Buffers and Titrations

Core Review

Buffers

A buffer solution resists changes in pH upon addition of small amounts of acid or base. A buffer consists of either:

• A weak acid + its conjugate base (e.g., CH₃COOH / CH₃COO⁻)
• A weak base + its conjugate acid (e.g., NH₃ / NH₄⁺)

When acid (H⁺) is added, the conjugate base neutralizes it: A⁻ + H⁺ → HA. When base (OH⁻) is added, the weak acid neutralizes it: HA + OH⁻ → A⁻ + H₂O. In both cases, the pH changes only slightly.

Henderson-Hasselbalch Equation:

pH = pK_a + log([A⁻] / [HA])

For a base buffer: pOH = pK_b + log([BH⁺] / [B]).

This equation tells you the pH of a buffer given the ratio of conjugate base to acid. When [A⁻] = [HA], pH = pK_a — this is the half-equivalence point, where the buffer is most effective.

Buffer capacity is the amount of acid or base a buffer can neutralize before significant pH change. Capacity is highest when:

• The concentrations of buffer components are high.
• [A⁻] / [HA] is close to 1 (pH ≈ pK_a).

Effective buffer range: pH = pK_a ± 1. Outside this range, the buffer has minimal capacity.

Worked Example: A buffer contains 0.50 M CH₃COOH (pK_a = 4.74) and 0.75 M CH₃COONa. What is the pH?

• pH = 4.74 + log(0.75 / 0.50) = 4.74 + log(1.5) = 4.74 + 0.18 = 4.92

Titrations

A titration is the gradual addition of a titrant of known concentration to an analyte of unknown concentration until complete reaction. The equivalence point is when stoichiometrically equivalent amounts of acid and base have reacted. The endpoint is the observable signal (color change of indicator) that approximates the equivalence point.

Strong Acid + Strong Base (e.g., HCl + NaOH):

• Equivalence point pH = 7.00 (neutral salt, no hydrolysis).
• Curve: flat initial region, sharp vertical jump at equivalence.
• Indicator: phenolphthalein (colorless → pink, pH 8.2–10.0) or bromothymol blue (6.0–7.6).

Weak Acid + Strong Base (e.g., CH₃COOH + NaOH):

• Initial pH > strong acid (weak acid is partially dissociated).
• Buffer region before equivalence (resists pH change).
• Half-equivalence point: pH = pK_a (buffer components are equal).
• Equivalence point pH > 7 (conjugate base CH₃COO⁻ hydrolyzes to produce OH⁻).
• Indicator: phenolphthalein (pH 8.2–10.0).

Weak Base + Strong Acid (e.g., NH₃ + HCl):

• Equivalence point pH < 7 (conjugate acid NH₄⁺ hydrolyzes to produce H⁺).
• Indicator: methyl red (pH 4.4–6.2) or bromocresol green (3.8–5.4).

Key features of a weak acid-strong base titration curve:

1. Initial gradual rise (weak acid buffer region).
2. Steepest slope at the half-equivalence point (maximum buffering).
3. Vertical jump through the equivalence point.
4. pH at equivalence = determined by conjugate base hydrolysis.
5. After equivalence, pH levels off as excess strong base dominates.

Indicator Selection

An indicator is itself a weak acid (HIn ⇌ H⁺ + In⁻) with different colors for HIn and In⁻. Color change occurs over pH = pK_a(In) ± 1. Choose an indicator whose pK_a is close to the equivalence point pH.

Polyprotic Acid Titrations

Polyprotic acids (H₂A, H₃A) titrate in steps. Each acidic proton has its own equivalence point and buffer region. H₂CO₃ has two equivalence points; H₃PO₄ has three. Each half-equivalence point corresponds to pH = pK_a for that proton.

Key Equations

Common Traps

• Thinking HCl + NaCl is a buffer (it's not — HCl is a strong acid).
• Forgetting that at the equivalence point, you have only the salt — use hydrolysis to find pH.
• Confusing equivalence point (stoichiometric) with endpoint (indicator change).
• Using concentration instead of moles at equivalence: M_acid × V_acid = M_base × V_base works only for 1:1 stoichiometry.
• Assuming all titration curves have pH = 7 at equivalence.