Acid–Base Titration Curves

Core Concept

A titration curve plots pH against the volume of titrant added. Its shape reveals the nature of the acid and base: a strong-acid/strong-base curve is nearly flat then vertical through pH 7; a weak-acid/strong-base curve rises gradually through a buffered region and turns vertical at an equivalence point above pH 7. The equivalence point is where moles of acid equal moles of base (stoichiometric equivalence); the endpoint is where an indicator changes color. At the half-equivalence point of a weak-acid titration, exactly half the acid has been converted, so [HA] = [A⁻] and pH = pKa.

Key Ideas

• Equivalence point: moles H₃O⁺ supplied = moles OH⁻ supplied (the stoichiometric point).
• Endpoint: the observed color change of an indicator — an approximation of the equivalence point.
• Strong–strong: equivalence at pH 7; huge, near-vertical jump in the middle.
• Weak acid + strong base: equivalence point above pH 7 (conjugate base hydrolyzes); buffered region before it.
• Weak base + strong acid: equivalence point below pH 7 (conjugate acid hydrolyzes).
• Half-equivalence point: pH = pKa (for weak acid) or pOH = pKb (for weak base).

Equations and Variables

• Equivalence condition: M_acid × V_acid = M_base × V_base (at the equivalence point)
• Half-equivalence: [HA] = [A⁻] ⇒ pH = pKa
• Weak acid at equivalence: solution is the conjugate base salt; [OH⁻] = √(Kb × C_salt)
• Weak acid before equivalence (buffer region): pH = pKa + log([A⁻]/[HA])

How It Works

1. Start: pH is just that of the original acid (or base) solution.
2. Before equivalence (weak acid): each addition of strong base converts some HA to A⁻, creating a buffer; pH rises slowly and pH = pKa at the halfway point.
3. At equivalence: all HA has been converted to A⁻. The solution is now a salt of a weak acid, so it is basic (pH > 7). For strong–strong, the salt is neutral and pH = 7.
4. After equivalence: excess strong base (or acid) now simply accumulates; pH is set by the leftover titrant.
5. The steep vertical region brackets the equivalence point; an indicator whose color-change range falls inside it will signal the endpoint accurately.

Worked Example

50.0 mL of 0.100 M CH₃COOH (Ka = 1.8 × 10⁻⁵) is titrated with 0.100 M NaOH. Find (a) the volume at the equivalence point and (b) the pH at that point.

(a) moles acid = 0.0500 L × 0.100 M = 0.00500 mol. At equivalence, moles NaOH = 0.00500 mol, so V = 0.00500 mol / 0.100 M = 0.0500 L = 50.0 mL (total volume now 100 mL).

(b) At equivalence, all acid is now acetate ion, CH₃COO⁻, at:

C = 0.00500 mol / 0.100 L = 0.0500 M

Kb(CH₃COO⁻) = Kw/Ka = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵ = 5.6 × 10⁻¹⁰

[OH⁻] = √(Kb × C) = √(5.6 × 10⁻¹⁰ × 0.0500) = √(2.8 × 10⁻¹¹) = 5.3 × 10⁻⁶ M

pOH = 5.28 → pH = 14.00 − 5.28 = 8.72

The equivalence point (pH 8.72) is basic, as expected for a weak-acid/strong-base titration. (Half-equivalence occurs at 25.0 mL, where pH = pKa = 4.74.)

How it works

1. Start: pH is just that of the original acid (or base) solution.
2. Before equivalence (weak acid): each addition of strong base converts some HA to A⁻, creating a buffer; pH rises slowly and pH = pKa at the halfway point.
3. At equivalence: all HA has been converted to A⁻. The solution is now a salt of a weak acid, so it is basic (pH > 7). For strong–strong, the salt is neutral and pH = 7.
4. After equivalence: excess strong base (or acid) now simply accumulates; pH is set by the leftover titrant.
5. The steep vertical region brackets the equivalence point; an indicator whose color-change range falls inside it will signal the endpoint accurately.

Common confusions

• "Equivalence point = endpoint." — The equivalence point is a stoichiometric fact; the endpoint is an observed color change that only approximates it.
• "Weak-acid equivalence is at pH 7." — It is above 7 because the conjugate base hydrolyzes to give OH⁻.
• "pH = pKa at the equivalence point." — No; pH = pKa at the half-equivalence point, where [HA] = [A⁻].
• "The curve is steep only at pH 7." — The steep jump is centered on the equivalence pH, which is 7 only for strong–strong titrations.
• "More acid always means lower equivalence pH." — The equivalence pH is set by the salt formed, not by how much acid was present.

Quick review

• Curve = pH vs volume of titrant.
• Equivalence (stoichiometric) ≠ endpoint (indicator).
• Strong–strong equivalence at pH 7; weak-acid/strong-base above 7; weak-base/strong-acid below 7.
• Half-equivalence: pH = pKa.
• After equivalence, pH set by excess titrant.