7.2 Weak Acids, Weak Bases & Buffers

Strong vs. Weak Acids and Bases

Strong acids and strong bases dissociate (ionize) essentially completely in water — the equilibrium lies so far to the right that the reverse reaction is negligible. The MCAT expects you to recognize the short list of common strong acids and bases by name and formula.

Because a strong monoprotic acid dissociates completely, [H⁺] equals the initial acid concentration (0.10 M HNO₃ → [H⁺] = 0.10 M → pH = 1.00). Sulfuric acid is special: its first proton is strong, but the second (HSO₄⁻ ⇌ H⁺ + SO₄²⁻) is only moderately strong (pKa ≈ 2), so dilute H₂SO₄ contributes slightly more than one equivalent of H⁺ per mole.

Weak acids (acetic acid CH₃COOH, benzoic acid, carbonic acid, phosphoric acid, ammonium ion) and weak bases (ammonia NH₃, organic amines, acetate ion) only partially ionize, establishing a true equilibrium. You cannot set [H⁺] equal to the initial concentration; you must use Ka or Kb (or Henderson–Hasselbalch for buffers).

Ka, Kb, pKa, and pKb

For a weak acid HA ⇌ H⁺ + A⁻:

Ka = [H⁺][A⁻] / [HA]

For a weak base B + H₂O ⇌ BH⁺ + OH⁻:

Kb = [BH⁺][OH⁻] / [B]

Logarithmic forms: pKa = −log(Ka) and pKb = −log(Kb). A smaller pKa means a stronger acid (more dissociation); a smaller pKb means a stronger base. For any conjugate acid–base pair at 25°C:

Ka × Kb = Kw and pKa + pKb = 14

Acetic acid has Ka = 1.8 × 10⁻⁵ (pKa ≈ 4.74); benzoic acid has Ka ≈ 6.3 × 10⁻⁵ (pKa ≈ 4.20). The larger Ka (smaller pKa) of benzoic acid means it is the stronger of the two weak acids. Carbonic acid in blood is often treated with an effective pKa near 6.1 for the H₂CO₃/HCO₃⁻ pair under physiological conditions — a number that reappears in every arterial-blood-gas calculation.

Common-Ion Effect and Salt Hydrolysis

For a weak acid alone in water, an ICE table solves for [H⁺] from Ka. If a salt of the conjugate base is added (for example, sodium acetate in acetic acid), the extra A⁻ is a common ion that shifts HA ⇌ H⁺ + A⁻ left by Le Chatelier's principle, suppressing further ionization. This common-ion effect raises pH relative to the acid alone and is exactly what makes buffers work.

When a salt derived from a weak acid or weak base dissolves, its ions can react with water (hydrolysis) and shift pH away from 7:

• Weak acid + strong base salt (e.g., sodium acetate) → basic solution: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻
• Weak base + strong acid salt (e.g., NH₄Cl) → acidic solution: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺
• Strong acid + strong base salt (e.g., NaCl) → neutral — neither ion hydrolyzes appreciably

To calculate the pH of a hydrolyzing salt solution, treat the ion as a weak acid or base, find its Ka or Kb from Ka × Kb = Kw, and solve an ICE table.

Buffers and the Henderson–Hasselbalch Equation

A buffer resists large pH changes when small amounts of acid or base are added. Buffers are built from a weak acid paired with its conjugate base (or a weak base with its conjugate acid) in comparable concentrations. Added H⁺ is absorbed by A⁻; added OH⁻ is absorbed by HA. The pH barely moves until buffer capacity is exhausted — capacity is greatest when [HA] ≈ [A⁻] and when absolute concentrations are high.

The Henderson–Hasselbalch equation relates buffer pH to pKa and the conjugate ratio:

pH = pKa + log([A⁻]/[HA])

(or for a weak base: pOH = pKb + log([BH⁺]/[B]), equivalently pH = pKa + log([B]/[BH⁺]) using the conjugate acid's pKa).

Key corollaries the MCAT loves:

1. When [A⁻] = [HA], log(1) = 0, so pH = pKa exactly — this is also the half-equivalence point of a weak-acid titration.
2. Effective buffering is usually limited to roughly pKa ± 1 pH unit; outside that window one component dominates and capacity collapses.
3. Diluting a buffer equally leaves the ratio (and therefore pH) unchanged, but lowers capacity.

Worked Example: Henderson–Hasselbalch

Problem: What is the pH of a buffer made from 0.20 M acetic acid (Ka = 1.8 × 10⁻⁵) and 0.40 M sodium acetate?

Solution: pKa = −log(1.8 × 10⁻⁵) = 4.74.

pH = 4.74 + log(0.40/0.20) = 4.74 + log(2) = 4.74 + 0.30 = 5.04

Doubling conjugate base relative to acid shifts pH about 0.3 units above pKa — consistent with log 2 ≈ 0.30.

Blood Bicarbonate Buffer: The MCAT's Clinical Capstone

Human arterial blood is held between about pH 7.35 and 7.45 by several systems, but the dominant extracellular buffer is the open bicarbonate buffer:

CO₂(g) ⇌ CO₂(aq) + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻

Under physiological conditions this is often written with dissolved CO₂ rather than true H₂CO₃, and the effective Henderson–Hasselbalch form is:

pH ≈ 6.1 + log([HCO₃⁻] / (0.03 × PCO₂))

where [HCO₃⁻] is in mM and PCO₂ is in mmHg. Typical arterial values are [HCO₃⁻] ≈ 24 mM and PCO₂ ≈ 40 mmHg, giving log(24/1.2) = log(20) ≈ 1.3, so pH ≈ 6.1 + 1.3 = 7.4.

What makes this buffer special is that it is open: the lungs continuously adjust PCO₂ by ventilation, and the kidneys adjust [HCO₃⁻] over hours to days. That open exchange multiplies effective capacity far beyond a closed acetic acid/acetate flask of the same concentration.

Passage strategy: if a figure shows rising PCO₂ with falling pH, label respiratory acidosis first, then look for a secondary rise in [HCO₃⁻] as renal compensation. If [HCO₃⁻] falls first with falling pH and PCO₂ falls later, the primary process is metabolic acidosis with respiratory compensation. Intracellularly, the phosphate buffer (H₂PO₄⁻/HPO₄²⁻, pKa ≈ 7.2) and protein side chains (especially histidine) also absorb H⁺, but blood-gas questions almost always target bicarbonate.

On a titration curve, the buffer region appears as a relatively flat segment centered on the weak acid's pKa. In blood, continuous CO₂ removal keeps the system near the flat region even as metabolism dumps protons — the chemical reason ventilation rate is a life-or-death control variable.