Class 12 Chemistry Notes: Solutions (Chapter 2)
Master Chapter 2 of Class 12 Chemistry. Understand concentration units, Raoult's Law, colligative properties, van't Hoff factor, and abnormal molar masses with key formulas and PYQs.
The Solutions chapter introduces multiple ways to express concentration. Students try to memorise each formula separately — which leads to errors under pressure. The key distinction that separates the two most commonly confused units:
| Unit | Formula | Based On | Temperature Dependent? |
|---|---|---|---|
| Molarity (M) | moles of solute / L of solution | Volume of solution | Yes (volume changes with T) |
| Molality (m) | moles of solute / kg of solvent | Mass of solvent | No (mass is constant) |
| Mole Fraction (χ) | nₐ / (nₐ + n_B) | Moles of components | No |
| Mass % | (mass of solute / mass of solution) × 100 | Mass ratio | No |
⚠️ Watch Out! — Use Molality for Temperature-Variable Problems
Any question involving colligative properties at different temperatures, or asking for temperature-independent concentration, requires molality, not molarity.
Using molarity as a constant across temperature changes is one of the most frequent errors in this chapter.
2. Raoult's Law
Statement: The partial vapour pressure of any volatile component of a solution is equal to the vapour pressure of the pure component multiplied by its mole fraction in the solution.
pₐ = χₐ × p°ₐ
For a non-volatile solute, the total vapour pressure of the solution is lowered because the mole fraction of solvent decreases.
3. Deviations From Raoult's Law
| Type | Cause | Vapour Pressure | Example |
|---|---|---|---|
| Positive Deviation | Solute–solvent interactions weaker than pure components | Higher than ideal | Ethanol + Water |
| Negative Deviation | Solute–solvent interactions stronger (e.g., H-bonding) | Lower than ideal | Chloroform + Acetone |
4. Colligative Properties — One Underlying Principle
All four colligative properties arise from the same cause: the presence of solute particles reduces the chemical potential of the solvent.
The Four Colligative Properties and Their Formulas
- Relative Lowering of Vapour Pressure: Δp/p° = χ_solute
- Elevation of Boiling Point: ΔT_b = K_b × m
- Depression of Freezing Point: ΔT_f = K_f × m
- Osmotic Pressure: π = CRT (or π = nRT/V)
K_b and K_f are called the ebullioscopic constant and cryoscopic constant, and are properties of the solvent only (not the solute).
5. Van't Hoff Factor (i)
For electrolytes that dissociate in solution, the actual number of particles differs from the formula units dissolved. The van't Hoff factor corrects for this:
i = observed colligative property / calculated colligative property
- NaCl → Na⁺ + Cl⁻ → i = 2
- CaCl₂ → Ca²⁺ + 2Cl⁻ → i = 3
- Acetic acid in benzene (forms dimers) → i = 0.5
Summary: Formula Sheet
| Concept | Formula |
|---|---|
| Mole Fraction of solvent | χ₁ = n₁ / (n₁ + n₂) |
| Raoult's Law | p₁ = χ₁ × p°₁ |
| Boiling point elevation | ΔT_b = i × K_b × m |
| Freezing point depression | ΔT_f = i × K_f × m |
| Osmotic pressure | π = iCRT |
| Molar mass from ΔT_f | M₂ = (1000 × K_f × w₂) / (ΔT_f × w₁) |
Practice Questions (PYQs)
- Define molality and molarity. Why is molality preferred over molarity in expressing concentration for colligative property calculations?
- The vapour pressure of pure water at 298 K is 23.8 mm Hg. What is the vapour pressure of a solution containing 18 g of glucose dissolved in 90 g of water?
- What is the van't Hoff factor? Calculate i for K₂SO₄ assuming complete dissociation.
- 1.8 g of glucose (M = 180 g/mol) is dissolved in 100 g of water. Calculate the elevation in boiling point. (K_b for water = 0.52 K·kg/mol)
- Distinguish between positive and negative deviations from Raoult's Law with one example each. What causes each type of deviation?