The Discrepant Titration of a Cleaning Acid
A student standardises a batch of hydrochloric acid cleaner by titrating 25.00 mL aliquots against 0.1000 M NaOH using phenolphthalein. Three titres are 24.10 mL, 24.15 mL, and 28.90 mL. The student averages all three and reports [HCl] = 0.1030 M. A supervisor repeats the titration using methyl orange and obtains 24.12 mL. Separately, the cleaner is found to contain a small amount of dissolved CO2 from exposure to air, which forms carbonic acid (pKa1 = 6.35, pKa2 = 10.33). The endpoint with phenolphthalein is at pH ~8.2–10; with methyl orange it is at pH ~3.1–4.4.
1. Evaluate the student's reported concentration and give the correct value with justification.
Read the worked answer
The 28.90 mL titre is an outlier (about 20% above the others, far beyond the ~0.2% spread of the concordant pair). It must be rejected, not averaged.
Concordant mean titre = (24.10 + 24.15)/2 = 24.125 mL.
Moles NaOH = 0.1000 × 0.024125 = 2.4125 × 10⁻³ mol. For a 1:1 reaction, moles HCl = same.
[HCl] = 2.4125 × 10⁻³ / 0.02500 = 0.09650 M.
The student's 0.1030 M is inflated by including the outlier. Averaging an outlier is a calculation error, not a random error.
2. Explain why the two indicators give nearly identical titres here and whether dissolved CO2 threatens the accuracy of the result.
Read the worked answer
For a strong acid–strong base titration the pH jumps steeply (roughly pH 4 to 10) near the equivalence point, so any indicator whose transition range falls inside that jump gives essentially the same titre. Methyl orange (3.1–4.4) and phenolphthalein (8.2–10) both lie within the steep region, so both are acceptable - the agreement of 24.12 mL with 24.125 mL confirms this.
CO2 concern: Dissolved CO2 adds carbonic acid, which is titrated by NaOH. With phenolphthalein (endpoint near pH 8–9), carbonate is titrated essentially to bicarbonate (first equivalence, pH ~8.3) and beyond - so CO2 is counted as acid, slightly inflating the titre. With methyl orange (endpoint pH ~4), carbonic acid is largely not neutralised, so the strong acid is measured more selectively. The small discrepancy is therefore expected and the methyl orange result is the better measure of strong acid content. Boiling to remove CO2 before titration would also eliminate the error.