute itself (osmosis). Ionic stuff is sneakier because one "package" of salt actually splits into two or three kids when it dissolves, so it counts double or triple. (The analogy's limit: the "getting in the way" is really about surface blocking and solution entropy, but the key idea — count particles, not type — is the entire point of colligative properties.)

Worked example

Worked Example

(a) Calculate the freezing point of a solution of 25.0 g of ethylene glycol (C₂H₆O₂, 62.07 g/mol, a nonelectrolyte) in 250 g of water. (b) Calculate the osmotic pressure of 0.0100 M sucrose at 25 °C.

  1. (a) Molality. n = 25.0 / 62.07 = 0.4027 mol; m = 0.4027 / 0.250 kg = 1.611 m.
  2. (a) Freezing-point depression. ΔT_f = i·K_f·m = (1)(1.86 °C/m)(1.611 m) = 2.996 °C → T_f = 0 − 2.996 = −3.00 °C.
  3. (b) Osmotic pressure. Π = i·M·R·T = (1)(0.0100 mol/L)(0.08206 L·atm/mol·K)(298.15 K) = 0.245 atm.

Key takeaways

  • ### High-Yield Facts
  • Colligative properties depend on particle number, not identity.
  • Raoult: P_solution = X_solvent·P°.
  • ΔT_b = i·K_b·m; ΔT_f = i·K_f·m; Π = i·M·R·T.
  • Water: K_b = 0.512, K_f = 1.86 °C·kg/mol.
  • Ionic solutes: multiply by i (NaCl → 2, CaCl₂ → 3).
  • Osmotic pressure uses molarity (M); ΔTb/ΔTf use molality (m).
  • Osmosis: solvent moves toward higher solute concentration.

Keep learning

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Practice General Chemistry II

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Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • Define colligative property and explain the role of particle number.
  • State and apply Raoult's law for vapor-pressure lowering.
  • Calculate boiling-point elevation and freezing-point depression.
  • Calculate osmotic pressure.
  • Explain how the van't Hoff factor enters colligative calculations.

Sources & references

  1. OpenStax, *Chemistry 2e*, "11.4 Colligative Properties." https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties
  2. OpenStax, *Chemistry 2e*, "11.2 Electrolytes." https://openstax.org/books/chemistry-2e/pages/11-2-electrolytes
  3. NIST Chemistry WebBook. https://webbook.nist.gov/chemistry/
  4. OpenStax, *Chemistry 2e* (book home). https://openstax.org/details/books/chemistry-2e
  5. American Chemical Society. https://www.acs.org/

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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