Acids, Bases and Ionic Equilibrium

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your ECAT exam.

Acids and bases are fundamental to chemistry and appear frequently in the ECAT. The Arrhenius theory defines an acid as a substance that produces H⁺ ions in aqueous solution, while a base produces OH⁻ ions. However, the more broadly applicable Brønsted–Lowry theory describes an acid as a proton (H⁺) donor and a base as a proton acceptor. Conjugate acid–base pairs are related by the transfer of a single proton: for example, HCl donates a proton to become Cl⁻, where HCl/Cl⁻ is a conjugate pair.

The strength of an acid is measured by its acid dissociation constant, Kₐ. For the general reaction:

$$\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$$

$$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$$

Stronger acids have larger Kₐ values. pKₐ = −log₁₀(Kₐ). For weak acids like acetic acid (CH₃COOH), Kₐ ≈ 1.8 × 10⁻⁵ at 25 °C. The pH of a solution is defined as pH = −log₁₀[H⁺], and is central to ECAT calculations.

Key formulas to memorise:

• pH + pOH = 14 (at 25 °C)
• pH = pKₐ + log₁₀([A⁻]/[HA]) — Henderson–Hasselbalch equation
• Kₐ × Kᵦ = Kᵥ (for conjugate acid–base pairs in water)
• [H⁺] = √(Kₐ × C) for a weak acid of concentration C

⚡ ECAT exam tips:

• Questions on pH calculations are extremely common — practise [H⁺] from Kₐ and vice versa
• The Henderson–Hasselbalch equation appears almost every year; memorise it in the ratio form
• For buffer problems, identify the conjugate pair and apply the ratio formula
• Common mistake: confusing Kₐ with K_b — remember they multiply to 10⁻¹⁴ only for conjugate pairs in water
• A buffer resists pH change; its capacity is highest when [acid] = [conjugate base], i.e., pH = pKₐ

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🟡 Standard — Regular Study (2d–2mo)

For ECAT students who want genuine understanding of acid–base chemistry.

The Brønsted–Lowry Framework

Beyond Arrhenius, the Brønsted–Lowry definition encompasses reactions in non-aqueous solvents and even gas-phase acid–base behaviour. When ammonia (NH₃) dissolves in water, it accepts a proton from water, forming NH₄⁺ and OH⁻. Water itself is amphiprotic — it can act as both an acid and a base depending on the partner.

Strength in acids follows a clear periodic trend: electronegativity increases across a period, making the H–X bond more polar and the hydrogen more acidic. Down a group, the bond becomes longer and weaker, also increasing acidity. Hence HI > HBr > HCl > HF despite fluorine being most electronegative — bond dissociation energy dominates here.

Ionic Equilibrium of Weak Acids and Bases

For a weak base B reacting with water:

$$\text{B} + \text{H}_2\text{O} \rightleftharpoons \text{BH}^+ + \text{OH}^-$$

$$K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]}$$

The degree of ionisation (α) relates to Kₐ/K_b and concentration. For a weak acid: α = √(Kₐ/C). This approximation holds when C/Kₐ > 100 (i.e., the acid is sufficiently dilute or weak enough).

Salt Hydrolysis Salts of weak acids and strong bases produce basic solutions. For sodium acetate (CH₃COONa): CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻. The pH is given by:

$$[\text{OH}^-] = \sqrt{\frac{K_w \cdot C}{K_a}}$$

Salts of strong acids and weak bases (e.g., NH₄Cl) produce acidic solutions. Salts of both strong acids and bases (e.g., NaCl) are neutral.

Common Student Mistakes:

1. Using Kₐ directly when the acid is too strong (strong acids fully dissociate; Kₐ is irrelevant)
2. Forgetting that dilution shifts the pH toward 7 (pure water) — a 10× dilution of a weak acid does not halve [H⁺]
3. Applying the weak acid approximation α = √(Kₐ/C) when C is too high or Kₐ too large

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for ECAT and beyond — build complete mastery.

Polyprotic Acids

Polyprotic acids (e.g., H₂SO₄, H₃PO₄, H₂CO₃) can donate more than one proton. For H₂SO₄, the first proton dissociates completely (strong acid, Kₐ₁ ≈ 10³), but the second is moderately weak (Kₐ₂ ≈ 1.2 × 10⁻²). In calculations, the first dissociation usually dominates [H⁺]. For phosphoric acid (H₃PO₄): Kₐ₁ = 7.5 × 10⁻³, Kₐ₂ = 6.2 × 10⁻⁸, Kₐ₃ = 4.8 × 10⁻¹³ — each successive Kₐ is roughly 10⁻⁵ times smaller.

Buffer Systems in Detail

Buffers are critical in biological and industrial chemistry. The Henderson–Hasselbalch equation gives exact buffer pH (no approximation) when concentrations are not too low. Buffer capacity — the amount of strong acid or base the buffer can neutralise — is maximised when [acid] = [conjugate base] and increases with total concentration.

Real-world buffers relevant to ECAT: the carbonate buffer (HCO₃⁻/H₂CO₃) maintains blood pH at ~7.4. Phosphate buffers (H₂PO₄⁻/HPO₄²⁻) are common in biochemistry. The acetate buffer (CH₃COOH/CH₃COO⁻) is frequently used in laboratory preparations.

Solubility Equilibrium

For a sparingly soluble salt like AgCl:

$$\text{AgCl (s)} \rightleftharpoons \text{Ag}^+ + \text{Cl}^-$$

$$K_{sp} = [\text{Ag}^+][\text{Cl}^-] = 1.8 \times 10^{-10} \text{ at } 25^\circ\text{C}$$

The common ion effect suppresses solubility — adding AgNO₃ (which shares Ag⁺) dramatically reduces the solubility of AgCl. This principle is used in qualitative analysis to separate and identify ions.

Neutralisation Titrations

In a strong acid–strong base titration, pH changes sharply near the equivalence point (pH = 7). With weak acid–strong base, the equivalence point is above 7 (because the conjugate base hydrolyses). The reverse (weak base–strong acid) gives equivalence below 7. ECAT often asks you to sketch or interpret a titration curve — know the shape and the pH at equivalence for each combination.

Step-by-step: Solving a buffer problem

1. Identify the conjugate acid–base pair
2. Determine which is the acid (donates H⁺) and which is the base
3. Write the Henderson–Hasselbalch equation
4. Convert pKₐ to Kₐ if needed: Kₐ = 10^(-pKₐ)
5. Substitute concentrations (use initial concentrations; equilibrium shifts are small in buffers)
6. Solve for [H⁺] or pH

ECAT Previous Year Patterns:

• Calculation of pH from [H⁺] and vice versa: almost every year
• Henderson–Hasselbalch applications: every 2–3 years
• Salt hydrolysis and buffer pH: every 2 years
• Solubility and common ion effect: periodically tested
• Titration curves (shape, equivalence point pH): frequently tested in JEE Advanced, occasionally in ECAT

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