Diprotic Acid Titration with an Ambiguous Indicator Endpoint
A student titrates 25.00 mL of an unknown malonic acid solution with 0.1000 M NaOH. Malonic acid is diprotic with pKa1 = 2.83 and pKa2 = 5.69. The pH curve shows a buffer plateau near pH 2.8, a steep rise at 12.5 mL, a shallow plateau near pH 5.7, and a second steep rise at 25.0 mL. The student uses phenolphthalein (colorless to pink, 8.2–10.0) and sees the first persistent pink at 24.6 mL, then a deeper pink at 25.4 mL. The student claims the acid concentration is 0.1000 M because the second endpoint is near 25.0 mL. A lab partner argues that methyl orange (3.1–4.4) should have been used and that the first steep rise is the relevant equivalence point. The instructor asks the pair to resolve the disagreement using the titration curve and stoichiometry, not by picking the indicator that gives a prettier color change.
1. Which equivalence point should the students use to calculate the malonic acid concentration, and why? Include the expected pH at that point and the calculated concentration from the 12.5 mL volume.
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Use the first equivalence point at 12.5 mL. For a diprotic acid, the first equivalence pH is approximately the average of the two pKa values: (2.83 + 5.69)/2 = 4.26. That falls inside the methyl orange range (3.1–4.4), so methyl orange is the better indicator for the first proton. Phenolphthalein changes near the second equivalence point, where the pH is about 9.2, but the visible endpoint is gradual and the student sees pink early at 24.6 mL. At 12.5 mL, moles NaOH = 0.1000 M × 0.0125 L = 0.00125 mol. At the first equivalence point, one mole of NaOH neutralizes one mole of malonic acid, so moles acid = 0.00125 mol. Concentration = 0.00125 mol / 0.02500 L = 0.0500 M. The student's 0.1000 M claim is wrong because the second equivalence requires two moles of NaOH per mole of acid, not one.
2. The student obtained 24.6 mL and 25.4 mL for phenolphthalein endpoints. What does this imply about the precision of the concentration if the second equivalence volume is taken as 25.0 mL, and how could the procedure be improved?
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The two phenolphthalein readings differ by 0.8 mL, which is 3.2% of 25.0 mL. If the second equivalence volume is taken as 25.0 mL, the calculated acid concentration is 0.0500 M. Using 24.6 mL gives a proportionally lower result: (0.1000 × 0.0246)/2 / 0.02500 = 0.0492 M. Using 25.4 mL gives 0.0508 M. That is a spread of about ±1.6%, which is larger than the precision expected from a 25.00 mL buret reading. The problem is not that phenolphthalein is chemically wrong for the second equivalence; it is that the endpoint is not sharp enough to distinguish 24.6 from 25.4 mL by eye. A potentiometric pH titration would locate the steep rise more precisely. Alternatively, use the first equivalence with methyl orange, where the pH jump is better matched to the indicator, and calculate from the 12.5 mL first endpoint.