Standardising the Laboratory Acid
The school laboratory has a bottle labelled hydrochloric acid, about 0.10 mol/dm³. Before a practical exam, the exact concentration must be established. There is a standard sodium hydroxide solution of 0.100 mol/dm³, a 25.0 cm³ pipette, a burette reading to ±0.05 cm³, phenolphthalein, and methyl orange. A student titrates 25.0 cm³ portions of the acid and records 24.20, 24.05, and 26.80 cm³. A second student rinsed the pipette with distilled water only before use, and a third argues that phenolphthalein is the wrong indicator because the acid is in the flask, so the colour change is acid to base. The session lasts 40 minutes, only one titration set can be repeated, and the label must state a value to three significant figures with its uncertainty.
1. Which titre values should be used, and what is the acid concentration? Treat 26.80 cm³ as an outlier and justify that treatment.
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Use 24.20 and 24.05 cm³; they differ by 0.15 cm³, which is within about twice the burette reading uncertainty, and they are concordant. 26.80 cm³ is 2.6 cm³ above them - far outside reading error - and is best explained by running past the endpoint, so it must be excluded, not averaged. Mean volume = (24.20 + 24.05)/2 = 24.125 cm³ = 0.024125 dm³. Moles NaOH = 0.100 × 0.024125 = 2.4125 × 10⁻³ mol. HCl + NaOH → NaCl + H₂O is 1:1, so moles HCl in 25.0 cm³ = 2.4125 × 10⁻³ mol. Concentration = 2.4125 × 10⁻³ / 0.0250 = 0.0965 mol/dm³. To three significant figures the label value is 0.0965 mol/dm³. Averaging in 26.80 would give 25.02 cm³ and 0.1001 mol/dm³, a falsely neat result that hides the error. The outlier should be recorded in the lab book with the reason for rejection, because an examiner may ask why three titres produced only two used values.
2. Assess the indicator argument and the effect of rinsing the pipette with distilled water only.
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The indicator argument is confused. Phenolphthalein is suitable: this is a strong acid–strong base titration with a sharp pH jump, and phenolphthalein changes colourless to pink at about pH 8.2–10, inside the jump. Methyl orange would also work, but its change at pH 3.1–4.4 is less sharp and is not made correct by having acid in the flask. The direction of titration does not choose the indicator; the pH range of the equivalence jump does. The wet pipette is a real error: residual distilled water dilutes the 25.0 cm³ acid sample, so fewer moles of HCl are delivered, the titre falls, and the calculated concentration is systematically low. Rinsing with distilled water is correct for a burette but wrong for a pipette that must deliver a fixed amount of acid; the pipette should be rinsed with the acid solution. Because only one repeat is allowed, repeat the titration with a properly rinsed pipette before the label is signed, and keep the first set as a comparison.
3. Write the label and a one-line uncertainty statement. Should the value be reported as 0.0965 mol/dm³ or as about 0.10 mol/dm³?
Read the worked answer
Label: hydrochloric acid, 0.0965 mol/dm³, standardised against 0.100 mol/dm³ NaOH, mean of two concordant titres 24.20 and 24.05 cm³. Reporting about 0.10 would discard the purpose of the exercise and would be too coarse for a practical exam that needs a known concentration. The uncertainty is dominated by the burette: each reading is ±0.05 cm³, so a difference has roughly ±0.07 cm³ when combined in quadrature, or ±0.10 cm³ on a simple worst-case reading; with 24.125 cm³ that is about 0.3–0.4%. The pipette adds its own tolerance, and endpoint judgement adds a subjective component not captured by the graduations. A defensible statement is 0.0965 mol/dm³, estimated uncertainty ±0.0005 mol/dm³, about 0.5%. The outlier must not be included in the uncertainty estimate; it is an error, not a random fluctuation, and including it would inflate the uncertainty without improving the value.