Board exam focus — Solutions (CBSE & HBSE)

Types of solutions, concentration expressions (molarity, molality, mole fraction), Raoult's law, Henry's law, colligative properties (boiling point elevation, freezing point depression, osmotic pressure) and Van't Hoff factor.

Types of Solutions and Concentration Expressions

Solutions

Introduction

A solution is a homogeneous mixture of two or more substances. The substance present in larger amount is solvent; in smaller amount is solute.

Types of Solutions

Concentration Expressions

1. Mass percentage (w/w): % mass = (mass of solute / mass of solution) x 100 Example: 20% NaCl solution = 20 g NaCl in 100 g solution

2. Volume percentage (v/v): % volume = (volume of solute / volume of solution) x 100 Example: 70% ethanol = 70 mL ethanol in 100 mL solution

3. Molarity (M): M = moles of solute / volume of solution (in litres) Units: mol/L (or mol/dm^3) Depends on temperature (volume changes with T)

4. Molality (m): m = moles of solute / mass of solvent (in kg) Units: mol/kg Independent of temperature (mass doesn't change) Preferred for colligative properties.

5. Mole fraction (x): xA = nA / (nA + nB) Sum of all mole fractions = 1 Dimensionless.

6. Normality (N): N = equivalents of solute / volume of solution (in litres) N = M x n-factor

7. Parts per million (ppm): ppm = (mass of component / total mass of solution) x 10^6 Used for trace amounts.

Solubility

Solubility of solid in liquid increases with temperature (usually). Solubility of gas in liquid:

• Decreases with temperature (Henry's law: concentration proportional to partial pressure)
• p = KH x x (Henry's law; KH = Henry's constant)

Henry's Law

p = KH x x KH = Henry's law constant (characteristic of gas-solvent pair) Higher KH = lower solubility. Applications: Aerated drinks (CO2), diving physiology (N2 narcosis, decompression sickness).

Raoult's Law and Ideal/Non-ideal Solutions

Raoult's Law

Raoult's Law (1887)

For a solution of volatile liquids, the partial vapour pressure of each component is proportional to its mole fraction in solution.

pA = pA x xA where pA = partial VP of A in solution, pA = VP of pure A, xA = mole fraction of A.

Total pressure: P = pA + pB = pAxA + pBxB = pAxA + pB(1-xA) (for binary solution)

Relationship to concentration: As xA increases, pA increases linearly from 0 to pA. As xA → 0, pA → 0; as xA → 1, pA → pA.

Ideal Solutions

Solutions that obey Raoult's law over the entire range of composition. Conditions:

• A-B interactions ≈ A-A and B-B interactions
• No volume change on mixing
• No heat change on mixing (DeltaHmix = 0, DeltaVmix = 0)

Examples: Benzene + toluene, n-hexane + n-heptane, chlorobenzene + bromobenzene.

Non-Ideal Solutions

Deviate from Raoult's law.

Positive deviation: pA > pA xA and pB > pB xB A-B interactions weaker than A-A or B-B. DeltaHmix > 0, DeltaVmix > 0 (expansion on mixing) More volatile than ideal → boiling point LOWER than both components. Form minimum boiling azeotrope. Examples: Ethanol + water (95.6% EtOH, bp 78.1 C), acetone + CS2.

Negative deviation: pA < pA xA and pB < pB xB A-B interactions stronger than A-A or B-B. DeltaHmix < 0, DeltaVmix < 0 (contraction on mixing) Less volatile than ideal → boiling point HIGHER than both components. Form maximum boiling azeotrope. Examples: Chloroform + acetone, HNO3 + water (68% HNO3, bp 120 C).

Azeotropes

Mixtures with fixed boiling points that cannot be separated by simple distillation.

• Minimum boiling azeotrope: Positive deviation; bp lower than both components.
• Maximum boiling azeotrope: Negative deviation; bp higher than both components.

Ethanol-water mixture forms min boiling azeotrope at 95.6% ethanol (78.1 C). Cannot make 100% ethanol by distillation alone. Requires chemical drying agents or molecular sieves.

Colligative Properties

Colligative Properties

Introduction

Colligative properties depend only on the NUMBER of solute particles, not their nature (chemical identity). They arise from lowering of solvent chemical potential.

Four colligative properties:

1. Relative lowering of vapour pressure
2. Elevation of boiling point
3. Depression of freezing point
4. Osmotic pressure

1. Relative Lowering of Vapour Pressure (RLVP)

Raoul's law: p = p x x(solvent) Relative lowering: (p - p)/p* = x(solute) = n(solute) / [n(solute) + n(solvent)]

For dilute solution: ≈ n(solute) / n(solvent) Used to determine molar mass of solute.

2. Elevation of Boiling Point

Boiling point of solution > bp of pure solvent (less volatile due to solute). DeltaTb = Tb - Tb* = Kb x m Kb = molal elevation constant (ebullioscopic constant) Kb for water = 0.512 K kg/mol

Molar mass determination: M = (Kb x w x 1000) / (DeltaTb x W) where w = mass of solute, W = mass of solvent in g.

3. Depression of Freezing Point

Freezing point of solution < fp of pure solvent (solute interferes with crystal formation). DeltaTf = Tf* - Tf = Kf x m Kf = molal depression constant (cryoscopic constant) Kf for water = 1.86 K kg/mol Kf for benzene = 5.12 K kg/mol

Applications: Antifreeze in cars (ethylene glycol), salting roads in winter.

4. Osmotic Pressure

Osmosis: Solvent flows from lower to higher solute concentration through semipermeable membrane. Osmotic pressure: pi = CRT = nRT/V (Van't Hoff equation) where C = molar concentration, R = gas constant, T = temperature (K)

Applications: RO water purification (apply pressure > osmotic pressure), seawater desalination, IV drip fluids (isotonic).

Van't Hoff Factor (i)

For electrolytes that dissociate/associate in solution: i = observed colligative property / calculated colligative property = actual number of particles / number of particles if no dissociation

NaCl → Na+ + Cl- (i = 2 theoretically) CaCl2 → Ca2+ + 2Cl- (i = 3) Association: i < 1 (e.g., benzoic acid in benzene forms dimer, i ≈ 0.5)

Modified formulas: DeltaTb = i x Kb x m DeltaTf = i x Kf x m pi = i x CRT

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