Titration Trouble: A Flat Buffer Region
A student titrates 25.0 mL of an unknown weak monoprotic acid with 0.100 M NaOH, monitoring pH. The curve shows an initial pH of 2.9, a gradual rise, a buffer region, an equivalence point near pH 8.7 at 20.0 mL of NaOH, and a final plateau. The student reports the acid concentration as 0.100 M and the pKa as 4.8. A second student notices the pH at the half-equivalence volume (10.0 mL) is 4.8 but argues the pKa must be wrong because the buffer region is 'too flat' to read precisely. The first student also forgot to calibrate the pH meter, which reads 0.3 pH units high across the whole curve.
1. Using the titration data, calculate the concentration of the unknown acid and explain why the half-equivalence pH equals the pKa for a weak monoprotic acid.
Read the worked answer
At equivalence, moles NaOH = moles acid (monoprotic).
Moles NaOH = (0.100 mol/L)(0.0200 L) = 2.00×10⁻³ mol.
Moles acid = 2.00×10⁻³ mol in 25.0 mL = 0.0250 L.
[acid] = 2.00×10⁻³ mol / 0.0250 L = 0.0800 M.
Note: the student's reported 0.100 M is incorrect - it appears they used the NaOH concentration directly instead of dividing by the acid volume. The correct value is 0.0800 M.
Why half-equivalence pH = pKa: Henderson–Hasselbalch gives pH = pKa + log([A⁻]/[HA]). At half-equivalence, exactly half the acid has been neutralized, so [A⁻] ≈ [HA], the log term is zero, and pH = pKa. This holds for a weak monoprotic acid where volumes and activities are approximated by concentrations.
2. The pH meter reads 0.3 units high everywhere. Determine the corrected pKa and assess whether the concentration calculation is affected.
Read the worked answer
A constant offset is a systematic error. If the meter reads 0.3 high, every measured pH is 0.3 too large, so the true pH = measured − 0.3.
Measured half-equivalence pH = 4.8, so corrected pKa = 4.8 − 0.3 = 4.5.
The equivalence-point pH (8.7 measured → 8.4 true) is also shifted, but the equivalence volume is located from the steepest part of the curve (inflection in volume), not from a pH value. A constant pH offset does not move the equivalence volume, so the moles of NaOH and thus the acid concentration (0.0800 M) are unaffected.
Key judgment: a constant additive offset corrupts pH-derived quantities (pKa) but not volume-derived quantities (concentration). This is why calibration matters for pKa but a mis-set offset alone would not change the titration endpoint volume.
3. The second student says the buffer region is too flat to read pKa. Evaluate this claim and describe how the flatness actually reflects buffer chemistry.
Read the worked answer
The claim misreads the data. A flat buffer region is exactly what a good buffer produces: near half-equivalence, added OH⁻ converts HA to A⁻, but the ratio [A⁻]/[HA] changes slowly because both are present in comparable amounts. By Henderson–Hasselbalch, pH depends on the log of that ratio, which is least sensitive to added base when the ratio is near 1. Hence the curve is flattest at half-equivalence - that flatness is a signature of buffering, not a defect.
Precision concern: reading pKa from a flat region is actually more forgiving of small volume errors, because pH barely changes with volume there. The real precision limit is the meter's resolution and calibration, not the flatness. So the second student has the logic backwards: flatness aids, rather than hinders, the pKa determination, provided the meter is calibrated.