Solubility Product (Ksp): JEE Main Chemistry Guide

Solubility product is a compact but powerful topic in JEE Main ionic equilibrium, contributing one to two questions per session. The concept is simple — Ksp is the equilibrium constant for the dissolution of a sparingly soluble salt — but JEE Main tests it in several ways: basic solubility calculations, common ion effect, ionic product vs. Ksp comparison for precipitation, and selective precipitation. This guide covers all of them.

Ksp: Definition and Expression

For a sparingly soluble salt AgCl: AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq). Ksp = [Ag⁺][Cl⁻]. For Ag₂CrO₄: Ag₂CrO₄ ⇌ 2Ag⁺ + CrO₄²⁻. Ksp = [Ag⁺]²[CrO₄²⁻]. General rule: Ksp = ∏[ions]^stoichiometric coefficient. Note: solids are excluded from the expression. JEE Main tests writing the Ksp expression for various salts — know the stoichiometry of the dissolution.

Solubility s and Ksp relationship: for AB type (e.g., AgCl): s = √(Ksp). For AB₂ type (e.g., PbCl₂): Ksp = 4s³, so s = (Ksp/4)^(1/3). For A₂B type (e.g., Ag₂CrO₄): Ksp = 4s³ (same form). For A₂B₃ type: Ksp = 108s⁵. JEE Main tests computing s given Ksp and vice versa. Watch the stoichiometry — PbCl₂ gives [Pb²⁺] = s and [Cl⁻] = 2s, so Ksp = s × (2s)² = 4s³. For broader ionic equilibrium coverage, see our Ionic Equilibrium Guide.

Common Ion Effect on Solubility

Adding a common ion decreases solubility (Le Chatelier — equilibrium shifts left). Example: solubility of AgCl in 0.1 M NaCl. [Cl⁻] ≈ 0.1 M (from NaCl, much larger than from AgCl dissolution). [Ag⁺] = Ksp/[Cl⁻] = 1.8 × 10⁻¹⁰ / 0.1 = 1.8 × 10⁻⁹ M. Solubility in pure water: s = √(1.8 × 10⁻¹⁰) = 1.34 × 10⁻⁵ M. Common ion reduces solubility by factor ~7500. JEE Main gives Ksp and common ion concentration — calculate new solubility. Take a free mock test on ionic equilibrium to practise Ksp and common ion calculations.

Ionic Product (Q) and Precipitation

Ionic product Q is calculated from actual concentrations (not equilibrium concentrations). Compare Q with Ksp: Q < Ksp → solution is unsaturated, no precipitation. Q = Ksp → solution is saturated, at equilibrium. Q > Ksp → precipitation occurs until Q = Ksp. JEE Main sets up scenarios: two solutions are mixed, what is Q, does precipitation occur? Calculate the concentrations after mixing (using dilution: new concentration = original × volume/total volume), then compute Q and compare to Ksp.

Selective Precipitation

When a solution contains two different anions, adding a precipitating cation can selectively precipitate one salt before the other. The ion that forms the salt with smaller Ksp precipitates first. Example: solution contains both Cl⁻ and CrO₄²⁻. Adding Ag⁺: AgCl (Ksp = 1.8 × 10⁻¹⁰) precipitates before Ag₂CrO₄ (Ksp = 1.1 × 10⁻¹²). Wait — Ag₂CrO₄ has smaller Ksp but that doesn't directly determine which precipitates first because the stoichiometry differs. The ion that precipitates first is the one that requires less Ag⁺ to begin precipitation, i.e., the one with smaller [Ag⁺]_required to exceed Ksp: for AgCl: [Ag⁺] = Ksp/[Cl⁻]; for Ag₂CrO₄: [Ag⁺] = √(Ksp/[CrO₄²⁻]). Compare these to determine which precipitates at lower [Ag⁺].

Simultaneous Equilibria

Ksp is affected by pH when the anion is from a weak acid. Example: CaF₂ is more soluble in acidic solution than in neutral solution — because F⁻ reacts with H⁺ to form HF, decreasing [F⁻] and shifting the dissolution equilibrium to the right. Mg(OH)₂ dissolves in acidic solution: Mg(OH)₂ ⇌ Mg²⁺ + 2OH⁻; OH⁻ + H⁺ → H₂O. The solubility of metal hydroxides decreases as pH increases (more OH⁻ → common ion effect) and increases as pH decreases. JEE Main tests these pH-dependent solubility trends qualitatively.

Exam Strategy

Ksp problems have a fixed structure: write the expression, substitute stoichiometry, solve for the unknown. The most common error is the AB₂ stoichiometry — if s moles dissolve, [A²⁺] = s but [B⁻] = 2s. Always write out the dissolution equation and the ion concentrations in terms of s before substituting into Ksp. For the buffer and pH context, see our Buffer Solutions Guide. For complete physical chemistry, see our Chemical Equilibrium Guide. Upgrade for ₹149/month for 100+ Ksp problems at every difficulty level.