Solutions: Raoult's Law & Colligative Properties

Solutions chemistry connects intermolecular interactions to measurable physical properties. JEE emphasises colligative property calculations, Raoult's law applications, and the van't Hoff factor for electrolytes.

Types of Solutions: Solid in liquid (NaCl in water), liquid in liquid (ethanol in water), gas in liquid (CO₂ in soda). Concentration units: molarity (M = mol/L solution), molality (m = mol/kg solvent), mole fraction (x), mass percentage, ppm. Molality is temperature-independent (uses mass, not volume). Molarity changes with temperature.

Raoult's Law: For ideal solutions: $P_{A}$ = $x_{A}$ * $P_{A_standard}$ and $P_{B}$ = $x_{B}$ * $P_{B_standard}$.
Total vapour pressure: $P_{total}$ = $x_{A}$ * $P_{A_standard}$ + $x_{B}$ * $P_{B_standard}$ = $P_{B_standard}$ + ($P_{A_standard}$ - $P_{B_standard}$) * $x_{A}$. $P_{total}$ is linear in mole fraction for ideal solutions.
Composition of vapour: $y_{A}$ = $\frac{P_{A}}{P_{total}}$ = $x_{A}$ * $P_{A_standard}$ / $P_{total}$. The more volatile component is enriched in the vapour phase.

Ideal vs Non-Ideal Solutions:

• Ideal: obey Raoult's law, $\delta_{H_mix}$ = 0, $\delta_{V_mix}$ = 0. Example: benzene + toluene, n-hexane + n-heptane.

Ideal solution pair:

Benzene

Toluene — similar intermolecular forces as benzene, forms ideal solution

• Positive deviation: $P_{total}$ > predicted by Raoult's law. Weaker A-B interactions than A-A and B-B. Example: ethanol + water, acetone + CS₂. Forms minimum boiling azeotrope.

Positive deviation pair:

Acetone

Carbon disulfide (CS₂) — weaker A-B interactions than A-A or B-B

• Negative deviation: $P_{total}$ < predicted. Stronger A-B interactions. Example: acetone + chloroform, HCl + water. Forms maximum boiling azeotrope.

Negative deviation pair (acetone + chloroform):

Chloroform (CHCl₃) — forms H-bond with acetone's C=O, stronger A-B interaction

Azeotropes: Constant boiling mixtures that cannot be separated by simple distillation. Minimum boiling azeotrope: positive deviation, boils below both pure components. Maximum boiling azeotrope: negative deviation, boils above both pure components.

Henry's Law: For gases dissolved in liquids: $P_{gas}$ = $K_{H}$ * $x_{gas}$ (where $K_{H}$ is Henry's constant).
High $K_{H}$ = low solubility. Gas solubility increases with pressure and decreases with temperature. Applications: carbonated drinks (CO₂ under pressure), deep-sea diving (nitrogen narcosis), oxygen transport in blood.

Colligative Properties: Depend only on the number of solute particles, not their identity: 1.
Relative lowering of vapour pressure: $\frac{\delta_{P}}{P_{standard}}$ = $x_{solute}$ = $n_{solute}$/($n_{solute}$ + $n_{solvent}$). 2. Elevation of boiling point: $\delta_{Tb}$ = Kb * m * i (where Kb = molal elevation constant). 3. Depression of freezing point: $\delta_{Tf}$ = Kf * m * i (where Kf = molal depression constant). 4. Osmotic pressure: $\pi$ = iMRT (M = molarity, R = 0.0821 L.atm/(mol.K)).

Kb and Kf: Kb = R * $Tb^{2}$ * $M_{solvent}$ / (1000 * $\delta_{H_vap}$).
Kf = R * $Tf^{2}$ * $M_{solvent}$ / (1000 * $\delta_{H_fus}$).
For water: Kb = 0.512 K.kg/mol, Kf = 1.86 K.kg/mol.

Van't Hoff Factor (i): i = observed colligative property / calculated colligative property (for non-electrolyte). For electrolytes: i = 1 + (n-1)$\alpha$, where n = number of ions per formula unit, $\alpha$ = degree of dissociation. For association: i = 1 + (1/n - 1)$\alpha$, where n = number of molecules associating. NaCl (n=2): i approaches 2 at full dissociation. CaCl₂ (n=3): i approaches 3. Acetic acid in benzene dimerises: i approaches 0.5.

Osmosis and Osmotic Pressure: Osmosis: spontaneous flow of solvent through a semipermeable membrane from dilute to concentrated side. Osmotic pressure: minimum pressure needed to prevent osmosis.
$\pi$ = iCRT (C = molarity). Isotonic solutions have equal osmotic pressure. Hypertonic: higher $\pi$. Hypotonic: lower $\pi$. Reverse osmosis: applying P > $\pi$ to force solvent from concentrated to dilute side (water purification).

Abnormal Molar Mass: When a solute dissociates (electrolyte), colligative properties are larger than expected — molar mass appears lower (i > 1). When a solute associates, colligative properties are smaller — molar mass appears higher (i < 1).