7.4 Titration: Indicators, Neutralization & Titration Curves

Neutralization and the Titration Setup

Neutralization is the reaction of an acid with a base that consumes H⁺ and OH⁻ (or their Brønsted equivalents) in a stoichiometric ratio set by each species' proton-transfer capacity. A titration exploits this reaction: a solution of known concentration (the titrant) is added incrementally to a solution of unknown concentration (the analyte) until the reaction is stoichiometrically complete, allowing the analyte concentration to be calculated from titrant volume delivered.

The equivalence point is where moles of acid equal moles of base (accounting for stoichiometry) — a calculated stoichiometric quantity. The endpoint is the experimentally observed point where an indicator changes color. A well-chosen indicator makes the endpoint nearly coincide with equivalence, but the two concepts are distinct, and the MCAT tests that distinction directly.

Indicators

An indicator is itself a weak acid (or weak base) whose protonated and deprotonated forms have different colors. It changes color over a pH range roughly centered on its own pKa (typically pKa ± 1), where both forms coexist. Choose an indicator whose color-change window brackets the pH expected at equivalence.

Phenolphthalein (color change near pH 8–10) suits weak acid–strong base titrations, where equivalence is basic because the conjugate base hydrolyzes. Methyl orange suits titrations with an acidic equivalence point (weak base + strong acid). Using phenolphthalein for a weak base–strong acid titration would change color too late or give a misleading endpoint.

Interpreting Monoprotic Titration Curves

A titration curve plots pH (y-axis) against volume of titrant added (x-axis). Shape depends on the relative strengths of the acid and base.

Strong acid–strong base: starts low, stays relatively flat, then rises through a nearly vertical jump at equivalence (pH = 7.00 at 25°C). There is no meaningful buffer region because neither partner is a weak conjugate pair.

Weak acid–strong base: starts higher than the corresponding strong acid (partial ionization), rises gradually through a buffer region — a relatively flat stretch centered on the weak acid's pKa — then jumps at equivalence. Critically, equivalence occurs above pH 7 because A⁻ hydrolyzes water to produce OH⁻.

Weak base–strong acid: the mirror image — buffer region near the conjugate acid's pKa, and equivalence below pH 7 because BH⁺ hydrolyzes to give H₃O⁺.

The highest-yield reference point is the half-equivalence point, when exactly half the original weak acid (or base) has been neutralized. Then [HA] = [A⁻], so by Henderson–Hasselbalch:

pH = pKa (exactly)

Read pKa directly off a curve at the midpoint of the buffer region — a frequent discrete and passage skill.

Worked Example: Half-Equivalence

Problem: A 20.0 mL sample of 0.100 M acetic acid (Ka = 1.8 × 10⁻⁵, pKa = 4.74) is titrated with 0.100 M NaOH. What is the pH after 10.0 mL of NaOH has been added?

Solution: Initial moles HA = 0.100 × 0.0200 = 2.00 × 10⁻³ mol. Moles OH⁻ added = 0.100 × 0.0100 = 1.00 × 10⁻³ mol — exactly half, so this is half-equivalence. Thus pH = pKa = 4.74. No ICE table is required. At full equivalence (20.0 mL), all HA has become A⁻ and pH must be calculated from acetate hydrolysis (Kb = Kw/Ka), giving a basic pH — never 7 — for a weak acid–strong base titration.

Past equivalence in a strong acid–strong base titration, pH is set only by excess strong base (or acid). Example: 40.0 mL of 0.100 M HCl plus 50.0 mL of 0.100 M NaOH leaves 0.00100 mol excess OH⁻ in 90.0 mL → [OH⁻] ≈ 0.0111 M → pOH ≈ 1.95 → pH ≈ 12.05.

Polyprotic Acids and Amino Acid Titration Curves

Polyprotic acids (H₂CO₃, H₂SO₄, H₃PO₄, H₂C₂O₄) can donate more than one proton, each with its own Ka (Ka₁ > Ka₂ > Ka₃ typically). Their titration curves show multiple buffer regions and multiple equivalence points — one major jump per acidic proton that is stoichiometrically significant.

For a diprotic acid H₂A titrated with strong base:

1. Before any base: mostly H₂A; pH from Ka₁ (and concentration).
2. First half-equivalence: [H₂A] ≈ [HA⁻] → pH ≈ pKa₁.
3. First equivalence: mostly HA⁻ (ampholyte); pH ≈ average of pKa₁ and pKa₂ when concentrations are not extreme.
4. Second half-equivalence: [HA⁻] ≈ [A²⁻] → pH ≈ pKa₂.
5. Second equivalence: mostly A²⁻; pH from hydrolysis of A²⁻ (basic).

Phosphoric acid (H₃PO₄) extends the same pattern to three pKa values and three equivalence points — passages often ask you to identify which species dominates in a given pH window by comparing pH to the flanking pKa values.

Amino acids: polyprotic biomolecules

Amino acids are the MCAT's favorite polyprotic titration system. A neutral amino acid (side chain neither acidic nor basic) has at least two ionizable groups:

• Carboxylic acid: pKa₁ ≈ 2
• α-Ammonium: pKa₂ ≈ 9–10

Acidic amino acids (Asp, Glu) and basic amino acids (Lys, Arg, His) add a third side-chain pKa and a third equivalence point.

Start at very low pH with the fully protonated form: ⁺H₃N–CH(R)–COOH, net charge +1 for a neutral amino acid. Successive deprotonations:

1. Lose carboxylic H⁺ → zwitterion ⁺H₃N–CH(R)–COO⁻ (net 0)
2. Lose ammonium H⁺ → H₂N–CH(R)–COO⁻ (net −1)

The isoelectric point (pI) is the pH at which the amino acid's average net charge is zero. For a neutral amino acid:

pI ≈ (pKa₁ + pKa₂) / 2

For acidic amino acids, average the two lowest pKa values (the carboxylic pair that brackets the zwitterion with net zero charge); for basic amino acids, average the two highest pKa values. At pH < pI the molecule is net positive and migrates toward the cathode in electrophoresis; at pH > pI it is net negative and migrates toward the anode — a direct bridge to separation methods in content category 5C.

Curve-reading checklist for amino acid titrations:

• Vertical jumps ≈ equivalence points (complete conversion between charge forms)
• Flat midpoints of buffer regions ≈ half-equivalence → pH = that group's pKa
• pI sits at the average of the two pKa values that flank the zero-charge form
• Histidine's imidazole side chain (pKa ≈ 6.0) is especially testable because it ionizes near physiological pH and appears in enzyme active sites and hemoglobin's Bohr effect

Redox Titrations

A redox titration uses the same volumetric logic as an acid–base titration, but the reaction is electron transfer rather than proton transfer. The titrant is chosen so that its own color change (or a separate redox indicator) signals when moles of oxidizing agent equal moles of reducing agent, adjusted for electrons transferred per mole.

Classic example: titration with potassium permanganate (KMnO₄). MnO₄⁻ is intensely purple; its reduction product in acidic solution (Mn²⁺) is nearly colorless, so KMnO₄ acts as its own indicator — a faint, persistent pink/purple tint marks the endpoint when excess MnO₄⁻ remains. Dichromate and iodine/thiosulfate titrations appear less often but follow the same mole-ratio logic: balance the half-reactions, then convert volumes and molarities to moles of electrons transferred.

Putting It Together for Passages

Titration passages often combine a curve figure with a table of pKa values. Strategy:

1. Count the steep jumps to decide monoprotic vs polyprotic.
2. Read pKa at each half-equivalence plateau.
3. Predict equivalence pH from whether the residual species is a weak acid, weak base, or neither.
4. For amino acids, convert pKa values into charge ladder and pI, then answer electrophoresis or solubility questions.
5. Match indicator pKa window to equivalence pH — not to starting pH.

These skills recycle every time a biochemistry passage shows a histidine titration, a phosphate buffer recipe, or a clinical bicarbonate titration of metabolic acid.