Overview — Module 5: Ionic Equilibrium

In the first lesson of Module 5 you studied chemical equilibrium and Le Chatelier's principle. This lesson extends those ideas to equilibria involving ions — especially acid-base equilibria and solubility equilibria of sparingly soluble salts. Acid-base chemistry is central to living systems (blood pH ~7.4, saliva ~6.8), agriculture, and industrial processes. Buffer solutions maintain pH; the solubility product governs precipitation — including the calcium phosphate in bones and teeth.

You will learn strong and weak electrolytes, degree of ionization and Ostwald's dilution law, Arrhenius/Brønsted-Lowry/Lewis acid-base concepts, K_a and K_b, auto-ionization of water and K_w, the pH scale, common ion effect, buffer solutions and the Henderson-Hasselbalch equation, salt hydrolysis, solubility product K_sp, and applications in qualitative analysis.

Section 1: Strong and Weak Electrolytes (12.1)

Electrolytes are compounds that produce ions in aqueous solution and conduct electricity. Strong electrolytes (NaCl, KCl, HCl, NaOH) ionize almost completely — shown with a single arrow. Weak electrolytes (CH₃COOH, NH₄OH, C₆H₅NH₂) ionize partially; a dynamic ionic equilibrium exists between unionized molecules and ions (reversible arrows).

The degree of ionization α is the fraction of electrolyte present as ions. For AB ⇌ Aⁿ⁺ + Bⁿ⁻ with initial concentration c:

At equilibrium: concentrations are c(1−α) for AB, cα for each ion. For weak electrolytes α ≪ 1, so (1−α) ≈ 1 and K ≈ cα². Qualitatively, dilution promotes ionization — more water molecules available to solvate ions.

The ionization constant K is a characteristic property of the electrolyte at a given temperature. Strong electrolytes have very large effective K values (complete dissociation), while weak electrolytes have small K values reflecting partial ionization. Conductivity measurements and colligative properties (from L7) can also reveal the extent of dissociation — electrolytes with i > 1 show abnormal colligative behavior when dissociation occurs.

Dynamic equilibrium means the rates of forward (ionization) and reverse (recombination) processes are equal. Adding solvent (dilution) decreases c and shifts equilibrium toward more ionized form per Ostwald's law — this is why weak acid conductivity increases on dilution even though total ion count per unit volume may change in a complex way.

Section 2: Acid-Base Concepts (12.2–12.3)

12.2.1 Arrhenius Concept

Acid: produces H⁺ (H₃O⁺) in water — HA → H⁺ + A⁻. Base: produces OH⁻ — MOH → M⁺ + OH⁻. Limitations: aqueous only; cannot explain acidic AlCl₃ or basic NH₃/Na₂CO₃ (no OH⁻ in formula).

12.2.2 Brønsted-Lowry Concept

Acid: proton (H⁺) donor. Base: proton acceptor. NH₃ + H₂O ⇌ NH₄⁺ + OH⁻ — NH₃ accepts proton (base), H₂O donates (acid). Conjugate acid-base pairs differ by one H⁺: NH₃/NH₄⁺, H₂O/OH⁻, CH₃COOH/CH₃COO⁻. In any acid-base reaction, the product on the left is the conjugate base of the reactant acid, and vice versa.

12.2.3 Lewis Concept

Acid: electron pair acceptor (AlCl₃, BF₃, Fe³⁺). Base: electron pair donor (NH₃). AlCl₃ + NH₃ → Cl₃Al←NH₃ (coordinate bond). Explains acidity without H⁺. All Brønsted acids are also Lewis acids (H⁺ accepts electron pair from base), but Lewis definition is broader — CO₂ + H₂O → H₂CO₃ involves Lewis acid-base interaction at carbon. Fajan's rules and polarizing power connect to Lewis acidity of small, highly charged cations that hydrolyze water.

Relative strength (12.3): Strong acids (HCl) ionize completely; weak acids (CH₃COOH) partially. Strong bases (NaOH) fully dissociate; weak bases (NH₄OH) establish equilibrium. Larger K_a → stronger acid; larger K_b → stronger base.

In Brønsted equilibria, the stronger acid has the weaker conjugate base. HCl is completely ionized because Cl⁻ is a weaker base than H₂O — it cannot accept the proton back. HF is only partially ionized because F⁻ is a stronger base than H₂O and competes for the proton. This inverse relationship between acid strength and conjugate base strength is fundamental to predicting reaction direction: acids react with bases whose conjugate acids are weaker.

Amphiprotic species can act as both acid and base — HCO₃⁻ is basic toward HF but acidic toward CN⁻; H₂O is acidic toward NH₃ and basic toward HCl. Neutralization in Arrhenius terms (H⁺ + OH⁻ → H₂O) is proton transfer in Brønsted terms. The Lewis concept completes the picture for reactions like AlCl₃ + NH₃ where no proton transfers but a coordinate bond forms.

Section 3: Quantitative Strengths — K_a, K_b, α (12.4)

Weak acid: HA + H₂O ⇌ H₃O⁺ + A⁻

Degree of dissociation: α = √(K/c) for weak acids/bases when α is small. Example 12.2: For weak base with K_b and concentration c, same Ostwald form applies. Percent dissociation = α × 100.

Polyprotic acids (H₂SO₄, H₃PO₄) ionize stepwise; each step has its own K_a. First ionization is always strongest because removing H⁺ from a neutral molecule is easier than from a negatively charged ion.

For a conjugate acid-base pair: K_a × K_b = K_w. A weak acid with K_a = 1.8×10⁻⁵ has conjugate base CH₃COO⁻ with K_b = K_w/K_a = 5.6×10⁻¹⁰. Example 12.1 asks for K_a expression for acetic acid: K_a = [H₃O⁺][CH₃COO⁻]/[CH₃COOH]. Comparing K_a values ranks acid strength: acetic acid (1.8×10⁻⁵) is much stronger than hydrocyanic acid (4.9×10⁻¹⁰).

Percent dissociation = α × 100%. As concentration increases, α decreases (Ostwald) even though absolute ion concentration may increase. Exam problems often give K and c and ask for α, [H₃O⁺], or pH — always write the equilibrium table with initial and equilibrium concentrations first.

Section 4: Auto-Ionization, pH and Common Ion Effect (12.5)

Water self-ionizes: 2H₂O ⇌ H₃O⁺ + OH⁻. Ionic product: K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. In pure water: [H₃O⁺] = [OH⁻] = 10⁻⁷ M (neutral).

Example 12.3: In 0.01 M HCl, [H₃O⁺] ≈ 0.01 M (strong acid dominates); [OH⁻] = K_w/0.01 = 10⁻¹² M. Example 12.7: 0.1 M CH₃COOH, α=0.0134 → [H₃O⁺]=0.00134 → pH=2.87.

The p notation extends beyond pH: pOH = −log[OH⁻], pK_a = −log K_a, pK_w = 14. Taking logs of K_w = [H₃O⁺][OH⁻] gives pK_w = pH + pOH. Strongly acidic solutions can have pH < 0; strongly alkaline can exceed 14 — but the 0–14 range covers most laboratory and biological systems. Sorensen's pH scale (1909) replaced awkward powers of ten with manageable numbers.

Self-ionization equilibrium applies in every aqueous solution — even strong acid solutions contain trace OH⁻ from water, and strong base solutions contain trace H₃O⁺. The dominant species sets pH; the minor species comes from K_w. In 0.01 M HCl, water's contribution to [H₃O⁺] (10⁻¹²) is negligible compared to 0.01 — validating the assumption that [H₃O⁺] equals strong acid concentration.

12.5.3 Common Ion Effect

Adding a salt with a common ion suppresses dissociation of weak acid/base (Le Chatelier). CH₃COOH + CH₃COONa: acetate ion shifts equilibrium left — α decreases. Example 12.8: 0.1 M CH₃COOH + 0.1 M CH₃COONa → [H₃O⁺]=1.85×10⁻⁵, pH=4.73, α=1.85×10⁻⁴.

Section 5: Buffer Solutions (12.6)

Buffers resist pH change when small amounts of acid or base are added. Two types: (i) weak acid + salt of conjugate base (CH₃COOH + CH₃COONa — acidic buffer, pH < 7); (ii) weak base + salt of conjugate acid (NH₄OH + NH₄Cl — basic buffer, pH > 7).

When [Salt]=[Acid], pH = pK_a. Biological fluids use carbonate, phosphate, and protein buffers to maintain pH within narrow limits essential for enzyme activity and oxygen transport.

Example 12.10: 0.1 M NH₄OH + 0.01 M NH₄Cl gives pOH = 9.25 + log(0.01/0.1) = 8.25, hence pH = 5.75. Buffer capacity depends on total concentrations of acid and base reserves — higher concentrations absorb more added acid/base before pH shifts significantly. Buffer action fails if large amounts of strong acid or base are added (reserves exhausted) or if components are too dilute.

The common ion effect and buffer action are linked: a buffer is essentially a weak electrolyte solution with high common-ion concentration from added salt. CH₃COOH alone has pH ~2.87 (0.1 M); adding CH₃COONa raises pH toward pK_a and stabilizes it against further change.

Section 6: Salt Hydrolysis (12.7)

Some salts give acidic or basic solutions through hydrolysis (reaction with water):

• SA + SB (NaCl): no hydrolysis → neutral
• SA + WB (NH₄Cl): NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺ → acidic
• WA + SB (CH₃COONa): CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻ → basic
• WA + WB (CH₃COONH₄): both ions hydrolyze — nature depends on relative K_a and K_b

Cations of weak bases and anions of weak acids hydrolyze; ions from strong acids/bases do not. This explains why Na₂CO₃ is basic despite no OH⁻ in the formula — CO₃²⁻ hydrolyzes.

For WA + WB salts like CH₃COONH₄, both NH₄⁺ (weak base cation) and CH₃COO⁻ (weak acid anion) hydrolyze. If K_a of the acid part equals K_b of the base part, the solution is approximately neutral. If K_a > K_b, solution is slightly acidic; if K_b > K_a, slightly basic. Hydrolysis constant K_h = K_w/K for the conjugate — weaker conjugate means stronger hydrolysis.

Practical applications: aqueous FeCl₃ is acidic (Fe³⁺ hydrolyzes — Lewis acid behavior); baking soda (NaHCO₃) is weakly basic; laundry detergents often contain basic phosphates. Understanding salt hydrolysis explains why pH indicators behave differently in solutions of different salts.

Section 7: Solubility Equilibrium (12.8)

For sparingly soluble salts like AgCl: AgCl(s) ⇌ Ag⁺ + Cl⁻ (heterogeneous equilibrium). Solubility product: K_sp = [Ag⁺][Cl⁻]. Solid activity = 1 by convention.

12.8.3 Qualitative analysis: Cation group separation uses controlled [S²⁻] via H₂S dissociation — acidic medium precipitates Group II sulphides (low [S²⁻]); alkaline medium precipitates Group IV (higher [S²⁻]). K_sp determines whether precipitation occurs when ion product exceeds K_sp.

Ion product Q compared to K_sp: if Q < K_sp, unsaturated (no precipitate); Q = K_sp, saturated; Q > K_sp, supersaturated — precipitation occurs until Q returns to K_sp. Ca₃(PO₄)₂ in bones has very small K_sp — slightly soluble but biologically essential. Fluoridation shifts equilibrium by common ion effect (F⁻) modifying tooth enamel solubility.

Example 12.13 dramatically shows common ion suppression: AgI solubility drops from 9.2×10⁻⁹ M in water to 8.5×10⁻¹⁶ M in 0.1 M AgNO₃ — a factor of ~10⁷. This principle is used in gravimetric analysis (precipitating ions completely) and in controlling water hardness removal.

Exam Connections and Chapter Summary

Terminal exercises cover: α and K calculations; pH of strong/weak acids and bases; Henderson equation for buffers; K_sp and solubility conversions; common ion effect on solubility. Intext 12.1 tests conjugate pairs and Lewis acids. Intext 12.2: HF K_a expression, glycine pH, lime juice pH.

Key skills: write K_a, K_b, K_sp expressions; use K_w to find [H₃O⁺] or [OH⁻]; apply Henderson-Hasselbalch; predict salt solution pH from hydrolysis type; calculate s from K_sp and vice versa; explain how buffers and common ions work via Le Chatelier.

Ionic equilibrium connects the abstract equilibrium constant to measurable pH, buffer design, water chemistry, bone mineral solubility, and laboratory qualitative analysis — one of the most practically important chapters in NIOS Class 12 Chemistry.

Intext 12.3 practice: benzoic acid/sodium benzoate buffer with pK_a=4.2 — apply Henderson directly. Ag₂SO₄ K_sp from [SO₄²⁻]=2.5×10⁻² requires writing correct dissolution stoichiometry (2 Ag⁺ per formula unit). Always state whether assumptions (α << 1, [common ion] dominates) are valid and check them after calculation.

Module 5 links equilibrium (Lesson 1) with ionic systems (this lesson) and will extend to electrochemistry (L13) where electrode potentials relate to Gibbs energy and equilibrium constants. Mastering K, K_a, K_b, K_w, and K_sp as specific applications of the law of mass action prepares you for the unified treatment of chemical thermodynamics and kinetics across the syllabus.