Learning Objectives
- Understand different types of solutions and concentration terms
- Study Raoult's law and colligative properties
- Learn about ideal and non-ideal solutions
- Calculate molecular mass from colligative properties
- Understand van't Hoff factor and abnormal molar masses
Key Concepts
Types of Solutions
Solutions can be solid-solid, solid-liquid, liquid-liquid, gas-liquid, etc. Most commonly studied: solid in liquid and liquid-liquid.
Concentration Terms
Molarity (M): moles of solute / L of solution. Temperature dependent (volume changes).
Molality (m): moles of solute / kg of solvent. Temperature independent.
Mole fraction (x): xₐ = nₐ/(nₐ + n_b). Mass %: (mass solute/mass solution) × 100.
ppm: parts per million = (mass solute/mass solution) × 10⁶.
Solubility
Henry's Law: p = KH × x (partial pressure of gas ∝ mole fraction in solution). Applications: deep sea diving (bends), carbonated drinks.
Solubility of gases decreases with temperature increase.
Raoult's Law
For volatile solutes: p_A = x_A × p°_A and p_B = x_B × p°_B. Total pressure: P = p_A + p_B.
For non-volatile solute: p = x_solvent × p°_solvent. Relative lowering of vapour pressure: (p° - p)/p° = x_solute.
Ideal and Non-Ideal Solutions
Ideal: Obey Raoult's law. ΔH_mix = 0, ΔV_mix = 0. Example: benzene + toluene, n-hexane + n-heptane.
Positive deviation: P_total > Raoult's law. Weaker A-B interactions. ΔH > 0, ΔV > 0. Example: ethanol + water, acetone + CS₂. Form minimum boiling azeotrope.
Negative deviation: P_total < Raoult's law. Stronger A-B interactions. ΔH < 0, ΔV < 0. Example: chloroform + acetone, HCl + water. Form maximum boiling azeotrope.
Azeotropes: Constant boiling mixtures that cannot be separated by distillation.
Colligative Properties
Properties that depend on the number of solute particles, not their nature.
1. Relative lowering of vapour pressure: (p° - p)/p° = x₂ = n₂/(n₁ + n₂)
2. Elevation of boiling point: ΔT_b = K_b × m (K_b = molal elevation constant).
3. Depression of freezing point: ΔT_f = K_f × m (K_f = molal depression constant/cryoscopic constant).
4. Osmotic pressure: π = CRT = (n₂/V)RT. Used for high molecular mass solutes (polymers, proteins).
K_b = RT²_b M₁/(1000 × ΔH_vap); K_f = RT²_f M₁/(1000 × ΔH_fus).
Determination of Molar Mass
M₂ = K_b × w₂ × 1000 / (ΔT_b × w₁) [from boiling point elevation]
M₂ = K_f × w₂ × 1000 / (ΔT_f × w₁) [from freezing point depression]
M₂ = w₂RT / (πV) [from osmotic pressure]
Abnormal Molar Mass and van't Hoff Factor
van't Hoff factor: i = observed colligative property / calculated colligative property = normal molar mass / observed molar mass.
For dissociation: i > 1 (more particles). For association: i < 1 (fewer particles).
i = 1 + (n-1)α (for dissociation into n ions, α = degree of dissociation).
Modified equations: ΔTb = iKbm, ΔTf = iKfm, π = iCRT.
Summary
Solutions are described by various concentration terms. Raoult's law relates vapour pressure to mole fraction. Deviations lead to azeotropes. Four colligative properties depend on solute particle count. Molar mass is determined from colligative property measurements. The van't Hoff factor accounts for dissociation or association of solutes.
Important Terms
- Raoult's Law: Vapour pressure of component ∝ its mole fraction
- Colligative Property: Depends on number of solute particles
- Azeotrope: Constant boiling mixture
- Osmotic Pressure: Minimum pressure to prevent osmosis
- Henry's Law: Gas solubility ∝ partial pressure
- van't Hoff Factor (i): Accounts for association/dissociation
Quick Revision
- Raoult: p = x × p°; Henry: p = KH × x
- ΔTb = iKbm; ΔTf = iKfm; π = iCRT
- +ve deviation: weaker A-B bonds, min boiling azeotrope
- -ve deviation: stronger A-B bonds, max boiling azeotrope
- i > 1: dissociation; i < 1: association; i = 1: no change
- M₂ = Kf w₂ × 1000 / (ΔTf × w₁)