Titration Endpoint Judgement
A student titrates 25.0 cm³ of a colourless weak acid solution of unknown concentration with 0.100 mol/dm³ NaOH from a burette. Phenolphthalein is the indicator. Three rough titres are 24.10, 24.05 and 24.15 cm³. A fourth careful run gives 24.12 cm³, but the student notices the flask was warm and the solution had a faint pink colour that faded after 20 s. The student must decide the reported concentration and whether the result is trustworthy.
1. Decide which titre values to use and calculate the acid concentration, stating assumptions.
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The four values 24.10, 24.05, 24.15 and 24.12 cm³ agree within 0.10 cm³, which is acceptable precision for a burette read to 0.05 cm³. The mean of the concordant values is (24.10 + 24.05 + 24.15 + 24.12)/4 = 24.105 ≈ 24.11 cm³. Using n(NaOH) = c·V = 0.100 × 0.02411 = 2.411 × 10^-3 mol. If the acid is monoprotic, n(acid) = 2.411 × 10^-3 mol in 25.0 cm³ = 0.0250 dm³, so c(acid) = 2.411 × 10^-3/0.0250 = 0.0964 mol/dm³. The critical assumption is the acid's basicity: if it is diprotic, the concentration halves to 0.0482 mol/dm³. The student must not report a single number without stating the assumed stoichiometry.
2. The faint pink colour fades after 20 s. Explain the significance and what the student should do.
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A pink colour that persists for only ~20 s and then fades indicates the endpoint was overshot or that CO2 from the air is neutralising the excess base, or that the flask was warm so the indicator's colour is less stable. Phenolphthalein should remain pink for at least 30 s at the endpoint. The correct action is to discard this run, cool the flask to room temperature, and repeat until a pink colour persists. The warm flask is a systematic error: it shifts the indicator's transition range and can also change the acid's dissociation, biasing the titre. The student should not average the suspect 24.12 cm³ value with the others merely because it is numerically close - agreement in number does not cure a procedural fault.
3. Estimate how a 0.05 cm³ reading uncertainty propagates to the final concentration.
Read the worked answer
The titre uncertainty is about ±0.05 cm³ on 24.11 cm³, a relative uncertainty of 0.05/24.11 ≈ 0.21%. The burette concentration is given to three significant figures, so its relative uncertainty is about 0.1%. The volume of acid (25.0 cm³, ±0.1 cm³ from a pipette) contributes 0.4%. Adding in quadrature: sqrt(0.21² + 0.1² + 0.4²) ≈ 0.46%. So c = 0.0964 mol/dm³ with an uncertainty of about ±0.0004 mol/dm³, i.e. 0.0964 ± 0.0004. This shows the dominant error is the pipetted volume, not the burette reading - a useful judgement for deciding where to improve technique.