Ever wondered why a sugar‑water solution boils hotter than pure water?
💡 In Simple Words: A solution is just a mixture where something (the solute) disappears into another thing (the solvent). Colligative properties are tricks that depend only on how many solute particles are present, not what they are.
What is a Solution?
A solution is a homogeneous (uniform) mixture of two or more substances. The solvent is the part that does the dissolving – usually a liquid like water. The solute is the part that gets dissolved – sugar, salt, or even a gas.
Think of the solvent as a river and the solute as pebbles you drop in. The river keeps flowing, but the pebbles spread out evenly throughout the water.
Key terms you’ll meet
- Molality (m): moles of solute per kilogram of solvent. It’s handy because it doesn’t change with temperature.
- Van’t Hoff factor (i): the number of particles a solute creates in solution. For NaCl, i≈2 because it splits into Na⁺ and Cl⁻.
- Ebullioscopic constant (Kb): a number that tells how much the boiling point of a solvent rises per molal unit.
- Cryoscopic constant (Kf): similar to Kb, but for freezing point depression.
Colligative Properties – The Big Picture
Colligative properties are those that depend only on the count of dissolved particles, not on their chemical identity. It’s like a crowd at a concert – the louder the noise depends on how many people are there, not on whether they’re wearing red or blue shirts.
Boiling Point Elevation
When you add a non‑volatile solute (one that doesn’t evaporate) to a solvent, the solution needs a higher temperature to boil. The rise, ΔTb, follows
ΔTb = i·Kb·m
where i is the van’t Hoff factor, Kb is the ebullioscopic constant, and m is the molality.
Example: Find the boiling point of a 0.5 m NaCl solution. Water’s Kb = 0.512 °C·kg/mol and i≈2.
- ΔTb = 2 × 0.512 × 0.5 = 0.512 °C.
- Pure water boils at 100 °C, so the solution boils at 100 + 0.512 = 100.512 °C.
Freezing Point Depression
Adding solute also makes a liquid freeze at a lower temperature. The drop, ΔTf, is given by
ΔTf = i·Kf·m
For water, Kf = 1.86 °C·kg/mol.
Example: What’s the freezing point of a 1.0 m glucose (i=1) solution?
- ΔTf = 1 × 1.86 × 1.0 = 1.86 °C.
- Pure water freezes at 0 °C, so the solution freezes at –1.86 °C.
Vapor Pressure Lowering
Raoult’s law says the vapor pressure of the solvent above a solution is proportional to its mole fraction (the part of the total moles that belongs to the solvent).
Psolution = Xsolvent·P°solvent
Here, P° is the vapor pressure of the pure solvent, and X is the mole fraction.
Example: A solution contains 0.9 mol water and 0.1 mol ethanol. Water’s pure vapor pressure at 25 °C is 23.8 mm Hg.
- Xwater = 0.9 / (0.9+0.1) = 0.9.
- Pwater,solution = 0.9 × 23.8 = 21.4 mm Hg.
Osmotic Pressure
Osmotic pressure (π) is the pressure needed to stop water from flowing through a semipermeable membrane into a solution. It follows
π = i·M·R·T
where M is molarity (moles per litre), R is the gas constant (0.0821 L·atm·K⁻¹·mol⁻¹), and T is temperature in Kelvin.
Example: Calculate π for a 0.2 M urea solution at 298 K (i=1).
- π = 1 × 0.2 × 0.0821 × 298 ≈ 4.9 atm.
Quick Comparison of Colligative Properties
| Property | Direction of Change | Key Formula |
|---|---|---|
| Boiling point | Increases | ΔTb = i·Kb·m |
| Freezing point | Decreases | ΔTf = i·Kf·m |
| Vapor pressure | Decreases | P = Xsolvent·P° |
| Osmotic pressure | Increases | π = i·M·R·T |
How to Solve a Colligative Property Question
📝 Likely Exam Questions
- Question: A 1.5 m solution of KBr (i≈2) raises the boiling point of water by how much?
Answer: ΔTb = 2 × 0.512 × 1.5 = 1.536 °C; boiling point = 101.536 °C. - Question: Explain why the freezing point of a solution depends only on the number of solute particles and not on their nature.
Answer: Colligative properties are governed by entropy changes that relate to particle count; identity cancels out in the derivation. - Question: Calculate the osmotic pressure of a 0.05 M NaCl solution at 310 K. (Assume i=2.)
Answer: π = 2 × 0.05 × 0.0821 × 310 ≈ 2.55 atm. - Question: A solution has a vapor pressure of 18 mm Hg at 25 °C. Pure solvent pressure is 23.8 mm Hg. Find the mole fraction of the solvent.
Answer: X = 18 / 23.8 ≈ 0.756.