Colligative Properties

A solution's boiling point, freezing point, vapor pressure, and osmotic pressure all shift once a solute is dissolved in it — and on the MCAT, the size of that shift almost never depends on what the solute is. This article covers what makes a property colligative, the van't Hoff factor that connects these formulas to electrolyte solutions, and the four classic colligative properties: vapor pressure lowering (Raoult's law), boiling point elevation, freezing point depression, and osmotic pressure.

Key Takeaways

• Colligative properties depend on the number of dissolved solute particles, not their identity: vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

• The van't Hoff factor (i) is the number of particles one formula unit produces in solution — i = 1 for nonelectrolytes, i = 2 for a 1:1 strong electrolyte (e.g., NaCl), i = 3 for a 1:2 strong electrolyte (e.g., CaCl₂).

• Raoult's law: P₁ = χ₁P°₁ — a solution's vapor pressure is proportional to the solvent's mole fraction.

• Boiling point elevation: ΔTb = iKbm, using the solvent's ebullioscopic constant Kb.

• Freezing point depression: ΔTf = iKfm, using the solvent's cryoscopic constant Kf (unrelated to the formation constant of the same symbol).

• Osmotic pressure: Π = iMRT — critical in biological systems for regulating water movement across cell membranes.

What Makes a Property Colligative

Colligative properties are physical properties of a solution that depend on the number of dissolved solute particles in a given amount of solvent — not on the identity, size, or chemical nature of those particles. A solution of glucose and a solution of sucrose at the same particle concentration will show the same boiling point elevation, even though the two molecules are chemically very different.

The mechanism is the same across all four colligative properties: dissolved solute particles get in the way of solvent-solvent interactions. They occupy space at the surface, interfere with the solvent's ability to form an ordered solid structure, or create a concentration imbalance across a membrane — and each of these disruptions shows up as a measurable physical change. The four colligative properties tested on the MCAT are vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

The Van't Hoff Factor

Because colligative properties depend on the number of particles, an electrolyte that dissociates into multiple ions has a bigger effect per mole dissolved than a solute that stays intact. The van't Hoff factor (i) accounts for this: it's the number of particles one formula unit of solute produces in solution.

• Nonelectrolytes (e.g., glucose, sucrose) don't dissociate, so i = 1.

• A 1:1 strong electrolyte like NaCl fully dissociates into Na⁺ and Cl⁻, so i = 2.

• A 1:2 strong electrolyte like CaCl₂ fully dissociates into Ca²⁺ and two Cl⁻, so i = 3.

Three of the four formulas below include i as a multiplier — skipping it is one of the most common MCAT colligative-properties mistakes when the solute is an electrolyte rather than a molecular compound.

Raoult's Law and Vapor Pressure Lowering

Raoult's law describes how dissolving a non-volatile solute lowers a solvent's vapor pressure. The solution's vapor pressure is directly proportional to the solvent's mole fraction:

P₁ = χ₁P°₁

where P₁ is the vapor pressure of the solution, χ₁ is the mole fraction of the solvent, and P°₁ is the vapor pressure of the pure solvent. This happens because solute particles occupy some of the surface area at the liquid-vapor interface, reducing the number of solvent molecules that can escape into the vapor phase. As more solute is dissolved, the solvent's mole fraction drops, and its vapor pressure drops with it. This vapor pressure lowering is the underlying cause of both boiling point elevation and freezing point depression below.

Worked example — Pure water has a vapor pressure of 23.8 mmHg at 25°C. What is the vapor pressure of a solution made by dissolving 1 mol of glucose (a nonelectrolyte) in 9 mol of water?

χ(water) = 9 mol / (9 mol + 1 mol) = 0.9

P₁ = χ₁P°₁ = 0.9 × 23.8 mmHg = 21.4 mmHg

Boiling Point Elevation

Boiling point elevation occurs when a non-volatile solute is added to a solvent, raising the solution's boiling point above that of the pure solvent. Because the solute lowers the solvent's vapor pressure (Raoult's law above), a higher temperature is required to bring the vapor pressure back up to the point where boiling occurs. The boiling point elevation is:

ΔTb = iKbm

where i is the van't Hoff factor, Kb is the solvent's ebullioscopic constant (a solvent-specific property; for water, Kb = 0.512 °C·kg/mol), and m is the solution's molality.

Worked example — What is the boiling point of a 1.0 m aqueous NaCl solution?

NaCl is a 1:1 strong electrolyte, so i = 2:

ΔTb = iKbm = 2 × 0.512 °C·kg/mol × 1.0 m = 1.024°C

New boiling point = 100°C + 1.024°C = 101.0°C

Freezing Point Depression

Freezing point depression occurs when a non-volatile solute is added to a solvent, lowering the solution's freezing point below that of the pure solvent. Solute particles interfere with the solvent's ability to form an ordered solid structure, so a lower temperature is needed to reach the solid-liquid phase transition. The freezing point depression is:

ΔTf = iKfm

where Kf is the solvent's cryoscopic constant (for water, Kf = 1.86 °C·kg/mol). This Kf is a different quantity from the formation constant Kf covered in "Solution Equilibria" — the two share a symbol by convention but have no other relationship.

Worked example — What is the freezing point of a 0.50 m aqueous CaCl₂ solution?

CaCl₂ is a 1:2 strong electrolyte (one Ca²⁺, two Cl⁻ per formula unit), so i = 3:

ΔTf = iKfm = 3 × 1.86 °C·kg/mol × 0.50 m = 2.79°C

New freezing point = 0°C − 2.79°C = −2.79°C

Osmotic Pressure

Osmotic pressure (Π) is the pressure required to stop the net flow of solvent molecules across a semipermeable membrane, from the side with lower solute concentration to the side with higher solute concentration. Osmosis happens because solvent molecules move to equalize solute concentration on both sides of the membrane; applying enough external pressure to the more concentrated side can counteract that flow. Osmotic pressure is calculated as:

Π = iMRT

where M is the solution's molarity, R is the gas constant (0.0821 L·atm/(mol·K)), and T is the absolute temperature in Kelvin.

Osmotic pressure is especially important in biological systems, where it governs the movement of water and nutrients into and out of cells across cell membranes.

Worked example — What is the osmotic pressure of a 0.15 M NaCl solution at body temperature (37°C = 310 K)?

NaCl has i = 2:

Π = iMRT = 2 × 0.15 M × 0.0821 L·atm/(mol·K) × 310 K ≈ 7.6 atm

(This is close to the actual osmotic pressure of human blood plasma, which is roughly isotonic to a 0.15 M NaCl — i.e., "normal saline" — solution.)

Common MCAT Mistakes

• Forgetting the van't Hoff factor for electrolytes. Treating NaCl or CaCl₂ as i = 1, the same as a nonelectrolyte, understates every colligative effect that uses i — always identify whether (and how many ions) the solute dissociates into first.

• Mixing up boiling point elevation and freezing point depression. ΔTb = iKbm raises the boiling point; ΔTf = iKfm lowers the freezing point — using the wrong constant (Kb vs. Kf) or the wrong sign gives an answer in the wrong direction.

• Plugging molarity into a molality-based formula. ΔTb and ΔTf both use molality (m, mol solute/kg solvent), not molarity (M, mol solute/L solution) — the two units diverge as concentration increases.

• Confusing the cryoscopic constant Kf with the complex-ion formation constant Kf. They share a symbol by convention but describe unrelated quantities — one is a solvent property used in freezing point depression, the other is an equilibrium constant for complex ion formation.

MCAT-Style Concept Check

Question: What is the osmotic pressure of a 0.20 M CaCl₂ solution at 25°C (298 K)?

• A) 4.9 atm

• B) 9.8 atm

• C) 14.7 atm

• D) 24.5 atm

Answer: C

Explanation: CaCl₂ is a 1:2 strong electrolyte, so i = 3. Π = iMRT = 3 × 0.20 M × 0.0821 L·atm/(mol·K) × 298 K ≈ 14.7 atm. Using i = 1 (forgetting dissociation) would incorrectly give about 4.9 atm — choice A.

FAQ

What makes a property "colligative"?

A colligative property depends only on the number of dissolved solute particles in a given amount of solvent, not on what those particles are chemically. That's why equal particle concentrations of chemically different solutes (like glucose and sucrose) produce the same boiling point elevation.

Why does the van't Hoff factor matter for electrolyte solutions?

The van't Hoff factor (i) accounts for how many particles one formula unit of solute actually produces in solution. Since colligative effects scale with particle count, an electrolyte like CaCl₂ (i = 3) produces three times the colligative effect per mole dissolved compared to a nonelectrolyte like glucose (i = 1).

What's the difference between the boiling point elevation and freezing point depression formulas?

Boiling point elevation is ΔTb = iKbm, using the solvent's ebullioscopic constant Kb, and raises the boiling point above the pure solvent's. Freezing point depression is ΔTf = iKfm, using the solvent's cryoscopic constant Kf, and lowers the freezing point below the pure solvent's. Both use the solution's molality (m), not molarity.

How is osmotic pressure calculated, and why does it matter biologically?

Osmotic pressure is Π = iMRT, where M is molarity, R is the gas constant, and T is absolute temperature. It matters biologically because it governs how water and nutrients move across semipermeable cell membranes — human blood plasma's osmotic pressure is close to that of a 0.15 M NaCl (normal saline) solution.