Chemistry 2e · Solutions and Colloids
Colligative Properties
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A colligative property A solution property that depends only on the number of solute particles, not their identity Full entry → is a property of a solution that depends on the number of dissolved solute particles, not on the chemical identity of those particles. Four properties behave this way: vapor-pressure lowering, boiling-point elevation, freezing-point depression, and osmotic pressure. The name comes from the Latin colligare, "to bind together" — all four are tied to the same underlying cause: adding solute dilutes the solvent and makes it harder for solvent molecules to escape the liquid phase.
Here is the common mechanism. Solute particles occupy space in the liquid and reduce the mole fraction of solvent at the surface, so fewer solvent molecules escape into the vapor each second. A lower vapor pressure means the solution must be heated to a higher temperature before its vapor pressure matches the external pressure (boiling-point elevation). It also means the solution must be cooled further before solvent molecules can organize into a solid lattice (freezing-point depression). When a membrane that lets only solvent pass separates two solutions, the more concentrated side pulls solvent across, creating osmotic pressure.
Because the identity of the solute does not matter — only how many particles are present — a mole of table sugar and a mole of urea (very different molecules) affect these properties identically, as long as neither dissociates. Electrolytes are the exception that proves the rule: they split into multiple ions per formula unit, so each formula unit counts as several particles.
Why this matters
Colligative properties are engineered into everyday products and medical fluids:
- Antifreeze: Ethylene glycol added to a car radiator lowers the freezing point of the coolant (so the engine block survives winter) and raises its boiling point (so the coolant survives summer).
- Road de-icing: Salt (NaCl or CaCl₂) spread on ice forms a brine whose freezing point is below 0 °C, so ice melts even when the air temperature is below freezing.
- Intravenous fluids: Solutions given by IV — such as 0.9% NaCl ("normal saline") and 5% dextrose — are formulated to be isotonic with blood so their osmotic pressure roughly matches that of red blood cells, preventing cells from swelling or shrinking.
- Food preservation: Sugar in jam and salt in pickles create solutions with high osmotic pressure that draw water out of microbes, slowing spoilage without cooking.
- Kidney dialysis: Dialysis membranes rely on the same semipermeable-membrane behavior behind osmotic pressure to remove small waste molecules from blood while keeping large proteins in.
The college version
Core Concepts
Vapor-pressure lowering and Raoult's law
For a solution containing a nonvolatile solute, the vapor pressure of the solvent is lowered in proportion to the solvent's mole fraction. This is Raoult's law PA = XA PA°: solvent vapor pressure equals its mole fraction times the pure-solvent vapor pressure Full entry →:
PA = XA PA°
where PA is the solvent's vapor pressure above the solution, XA is the solvent's mole fraction, and PA° is the vapor pressure of the pure solvent at the same temperature. Since XA = 1 - XB (where XB is the solute's mole fraction), the vapor-pressure lowering is:
ΔP = XB PA°
Doubling the number of solute particles doubles the lowering — identity is irrelevant. This relationship holds for ideal (dilute) solutions of nonvolatile solutes.
Boiling-point elevation
Because the solution's vapor pressure is lower, it must be heated to a higher temperature to boil. The elevation is directly proportional to the molality of solute particles:
ΔTb = Kb m
Here m is the molality (moles of solute particles per kilogram of solvent) and Kb is the molal boiling-point-elevation constant, which is a property of the solvent. For water, Kb = 0.512 °C kg mol-1 (often written 0.512 °C/m). The normal boiling point of pure water is 100.00 °C; a 1 molal solution of a nonvolatile nonelectrolyte A solute that dissolves without forming ions (e.g., sugar) Full entry → boils near 100.51 °C.
Freezing-point depression
The same dilution that lowers vapor pressure also makes it harder for solvent molecules to form a solid lattice, so the solution freezes at a lower temperature:
ΔTf = Kf m
For water, Kf = 1.86 °C kg mol-1 (1.86 °C/m). Note that Kf is much larger than Kb, so freezing-point depression is usually the more dramatic effect — which is why road salt works at modest concentrations.
Osmotic pressure
Osmosis is the net movement of solvent through a semipermeable membrane A barrier that lets solvent pass but blocks solute particles Full entry → from a region of lower solute concentration to a region of higher solute concentration. The pressure that must be applied to the more concentrated side to stop this flow is the osmotic pressure:
Π= MRT
where M is the molarity of solute particles, R is the ideal gas constant (0.08206 L atm mol-1K-1), and T is the temperature in kelvin. Because osmotic pressure depends on particle count (through M), it is a colligative property too — and it is by far the most sensitive one, which is why it is used to measure the molar masses of large molecules such as proteins.
Electrolytes and the van't Hoff factor
A strong electrolyte such as NaCl dissociates completely into two ions per formula unit, so one mole of NaCl contributes two moles of particles. The van't Hoff factor, i, is the number of particles produced per formula unit. For an ideal strong electrolyte, i equals the number of ions (NaCl → 2, CaCl₂ → 3, Na₂SO₄ → 3). The colligative formulas become:
ΔTb = i Kb m ΔTf = i Kf m Π= iMRT
In real solutions, ion pairing makes the measured i slightly smaller than the ideal value (for example, NaCl in water behaves more like i ≈ 1.9 at moderate concentration), but exam problems almost always use the ideal integer value unless told otherwise.
Why molality, not molarity
Boiling- and freezing-point formulas use molality (moles of solute per kilogram of solvent) rather than molarity (moles per liter of solution). Molality is based on masses, which do not change with temperature; molarity is based on volume, which expands and contracts with temperature. Because colligative measurements themselves involve temperature changes, molality keeps the solute-to-solvent ratio fixed. Osmotic pressure, measured at a single temperature, is expressed with molarity.
Common Confusions
| Do not confuse | With | Difference |
|---|---|---|
| "Salt makes water boil faster" | Boiling-point elevation | Salt raises the boiling point; the solution needs more heat, so it boils at a higher temperature, not sooner |
| "Colligative properties depend on the solute" | Particle count | They depend on the number of particles; identity (molecule type) does not matter |
| Molarity (M) | Molality (m) | Molarity = mol solute per L solution (volume-based, temperature-dependent); molality = mol solute per kg solvent (mass-based, temperature-independent) |
| "1 mole of NaCl gives 1 mole of particles" | van't Hoff factor | NaCl gives ~2 moles of particles (i = 2); always count ions for electrolytes |
| "Freezing-point depression means the solution freezes warmer" | Direction of the shift | Depression means the freezing point goes down (below 0 °C for water); elevation means the boiling point goes up |
| A volatile solute in Raoult's law | Nonvolatile solute | Raoult's law as written assumes the solute does not contribute to vapor pressure; a volatile solute (e.g., alcohol in water) complicates the calculation |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Think of water molecules as students trying to leave a classroom (escape as vapor). A solute particle is a big desk blocking the door: every desk you add blocks a little more, no matter whether the desk is red or blue. With desks in the way, the class "boils" only when it is hotter, "freezes" only when it is colder, and water on the other side of a special door rushes toward the room with more desks. Only the number of desks matters — never their color.
Worked example
Example 1: Freezing-point depression with antifreeze
A car radiator holds 250.0 g of water mixed with 45.0 g of ethylene glycol (C₂H₆O₂, molar mass 62.07 g mol⁻¹). At what temperature does this solution freeze?
Formula first: ΔTf = Kf m, then freezing point = 0.00 °C - ΔTf.
Step 1 — moles of solute:
n = 45.0 g62.07 g mol-1 = 0.725 mol
(Unit check: g ÷ g mol⁻¹ = mol ✓)
Step 2 — molality:
m = 0.725 mol0.2500 kg = 2.90 mol kg-1 = 2.90 m
Step 3 — temperature change:
ΔTf = (1.86 °C kg mol-1)(2.90 mol kg-1) = 5.39 °C
(Unit check: (°C kg mol⁻¹)(mol kg⁻¹) = °C ✓)
Step 4 — freezing point:
Tf = 0.00 °C - 5.39 °C = -5.39 °C
This coolant freezes near −5.4 °C instead of 0 °C — enough protection for a mild winter day.
Example 2: Boiling-point elevation with an electrolyte
11.7 g of NaCl (molar mass 58.44 g mol⁻¹) is dissolved in 500.0 g of water. What is the boiling point of the solution?
Formula first: ΔTb = i Kb m, then boiling point = 100.00 °C + ΔTb.
Step 1 — moles and molality:
nNaCl = 11.7 g58.44 g mol-1 = 0.200 mol
m = 0.200 mol0.5000 kg = 0.400 mol kg-1
Step 2 — apply the van't Hoff factor. NaCl dissociates into Na⁺ and Cl⁻, so i = 2:
ΔTb = (2)(0.512 °C kg mol-1)(0.400 mol kg-1) = 0.410 °C
Step 3 — boiling point:
Tb = 100.00 °C + 0.410 °C = 100.41 °C
Notice the electrolyte doubles the effect: without the factor i = 2, the predicted elevation would be only 0.205 °C — a classic exam trap.
Example 3: Finding concentration from osmotic pressure
A protein solution exerts an osmotic pressure of 0.100 atm at 25 °C. What is its molarity?
Formula first: Π= MRT, so rearrange to M = ΠRT.
Substitution:
M = 0.100 atm(0.08206 L atm mol-1K-1)(298.15 K) = 4.09 × 10-3 mol L-1
(Unit check: atm ÷ (L atm mol⁻¹ K⁻¹ × K) = mol L⁻¹ ✓)
A molarity of only about 4 × 10-3 M produces a measurable osmotic pressure — this sensitivity is exactly why osmotic pressure is used to find molar masses of macromolecules, which are far too dilute to measure by freezing-point methods.
Key takeaways
- A colligative property depends on the number of solute particles, never their identity.
- The four colligative properties: vapor-pressure lowering, boiling-point elevation, freezing-point depression, osmotic pressure.
- Raoult's law: PA = XA PA°, with lowering ΔP = XB PA°.
- Boiling-point elevation: ΔTb = Kb m; freezing-point depression: ΔTf = Kf m.
- Osmotic pressure: Π= MRT — the most sensitive colligative property.
- Water constants: Kb = 0.512 °C/m, Kf = 1.86 °C/m.
- Electrolytes multiply every colligative effect by the van't Hoff factor i (NaCl → 2, CaCl₂ → 3).
- Use molality in boiling/freezing formulas; molality is temperature-independent because it is mass-based.
- For nonelectrolytes, 1 mole of solute ≈ 1 mole of particles; for strong electrolytes, 1 mole of solute ≈ i moles of particles.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
What makes a property "colligative," and what are the four colligative properties?
Show answer
A colligative property depends only on the number of solute particles, not their identity. The four are vapor-pressure lowering, boiling-point elevation, freezing-point depression, and osmotic pressure.
Which is larger for a given aqueous solution: ΔTf or ΔTb? Why?
Show answer
ΔTf is larger because Kf (1.86 °C/m) is about 3.6 times Kb (0.512 °C/m) for water — freezing-point depression is the more sensitive effect.
Which freezes at a lower temperature: a 1.0 m glucose solution or a 1.0 m NaCl solution? Explain.
Show answer
The NaCl solution. NaCl dissociates into two ions, so 1.0 m NaCl behaves like 2.0 m particles, and ΔTf = iKf m gives about 3.7 °C versus about 1.9 °C for glucose.
Why is molality preferred over molarity in the boiling- and freezing-point formulas?
Show answer
Molality is based on solvent mass, which does not change with temperature; molarity is based on solution volume, which changes with temperature. The colligative measurement itself involves temperature change.
What is the van't Hoff factor for CaCl₂, and how does it enter the osmotic-pressure formula?
Show answer
CaCl₂ dissociates into 3 ions, so i = 3; the osmotic pressure becomes Π= iMRT.
A 0.10 M nonelectrolyte solution at 25 °C — what osmotic pressure does it exert?
Show answer
Π= MRT = (0.10 mol L-1)(0.08206 L atm mol-1K-1)(298.15 K) ≈ 2.4 atm.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- colligative property
- A solution property that depends only on the number of solute particles, not their identity
- Raoult's law
- PA = XA PA°: solvent vapor pressure equals its mole fraction times the pure-solvent vapor pressure
- molality (m)
- Moles of solute per kilogram of solvent (mol kg⁻¹)
- van't Hoff factor (i)
- Number of particles a formula unit produces on dissolving
- osmotic pressure (Pi)
- Pressure needed to stop solvent flow through a semipermeable membrane
- semipermeable membrane
- A barrier that lets solvent pass but blocks solute particles
- nonelectrolyte
- A solute that dissolves without forming ions (e.g., sugar)
Sources & references
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