Buffers & Titration Curves
Buffer action, Henderson-Hasselbalch, effective range, the four titration regions, and indicators.
What makes a buffer
CORE RULEA buffer needs appreciable amounts of BOTH a weak acid and its conjugate base (or a weak base and its conjugate acid), with a non-hydrolyzing spectator counter-ion. Strong-acid- or strong-base-only solutions cannot buffer.
How it resists
CORE RULEAdded base is neutralized by the weak acid: HA + OH⁻ → A⁻ + H₂O. Added acid by the conjugate base: A⁻ + H₃O⁺ → HA + H₂O. Each added strong species becomes a weak conjugate-pair member.
Henderson-Hasselbalch
CORE RULEpH = pKa + log([A⁻]/[HA]). Basic buffer: pOH = pKb + log([BH⁺]/[B]), pH = 14 − pOH. Volume cancels in the ratio, so moles can be used directly.
Polyprotic buffer pKa
CORE RULEUse the pKa of the step whose two species ARE the buffer pair. H₃PO₄/H₂PO₄⁻ → pKa1 (2.12); H₂PO₄⁻/HPO₄²⁻ → pKa2 (7.21); HPO₄²⁻/PO₄³⁻ → pKa3 (12.32).
Ratio for a target pH
CORE RULEInverse H-H: [A⁻]/[HA] = 10^(pH − pKa). Used for buffer prep and post-perturbation pH. Give the ratio in the direction the problem asks; the reciprocal is a different quantity.
Effective range & capacity
CORE RULEA buffer works over pKa ± 1 (ratio 0.1 to 10). For a target pH, pick a weak acid with pKa ≈ pH. Capacity scales with absolute concentrations: 1.0 M/1.0 M holds ~10× more than 0.1 M/0.1 M at the same pH.
Four titration regions
METHOD(1) Initial: analyte alone. (2) Buffer region (weak analyte only): both analyte + formed conjugate, use H-H. (3) Equivalence: only the salt (strong-strong pH 7; weak acid + strong base pH > 7; weak base + strong acid pH < 7). (4) Post-equivalence: excess titrant.
Half-equivalence = pKa
CORE RULEAt V = V_equiv/2, half the weak acid is neutralized so [HA] = [A⁻] and pH = pKa. (Weak base + strong acid: pOH = pKb there.) Read pKa straight off the curve.
Curve features
CORE RULEEquivalence point = the volume where pH rises most steeply; half-equivalence = half that volume; the buffer region is the slow-changing pre-equivalence span. A weak-acid curve starts higher and has a smaller equivalence jump than strong-strong.
Indicator selection
CORE RULEAn indicator changes colour over pKa(ind) ± 1. Pick one with pKa ≈ equivalence pH. Weak acid + strong base (equiv > 7): phenolphthalein (9.4). Weak base + strong acid (equiv < 7): methyl red (5.1).