Vinegar Titration: Indicator Choice and the Fading Endpoint
An undergraduate analyzes a commercial vinegar labelled '5.0% acetic acid (w/v)'. She pipettes 25.00 mL of vinegar into a 250.0 mL volumetric flask, dilutes to the mark, and titrates 25.00 mL aliquots with NaOH that was standardized against potassium hydrogen phthalate to 0.1000 M. Three burette readings give 22.35 mL, 22.40 mL and 22.30 mL to a pale-pink phenolphthalein endpoint that persists for about 30 s and then fades. A second student repeats the titration with methyl orange and obtains a much lower mean titre, with a sharp colour change near pH 3.8. The first student reports 5.37% and claims the label is false. The instructor asks the group to distinguish random from systematic error before writing the conclusion, and to justify the indicator on chemical grounds rather than habit.
1. Calculate the acetic acid content from the data and check whether 5.37% is arithmetically correct. What does the titre spread imply about random error, and is the label discrepancy explained by it?
Read the worked answer
Mean titre = 22.35 mL, so n(NaOH) = 0.02235 L × 0.1000 mol/L = 2.235 × 10⁻³ mol. Acetic acid reacts 1:1, so the aliquot contains 2.235 × 10⁻³ mol. Mass = 2.235 × 10⁻³ × 60.05 = 0.1342 g. The aliquot is 25.00/250.0 = one-tenth of the diluted sample, so it represents 2.500 mL of original vinegar. Content = 0.1342/2.500 × 100 = 5.37 g/100 mL, i.e. 5.37% w/v. The arithmetic is correct. The three titres span 0.10 mL; the mean deviation is about 0.03 mL, roughly 0.13%, and even a 0.05 mL burette-reading uncertainty is only 0.22%. The 7.4% gap from the label is far too large to be random error, so a systematic cause or a label-unit issue must be investigated.
2. Which indicator is chemically appropriate, and why does methyl orange give a lower titre?
Read the worked answer
Acetic acid is a weak acid (pKa ≈ 4.76). At the equivalence point the solution contains acetate ion, which hydrolyses to give a mildly basic solution, typically around pH 8.7 for these concentrations. Phenolphthalein changes over about pH 8.3–10.0, so its endpoint brackets the equivalence pH. Methyl orange changes near pH 3.1–4.4, where the acid is still only partly neutralized; the sharp colour change occurs before the equivalence point, so the titre is systematically low. This is a systematic method error, not an accident. The correct justification is the pH at equivalence, not the sharpness of the colour change.
3. The phenolphthalein endpoint fades after about 30 s. Should she add more NaOH until the pink is permanent? Explain the likely cause and the correct practical decision.
Read the worked answer
No. A pale pink that persists for about 30 s is the usual endpoint; slight fading can occur because atmospheric CO₂ dissolves and forms carbonic acid, or because the NaOH has absorbed CO₂ to form carbonate. The solution is not 'under-titrated' in the simple sense, and chasing a permanent pink adds excess base, creating a positive systematic error. She should add NaOH dropwise near the endpoint, swirl, and take the first pale pink that survives about 30 s. A blank titration on boiled, CO₂-free water can quantify the carbonate contribution. She should report the measured 5.4% w/v and check whether the label is w/v, w/w or a minimum value; vinegar density near 1.01 g/mL would shift a w/w comparison by only about 1%, not 7%.