Acid–Base Titration: Indicator Endpoint Versus Equivalence
A student titrates 20.0 cm³ of 0.100 M ethanoic acid (Ka = 1.8 × 10⁻⁵) with 0.100 M NaOH, using phenolphthalein. The burette reading at the first persistent pale pink, lasting 30 s, is 19.70 cm³. The pH at 10.00 cm³ added is 4.62. The student calculates Ka from this half-equivalence pH and gets 2.4 × 10⁻⁵, then claims the literature value is wrong and that the endpoint shows the acid was actually 0.0985 M. A pH meter calibrated with pH 7 buffer only is used. The burette was rinsed with distilled water rather than NaOH. The teacher notes that the equivalence volume should be 20.00 cm³. The student asks which conclusions are justified, whether the indicator is suitable, and how to calculate the pH at equivalence.
1. Calculate the pH at equivalence and decide whether phenolphthalein is suitable.
Read the worked answer
At equivalence, 20.00 cm³ of 0.100 M NaOH has been added, so total volume is 40.00 cm³ and [A⁻] = 0.100 × (20.00/40.00) = 0.0500 M. K_b = K_w/K_a = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵ = 5.56 × 10⁻¹⁰. [OH⁻] = √(K_b C) = √(5.56 × 10⁻¹⁰ × 0.0500) = 5.27 × 10⁻⁶ M. pOH = 5.28, pH = 8.72. Phenolphthalein's range is about 8.2–10.0, so pH 8.72 lies in the transition and the indicator is suitable in principle. However, at pH 8.2 the titration is already 99.97% complete, so the colour change should occur within about 0.01 cm³ of equivalence, not 0.30 cm³ before it.
2. Use the half-equivalence pH to calculate Ka and assess whether the discrepancy is significant. What does the burette rinse imply?
Read the worked answer
At half-equivalence, [HA] ≈ [A⁻], so pH ≈ pKa. Thus K_a = 10⁻⁴·⁶² = 2.40 × 10⁻⁵, versus 1.8 × 10⁻⁵ (pKa 4.74). The difference is 0.12 pH unit, a factor 1.33 in K_a. A meter calibrated only at pH 7 can easily be off by 0.1 at pH 4.6, and activity effects also shift the measured pH. This is not strong evidence that the literature value is wrong. The claim that the acid is 0.0985 M assumes endpoint = equivalence, which the indicator does not guarantee; the burette rinsed with water would dilute NaOH and make the titre larger, not smaller. The low 19.70 cm³ is more likely a reading or endpoint error.
3. Test the consistency of the reported endpoint volume with the observed pink colour, and state the best estimate of the acid concentration and a better procedure.
Read the worked answer
At 19.70 cm³, the fraction neutralised is 19.70/20.00 = 0.985, so [A⁻]/[HA] = 0.985/0.015 = 65.7 and pH = 4.74 + log 65.7 = 6.56. That solution would be colourless, not pale pink. Therefore the reported 19.70 cm³ and the observed pink colour are mutually inconsistent; the volume is probably misread. The best estimate of the acid concentration is the prepared 0.100 M, confirmed by a corrected titre close to 20.00 cm³. To reduce ambiguity, record a full pH curve, calibrate the meter with pH 4 and pH 7 buffers, and use the steepest part of the curve or a blank-corrected indicator endpoint.