Calibrating a Student-Made Standard for a Titration
A Year 11 class prepares a sodium hydroxide standard by dissolving 2.00 g of impure NaOH pellets (labelled 96% pure) in water and making the volume to 500.0 mL in a volumetric flask. A student then titrates 20.00 mL aliquots of this base against a 0.100 M hydrochloric acid standard using phenolphthalein. Two concordant titres average 21.35 mL. The teacher notes the pellets were stored in a damp cupboard and may have absorbed carbon dioxide, forming sodium carbonate. The student's calculated base concentration is 0.1068 M. The teacher asks the class to judge whether the standard is fit for purpose before it is used to analyse vinegar samples.
1. Calculate the base concentration the student obtained and compare it with the concentration expected from the labelled purity. Explain the direction of any discrepancy.
Read the worked answer
Moles of HCl used = 0.100 mol/L × 0.02135 L = 2.135 × 10⁻³ mol. From NaOH + HCl → NaCl + H₂O, moles of NaOH in 20.00 mL = 2.135 × 10⁻³ mol. Concentration = 2.135 × 10⁻³ / 0.02000 = 0.1068 mol/L.
Expected from label: mass of pure NaOH = 2.00 g × 0.96 = 1.92 g. Moles = 1.92 / 40.00 = 0.0480 mol. Concentration = 0.0480 / 0.5000 = 0.0960 mol/L.
The measured value (0.1068 M) is higher than expected (0.0960 M). This is the opposite of what simple impurity would give: inert impurities would lower the concentration. A higher-than-expected result means more acid-neutralising base was present than the label accounts for, or the pellets were wet with water rather than contaminated with carbonate. Water alone would not raise the concentration per gram, but absorbed moisture plus inaccurate mass measurement could. The key judgement is that the discrepancy is real and must be explained before trusting the value.
2. The teacher suspects absorbed CO₂ formed Na₂CO₃. Would carbonate contamination raise or lower the apparent base concentration in this titration? Justify with equations.
Read the worked answer
Carbonate contamination raises the apparent concentration in this particular titration.
When CO₂ is absorbed: 2NaOH + CO₂ → Na₂CO₃ + H₂O. Two moles of NaOH become one mole of Na₂CO₃. During titration with HCl, carbonate reacts in two stages: CO₃²⁻ + H⁺ → HCO₃⁻, then HCO₃⁻ + H⁺ → H₂CO₃. Phenolphthalein changes colour near the first endpoint (around pH 8.3), so it signals completion of the first protonation only. That means each mole of Na₂CO₃ consumes one mole of HCl at the phenolphthalein endpoint, whereas the two moles of NaOH it replaced would have consumed two moles.
So carbonate contamination should lower, not raise, the apparent NaOH concentration at the phenolphthalein endpoint. Since the student's value is higher than expected, carbonate cannot be the main explanation. The discrepancy more likely reflects wet pellets (mass includes water, so the true NaOH mass is lower than 96% of 2.00 g) combined with a possible mass or volume error. The judgement is that the carbonate hypothesis fails to explain the direction of the error, so the standard is unreliable.
3. Recommend what the class should do before using this standard to analyse vinegar, and state the criterion for accepting a standard.
Read the worked answer
The standard should not be used as prepared. Recommended actions:
- Prepare a fresh standard from dried, analytical-grade NaOH or, better, use a primary standard such as potassium hydrogen phthalate to standardise the NaOH solution accurately.
- Weigh by difference on an analytical balance and record to 0.0001 g.
- Dry pellets to remove absorbed water, or use a carbonate-free preparation (boiled distilled water, protected from air).
- Re-titrate and check that replicate titres agree within about 0.05 mL.
Acceptance criterion: the experimentally determined concentration should agree with the expected value within the combined uncertainty of the balance, volumetric flask, pipette and burette. A discrepancy of about 11% (0.1068 vs 0.0960 M) is far outside that uncertainty, so the standard fails the criterion. Only a standard whose measured concentration is validated against a primary standard should be used to quantify vinegar, because any error in the base concentration propagates directly into the vinegar result.