Colligative Properties: JEE Main Complete Guide

Colligative properties — the four physical properties of solutions that depend on the number (not nature) of dissolved particles — are tested in every JEE Main Chemistry session. The four properties are: (1) relative lowering of vapour pressure, (2) elevation of boiling point, (3) depression of freezing point, and (4) osmotic pressure. Each has a single key formula, and the van't Hoff factor connects all four to the degree of dissociation or association. This guide covers every formula and every question type.

Relative Lowering of Vapour Pressure

Raoult's law for dilute solutions: P_solution = x_solvent × P°_solvent, where x_solvent is the mole fraction of solvent and P° is the vapour pressure of pure solvent. Relative lowering: (P° − P)/P° = x_solute = n_solute/(n_solute + n_solvent). For dilute solutions: (P° − P)/P° ≈ n_solute/n_solvent = w_solute × M_solvent/(M_solute × w_solvent). JEE Main uses this formula to determine molar mass of unknown solutes. Key point: relative lowering is independent of temperature — a classic JEE trap. For the general solutions chapter, see our Solutions Guide.

Elevation of Boiling Point

ΔT_b = K_b × m, where m is the molality (moles of solute per kg of solvent) and K_b is the ebullioscopic constant (specific to the solvent, units K·kg/mol). For water: K_b = 0.52 K·kg/mol. K_b = RT²b/(1000 × ΔH_vap), where T_b is the normal boiling point of pure solvent in K. JEE Main gives K_b and asks for the new boiling point: T'_b = T_b + ΔT_b. Common calculation: 18 g glucose (M=180) in 200 g water → molality = 0.1/0.2 = 0.5 mol/kg → ΔT_b = 0.52 × 0.5 = 0.26 K. Take a free mock test on solutions and colligative properties to practise these calculations.

Depression of Freezing Point

ΔT_f = K_f × m, where K_f is the cryoscopic constant. For water: K_f = 1.86 K·kg/mol. The relationship K_f/K_b = 1.86/0.52 ≈ 3.6 — K_f is always larger than K_b for the same solvent. Physical reason: freezing point depression is larger because the solvent's entropy change on freezing is larger than on vaporisation at the respective temperatures. JEE Main asks: if a solution of 5.85 g NaCl in 250 g water — what is the depression? NaCl dissociates into Na⁺ and Cl⁻ (van't Hoff factor i = 2). ΔT_f = i × K_f × m = 2 × 1.86 × (0.1/0.25) = 2 × 1.86 × 0.4 = 1.488 K ≈ 1.49°C.

Van't Hoff Factor and Degree of Dissociation

The van't Hoff factor i accounts for dissociation or association: i = (actual moles in solution)/(formula moles dissolved). For electrolytes: i > 1 (dissociation). For associated species (acetic acid in benzene dimers): i < 1. For non-electrolytes: i = 1. Degree of dissociation α for AB ⇌ A⁺ + B⁻: i = 1 + α. For A₂ ⇌ 2A: i = 1 + α. For AB ⇌ A + B: i = 1 + α. In general: i = 1 + (n−1)α, where n is the number of particles formed per formula unit. JEE Main gives experimental boiling point or freezing point data and asks for the degree of dissociation — compute i from the data and then solve for α.

Osmotic Pressure

Osmotic pressure π = CRT = (n/V)RT = iMRT, where C is molar concentration, R = 0.0821 L·atm/(mol·K), and T is in Kelvin. Van't Hoff equation: π = iCRT. Osmosis occurs when a semipermeable membrane separates a solution from pure solvent — solvent flows from low to high concentration. Reverse osmosis (RO): applying pressure greater than osmotic pressure forces solvent from solution to pure side — the basis of water purification.

Isotonic solutions have the same osmotic pressure. Hypertonic solution has higher osmotic pressure than cells — cells lose water (plasmolysis). Hypotonic solution has lower osmotic pressure — cells gain water (haemolysis for red blood cells). JEE Main tests isotonic solution calculations: two solutions are isotonic when C₁ = C₂ (for non-electrolytes) or i₁C₁ = i₂C₂ (for electrolytes).

Exam Strategy

Colligative properties questions are reliable mark sources in JEE Main. All four formulas are simple and the calculations are straightforward once you identify: (1) which colligative property is being asked, (2) what the solute is (electrolyte → i > 1, non-electrolyte → i = 1), and (3) what quantity the problem gives you (molality, molarity, mass of solute). Keep a formula card with K_b = 0.52, K_f = 1.86 for water. For the electrochemistry chapter where osmosis connects, see our Electrochemistry Guide. Upgrade for ₹149/month for 150+ solutions and colligative properties problems.