Ionic Equilibrium

Concept overview

Ionic equilibrium takes the equilibrium framework and applies it to weak acids, weak bases, salts, buffers and sparingly soluble ionic solids. The workhorse quantities are the acid dissociation constant K_a, the base dissociation constant K_b, the water ionic product K_w = 1.0 × 10⁻¹⁴ at 25°C, and the solubility product K_sp for sparingly soluble salts.

pH is defined as −log[H⁺]. For a strong acid or strong base you compute [H⁺] or [OH⁻] directly. For a weak acid, [H⁺] ≈ √(K_a × C) when α is small — a useful approximation but one you must verify. For salts of a weak acid and strong base (like sodium acetate), the salt hydrolyses to give a mildly basic solution; the anion behaves as a weak base with K_b = K_w/K_a.

Buffers resist pH change. A weak-acid buffer uses the Henderson-Hasselbalch equation: pH = pK_a + log([salt]/[acid]). This is a linear relation — as long as [salt]/[acid] stays within about a factor of 10 (i.e., ±1 pH unit around pK_a), the buffer works. Blood at pH 7.4 is a classic bicarbonate buffer example.

Solubility product K_sp = [cation]ⁿ[anion]ᵐ for a sparingly soluble salt A_nB_m ⇌ nA + mB. The common ion effect suppresses solubility — adding NaCl to a saturated solution of AgCl decreases the concentration of Ag⁺ that can coexist with the added Cl⁻. This is why silver halides are 'more insoluble' in salty water than in pure water.

Key formulas & concepts

• K_w at 25°C: K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴
• pH: pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14 (at 25°C)
• K_a of weak acid: [H⁺] ≈ √(K_a × C) when α is small
• K_a × K_b: K_a × K_b = K_w
• Henderson-Hasselbalch: pH = pK_a + log([salt]/[acid])
• K_sp of A_nB_m: K_sp = [A⁺]ⁿ × [B⁻]ᵐ
• Common ion effect: Adding common ion decreases the other ion's concentration proportionally

Common mistakes to avoid

• Using the [H⁺] = √(K_a × C) approximation when α is 20% or more — always check α = √(K_a/C) at the end.
• Applying pH + pOH = 14 at temperatures other than 25°C — K_w depends on T.
• Forgetting that K_a is the equilibrium constant for HA ⇌ H⁺ + A⁻ (not the reverse) — this matters for hydrolysis calculations.
• Adding K_sp values instead of comparing Q with K_sp when predicting precipitation.

JEE Main relevance

JEE Main asks 2–3 ionic equilibrium problems every paper: one pH numerical (strong or weak acid/base), one buffer calculation via Henderson-Hasselbalch, and often one K_sp or common-ion problem. All three archetypes recycle every 2–3 years.

JEE Advanced relevance

Advanced ionic-equilibrium problems combine multiple equilibria — for example, a weak acid dissolved in a buffer, or a salt whose cation hydrolyses while its anion doesn't. Selective precipitation problems (which cation precipitates first as you add a common ion?) are also common at the Advanced level.

Previous-year questions (PYQ)

Filter the PYQ bank by 'Ionic Equilibrium' and drill three passes — pH/pOH, buffers, and K_sp. Do not mix them until each is fluent — the algebraic setup for each archetype is different.