Equilibrium: Chemical & Ionic (pH, Buffer, Ksp)

Chemical equilibrium and ionic equilibrium form one of the highest-weightage topics in JEE Physical Chemistry. Mastery requires both conceptual understanding of Le Chatelier's principle and numerical fluency with pH, buffer, solubility, and equilibrium constant calculations.

Chemical Equilibrium: For a reversible reaction aA + bB <=> cC + dD, the equilibrium constant Kc = [C]^c[D]^d / [A]^a[B]^b. Only aqueous and gaseous species appear in the expression; pure solids and pure liquids are excluded (activity = 1). Kp = Kc(RT)^($\delta_{n_gas}$), where $\delta_{n_gas}$ = (c+d) - (a+b) for gaseous species only.

Relationship between K values: If a reaction is reversed, $K_{new}$ = 1/K. If multiplied by n, $K_{new}$ = K^n. If two reactions are added, $K_{new}$ = K₁ * K₂. These relationships are critical for combining equilibrium data.

Le Chatelier's Principle: When a system at equilibrium is disturbed, it shifts to counteract the disturbance. Adding reactant shifts right; adding product shifts left. Increasing pressure (for gas reactions) shifts toward the side with fewer moles of gas. Increasing temperature shifts toward the endothermic direction. A catalyst does NOT shift equilibrium — it only speeds attainment.

Reaction Quotient (Q): Q has the same form as K but uses current (non-equilibrium) concentrations. If Q < K, reaction proceeds forward. If Q > K, reaction proceeds backward. If Q = K, system is at equilibrium.

Ionic Equilibrium — Acids and Bases: Arrhenius: acids produce H+, bases produce OH-. Bronsted-Lowry: acids donate protons, bases accept protons. Lewis: acids accept electron pairs, bases donate electron pairs.

pH Scale: pH = -log[H+]. pOH = -log[OH-]. pH + pOH = 14 (at 25 degrees C). For strong acids, pH = -log($C_{acid}$) directly. For strong bases, pOH = -log($C_{base}$), then pH = 14 - pOH.

Weak Acid/Base Equilibrium:

Key weak acids and bases tested in JEE equilibrium problems:

Acetic acid (CH₃COOH) — the most commonly used weak acid example (Ka = 1.8 x $10^{-5}$)

Ammonia (NH₃) — the most commonly used weak base example (Kb = 1.8 x $10^{-5}$)

For weak acid HA with concentration C and dissociation constant Ka: Ka = C*$\alpha$² / (1 - $\alpha$), where $\alpha$ = degree of dissociation. If $\alpha$ << 1: Ka approximately equals C*$\alpha$², so $\alpha$ = $\sqrt{Ka/C}$. [H+] = C*$\alpha$ = $\sqrt{Ka * C}$, pH = ($\frac{1}{2}$)(pKa - log C) = ($\frac{1}{2}$)(pKa + pC).

For weak base B with Kb: [OH-] = $\sqrt{Kb * C}$, pOH = ($\frac{1}{2}$)(pKb + pC). Relationship: Ka * Kb = Kw = $10^{-14}$ (at 25 degrees C) for conjugate acid-base pairs.

Buffer Solutions: Resist pH changes upon addition of small amounts of acid or base. Acidic buffer: weak acid + its conjugate base (salt).

Acetate ion (CH₃COO-) — conjugate base of acetic acid, forms acidic buffer with CH₃COOH

pH = pKa + log([salt]/[acid]) — Henderson-Hasselbalch equation. Basic buffer: weak base + its conjugate acid (salt). pOH = pKb + log([salt]/[base]). Buffer capacity is maximum when [acid] = [salt] (pH = pKa).

Hydrolysis of Salts: Salt of strong acid + strong base: neutral (pH = 7). Salt of weak acid + strong base: basic (pH > 7). Salt of strong acid + weak base: acidic (pH < 7). Salt of weak acid + weak base: depends on Ka vs Kb.

pH of salt of weak acid + strong base: pH = 7 + ($\frac{1}{2}$)pKa + ($\frac{1}{2}$)log(C). pH of salt of strong acid + weak base: pH = 7 - ($\frac{1}{2}$)pKb - ($\frac{1}{2}$)log(C).

Solubility Product (Ksp): For a sparingly soluble salt AxBy dissolving as xA^(y+) + yB^(x-): Ksp = [A^(y+)]^x * [B^(x-)]^y. If ionic product (IP) > Ksp, precipitation occurs. If IP < Ksp, more salt dissolves. If IP = Ksp, saturated solution at equilibrium.

Common ion effect: Adding a common ion decreases solubility.
For AgCl (Ksp = 1.8 x $10^{-10}$) in 0.1 M NaCl: [Ag+] = Ksp/[Cl-] = 1.8 x $10^{-9}$ M (much lower than in pure water where [Ag+] = $\sqrt{Ksp}$ = 1.34 x $10^{-5}$ M).