Chemistry: Atoms First 2e · Solutions and Colloids
Colligative Properties
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Dissolving a solute in a solvent changes more than composition — it changes four measurable properties of the solvent: vapor pressure, boiling point, freezing point, and osmotic pressure. These are called colligative properties because they depend only on the number of dissolved solute particles, not on their identity: one mole of glucose and one mole of urea lower water's freezing point by the same amount.
The key quantity is the concentration of particles — total solute units (molecules or ions) per unit of solvent — which is why 1 m NaCl (two ions per formula unit) has roughly twice the freezing-point effect of 1 m glucose. This topic covers the four colligative properties, their equations, and the van't Hoff factor that corrects for ionic dissociation.
Why this matters
- Antifreeze and de-icing: ethylene glycol lowers engine coolant's freezing point; road salt melts ice by depressing water's freezing point.
- Cooking and food science: salt raises water's boiling point and lowers the freezing point of ice cream mix — why ice cream recipes call for salt.
- Medicine: IV fluids must be isotonic (matched osmotic pressure) with blood; a mismatch can rupture red blood cells (hemolysis) or shrivel them (crenation).
- Exam value: colligative-property calculations are a guaranteed problem type, and the van't Hoff factor is the classic trap.
The college version
Core Concepts
What "number of particles" means
A Colligative property A solution property depending only on the number of solute particles. Full entry → counts solute particles in solution, not moles of solute added. A nonelectrolyte (glucose, urea) contributes 1 particle per formula unit; a strong electrolyte contributes its full ion count. The van't Hoff factor i is the number of particles each formula unit produces:
- Nonelectrolytes: i = 1
- NaCl, KBr, NaOH: i = 2
- CaCl₂, Ba(NO₃)₂, Na₂SO₄: i = 3
Real solutions fall slightly short of these ideal values because ions associate, but ideal values are standard for introductory work.
Vapor-pressure lowering (Raoult's law)
A pure solvent has a characteristic vapor pressure. Adding a nonvolatile solute lowers it: solute particles crowd the surface and block solvent molecules from escaping. Raoult's law Vapor pressure of solvent in solution = mole fraction × pure vapor pressure. Full entry → states that the vapor pressure of the solvent in solution equals its mole fraction times the pure solvent's vapor pressure:
Psolution = χsolvent P°solvent
where P°solvent is the pure solvent's vapor pressure and χsolvent is its mole fraction in solution. Since the mole fraction is always less than 1, vapor pressure always drops when solute is added.
Boiling-point elevation
A liquid boils when its vapor pressure equals the external pressure; since solute lowers that pressure, the solution must be heated hotter before it boils. The boiling-point elevation is proportional to the molal particle concentration:
ΔTb = i Kb m
where ΔTb is the elevation, Kb is the solvent's molal boiling-point-elevation constant (water: Kb = 0.512 °C/m), and m is the molality (moles of solute per kilogram of solvent).
Freezing-point depression
Solute particles interfere with solvent molecules packing into a crystal lattice, so the solution must be cooled below the pure solvent's freezing point. The depression is also proportional to particle molality:
ΔTf = i Kf m
where Kf is the molal freezing-point-depression constant (water: Kf = 1.86 °C/m). Since Kf > Kb for water, freezing-point depression is the more sensitive effect — why salt melts ice so effectively.
Osmotic pressure
If two solutions of different concentration are separated by a Semipermeable membrane Barrier that lets solvent pass but blocks solute. Full entry → (permeable to solvent, not solute), solvent flows from the dilute side to the concentrated side — Osmosis Solvent flow through a semipermeable membrane toward higher solute concentration. Full entry →. The pressure needed to stop this flow is the osmotic pressure:
Π= i M R T
where M is the molarity, R is the gas constant (0.08206 L·atm·mol-1K-1), and T is the absolute temperature. Osmotic pressure is the largest of the four effects — a 0.1 M solution at 25 °C exerts roughly 2.4 atm — which is why it is the method of choice for measuring molar masses of large molecules like proteins.
Why molality, not molarity?
Molality m = moles of solute per kilogram of solvent — independent of temperature and volume. Molarity M = moles per liter of solution, which changes with temperature as liquids expand. Freezing- and boiling-point data use molality because solvent mass is fixed and colligative effects depend on the solute-to-solvent particle ratio.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Molality (m) | Molarity (M) | Molality = mol solute per kg solvent (used in ΔTb, ΔTf); molarity = mol solute per L solution (used in Π). |
| Colligative effect | Solute identity | The number of particles matters; identity (size, color, charge) does not — only dissociation changes the count. |
| Boiling-point elevation | Freezing-point depression | Both follow ΔT = i K m, but Kf (1.86) > Kb (0.512), so freezing is more sensitive. |
| van't Hoff factor | Stoichiometric coefficient | i counts particles in solution: NaCl → 2, CaCl₂ → 3; it is not the coefficient in a balanced equation. |
| Mole fraction | Molality | Mole fraction χ is used in Raoult's law for vapor pressure; molality is used in ΔTb and ΔTf. |
| Osmosis direction | "Water goes where it's wetter" | Water flows from the dilute side (higher solvent concentration) to the concentrated side — toward more solute. |
| Freezing-point depression | Negative ΔTf | ΔTf is a positive magnitude; the new freezing point is Tf = 0 - ΔTf. Don't double-subtract. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
A crowded swimming pool: each swimmer (solute particle) makes it a little harder for water to escape into the air, keeps it liquid longer when cold, and makes it boil later when hot. It doesn't matter if the swimmer is big or small — only how many there are. That's a colligative property: the effect depends on the number of particles, not their identity.
Worked example
Worked example 1 — freezing point of a NaCl solution. What is the freezing point of a solution made by dissolving 11.7 g of NaCl in 500.0 g of water? (Kf(water) = 1.86 °C/m, molar mass NaCl = 58.44 g/mol)
Step 1 — moles of solute (dimensional analysis):
11.7 g NaCl × 1 mol NaCl58.44 g NaCl = 0.200 mol NaCl
Step 2 — molality:
m = 0.200 mol0.5000 kg water = 0.400 m
Step 3 — freezing-point depression with i = 2 (NaCl → Na⁺ + Cl⁻):
ΔTf = i Kf m
ΔTf = (2)(1.86 °C/m)(0.400 m) = 1.49 °C
Step 4 — new freezing point:
Tf = 0.000 °C - 1.49 °C = -1.49 °C
The solution freezes at -1.49 °C; forgetting the van't Hoff factor would give -0.744 °C, a factor-of-2 error.
Worked example 2 — boiling point of a glucose solution. A solution contains 18.0 g of glucose (C₆H₁₂O₆, molar mass 180.16 g/mol) in 250.0 g of water. At what temperature does it boil? (Kb(water) = 0.512 °C/m, glucose is a nonelectrolyte, i = 1)
Step 1 — moles and molality:
18.0 g glucose × 1 mol180.16 g = 0.0999 mol
m = 0.0999 mol0.2500 kg = 0.400 m
Step 2 — boiling-point elevation:
ΔTb = i Kb m
ΔTb = (1)(0.512 °C/m)(0.400 m) = 0.205 °C
Step 3 — new boiling point:
Tb = 100.000 °C + 0.205 °C = 100.205 °C
The solution boils at 100.205 °C; the same molality of NaCl would give 2 × 0.205 = 0.410 °C — particle count, not mass, drives the effect.
Worked example 3 — osmotic pressure of an IV saline solution. Normal saline is 0.154 M NaCl at body temperature (37 °C). What is its osmotic pressure? (R = 0.08206 L·atm·mol-1K-1, i = 2)
Π= i M R T
Π= (2)(0.154 mol/L)(0.08206 L·atmmol·K)(310 K)
Π= 7.8 atm
This is why normal saline is safe to infuse: its osmotic pressure matches blood plasma, so red blood cells neither swell nor shrink.
Key takeaways
- Colligative properties depend on the number of particles, not particle identity: vapor-pressure lowering, boiling-point elevation, freezing-point depression, osmotic pressure.
- Raoult's law: Psolution = χsolvent P°solvent — adding nonvolatile solute lowers vapor pressure.
- Boiling-point elevation: ΔTb = i Kb m; water Kb = 0.512 °C/m.
- Freezing-point depression: ΔTf = i Kf m; water Kf = 1.86 °C/m.
- Osmotic pressure: Π= i M R T — the largest colligative effect.
- van't Hoff factor i: nonelectrolyte 1; NaCl 2; CaCl₂ 3. Multiply the colligative effect by i.
- Colligative equations use molality m (mol solute/kg solvent), except osmotic pressure which uses molarity M.
- Adding solute always lowers vapor pressure and freezing point and raises boiling point.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
Name the four colligative properties and state what they all depend on.
Show answer
Vapor-pressure lowering, boiling-point elevation, freezing-point depression, and osmotic pressure — all depend on the number of solute particles (not their identity).
What is the van't Hoff factor for CaCl₂, and why is it not 3.0 in a real solution?
Show answer
i = 3 (Ca²⁺ + 2 Cl⁻). Real solutions fall slightly below ideal because ion pairing reduces the effective particle count at moderate concentrations.
A solution freezes at -2.79 °C. What is its particle molality? (Kf = 1.86 °C/m)
Show answer
ΔTf = i Kf m ⇒ m = ΔTfi Kf. For a nonelectrolyte, m = 2.791.86 = 1.50 m.
Which has the higher osmotic pressure at the same molarity: 0.10 M glucose or 0.10 M NaCl? Why?
Show answer
0.10 M NaCl, because it dissociates into two particles: Π= iMRT gives roughly double the osmotic pressure of glucose (i = 1).
Why is molality preferred over molarity in freezing-point calculations?
Show answer
Molality uses mass of solvent, which does not change with temperature or volume; molarity changes as the solution expands or contracts.
Road crews salt icy roads in winter. Explain in one or two sentences why the salt makes ice melt at temperatures below 0 °C.
Show answer
The salt dissolves into particles that lower the freezing point of water below the road temperature, so ice that would be stable melts.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Colligative property
- A solution property depending only on the number of solute particles.
- van't Hoff factor (i)
- Number of particles each solute formula unit produces in solution.
- Molality (m)
- Moles of solute per kilogram of solvent.
- Molarity (M)
- Moles of solute per liter of solution.
- Raoult's law
- Vapor pressure of solvent in solution = mole fraction × pure vapor pressure.
- Osmosis
- Solvent flow through a semipermeable membrane toward higher solute concentration.
- Osmotic pressure (Pi)
- Pressure required to stop osmosis.
- Semipermeable membrane
- Barrier that lets solvent pass but blocks solute.
- molarity, M
- Moles of solute per liter of solution, mol/L.
Sources & references
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