Titration Curves & Buffer Design — Advanced
- Compute the pH in each region of a weak-acid/strong-base titration curve
- Explain why the equivalence point of a weak-acid titration lies above pH 7
- Design a buffer of a target pH by choosing a pKa and computing the [A⁻]/[HA] ratio
Four regions, four different calculations
A weak-acid/strong-base titration curve breaks into four regions, each solved a different way. (1) Initial point (no base added): a pure weak acid — solve with an ICE table using Ka. (2) Buffer region (before equivalence): both HA and A⁻ are present — use Henderson–Hasselbalch. (3) Equivalence point: all HA has become A⁻ — solve the conjugate base with Kb = Kw/Ka, giving pH > 7. (4) Beyond equivalence: excess strong base dominates — pH comes straight from the leftover [OH⁻]. Knowing which region you are in tells you which tool to grab.
Why the equivalence point is basic — and where pKa hides
At the equivalence point of a weak-acid titration the flask holds only the conjugate base A⁻, a weak base that pulls H⁺ from water and releases OH⁻, so the equivalence pH is above 7 (the weaker the acid, the higher it climbs). Halfway to equivalence, exactly half the acid is neutralized so [HA] = [A⁻]; the Henderson–Hasselbalch log term vanishes and pH = pKa. The buffer region spans roughly pKa ± 1, the window where the [A⁻]/[HA] ratio stays between 1:10 and 10:1 and the curve is flattest.
Designing a buffer on purpose
To build a buffer for a target pH, work backward through Henderson–Hasselbalch. Step 1: pick the acid. Choose a weak acid whose pKa is within about 1 unit of the target pH — that keeps the required ratio in the effective 1:10-to-10:1 range. Step 2: solve for the ratio. Rearrange to log([A⁻]/[HA]) = pH − pKa, then [A⁻]/[HA] = 10^(pH − pKa). A target above pKa needs more conjugate base (ratio > 1); below pKa needs more acid (ratio < 1). Then mix any amounts that meet that ratio.
Design a buffer with pH = 4.50 using formic acid (HCOOH, pKa = 3.75) and its salt sodium formate. What [A⁻]/[HA] ratio is required?
- 1.Confirm the acid is a good match: |4.50 − 3.75| = 0.75, within 1 unit of the target, so the ratio will stay in the effective range.
- 2.Start from pH = pKa + log([A⁻]/[HA]).
- 3.Solve for the log term: log([A⁻]/[HA]) = pH − pKa = 4.50 − 3.75 = 0.75.
- 4.Undo the log: [A⁻]/[HA] = 10^0.75 = 5.6.
- 5.So use about 5.6 mol formate per mol formic acid — e.g. 0.56 M sodium formate with 0.10 M formic acid.
- 6.Check: pH = 3.75 + log(5.6) = 3.75 + 0.75 = 4.50. ✓
Sanity-check every buffer answer against the direction of the pH shift: if the target pH is above pKa the ratio must exceed 1 (base-heavy); if below, it must be under 1 (acid-heavy). If your ratio lands on the wrong side of 1, you inverted the fraction.
The equivalence point of a weak-acid/strong-base titration is NOT pH 7. Only a strong acid + strong base gives a neutral equivalence point. Because the conjugate base remains, a weak-acid equivalence point is always above 7 — reach for Kb = Kw/Ka there, not the assumption pH = 7.
You need a buffer at pH 7.20. Which weak acid is the best choice for it?
To make a buffer at pH = 5.34 from acetic acid (pKa = 4.74) and acetate, what [A⁻]/[HA] ratio is needed?
Well beyond the equivalence point of a weak-acid/strong-base titration, how is the pH best calculated?
Free-response titration questions reward naming the region before calculating. Say "this is the buffer region, so I use Henderson–Hasselbalch" or "this is past equivalence, so I use excess [OH⁻]." Choosing the right tool for the region earns the method points even before the arithmetic.
Answer the 3 checkpoints as you read.
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