Chemistry • Year 11 • Module 2 • Lesson 18
Working Scientifically — Practical Investigations
Apply your understanding of error analysis, titration technique, and gravimetric procedures to real data, scenarios, and cause-and-effect reasoning.
1. Interpret titration data — finding concordant titres
A student titrates 25.0 mL of NaOH(aq) with 0.200 mol/L HCl(aq) using phenolphthalein indicator. The table below records five titre readings. 8 marks
| Titre number | Initial burette reading (mL) | Final burette reading (mL) | Titre (mL) | Include in average? (Y/N) |
|---|---|---|---|---|
| 1 (rough) | 0.00 | 19.45 | ||
| 2 | 0.15 | 18.50 | ||
| 3 | 0.30 | 18.65 | ||
| 4 | 0.10 | 18.55 | ||
| 5 | 0.20 | 19.90 |
1.1 Calculate each titre and complete the “Titre (mL)” column. 2 marks
1.2 Identify which titres are concordant (differ by ≤0.1 mL from each other) and complete the “Include in average?” column. State your reasoning. 2 marks
1.3 Calculate the average concordant titre and use it to find the concentration of the NaOH solution. (NaOH + HCl → NaCl + H2O; 1:1 molar ratio) 3 marks
1.4 Titre 5 is significantly larger than the others. Suggest one specific titration error that could explain this outlier and state the type of error (random or systematic). 1 mark
2. Cause-and-effect chain — air bubble in the burette
The boxes below describe a chain of consequences starting from a specific titration error. Complete each empty effect box. 5 marks (1 per effect + 1 overall outcome)
3. Interpret graph — titration reproducibility and precision
The graph below shows the titre values recorded by two students (A and B) across five titrations each. Both students were titrating the same NaOH solution with 0.100 mol/L HCl. The true titre for this solution is 20.0 mL. 7 marks
Figure 3. Titre values (mL) for five titrations each by Student A and Student B, titrating NaOH(aq) with 0.100 mol/L HCl. True titre = 20.0 mL. Illustrative data.
3.1 Describe the pattern in Student A’s results compared to Student B’s results. Use the terms precision and accuracy. 2 marks
3.2 Student A’s results are consistently about 2 mL above the true value. Suggest one specific systematic error in titration technique that would produce this pattern, and explain the mechanism. 3 marks
3.3 Would repeating Student A’s titrations fix the systematic error identified in 3.2? Justify your answer. 2 marks
4. Compare systematic and random errors across five features
Complete the two-column table below. For each feature, write a concise description that contrasts the two error types. 10 marks (1 per cell)
| Feature | Random error | Systematic error |
|---|---|---|
| Direction of effect | ||
| Property affected | ||
| Effect of repeating | ||
| Named titration example | ||
| How to fix/reduce |
Q1.1 — Calculate titres
Titre 1: 19.45 − 0.00 = 19.45 mL. Titre 2: 18.50 − 0.15 = 18.35 mL. Titre 3: 18.65 − 0.30 = 18.35 mL. Titre 4: 18.55 − 0.10 = 18.45 mL. Titre 5: 19.90 − 0.20 = 19.70 mL.
Q1.2 — Concordant titres
Titres 2, 3, and 4 (18.35, 18.35, 18.45 mL) are concordant — they differ by no more than 0.1 mL. Titre 1 is excluded as the rough titre. Titre 5 (19.70 mL) is an outlier, differing by more than 1.3 mL from the concordant set — exclude. Include: Titres 2, 3, 4. Exclude: Titres 1 and 5.
Q1.3 — Average titre and concentration of NaOH
Average concordant titre = (18.35 + 18.35 + 18.45) ÷ 3 = 18.38 mL = 0.01838 L.
n(HCl) = c × V = 0.200 × 0.01838 = 3.68 × 10−3 mol.
From 1:1 ratio: n(NaOH) = 3.68 × 10−3 mol.
c(NaOH) = n/V = 3.68 × 10−3 / 0.0250 = 0.147 mol/L.
Q1.4 — Cause of outlier Titre 5
Accept any one of: (i) overshooting the endpoint — student added excess HCl past the colour change; (ii) a parallax error in a different direction than previous readings; (iii) an air bubble expelled during this titration only. Any single titration producing an outlier is consistent with a random error.
Q2 — Cause-and-effect chain (air bubble)
Effect 1: The volume recorded by the burette is larger than the actual volume of solution dispensed (the expelled air volume is counted as solution).
Effect 2: The calculated titre is therefore larger than the true titre (too large).
Effect 3: The number of moles of HCl calculated is too large (n = cV; larger V gives larger n).
Effect 4: Via the 1:1 stoichiometric ratio, the calculated moles of NaOH appears too large.
Overall outcome: The calculated concentration of NaOH is an overestimate because c = n/V; with n too large (and V fixed at 25.0 mL), c(NaOH) is systematically too high. This is a systematic error because the same bubble affects every titration equally.
Q3.1 — Precision and accuracy (2 marks)
Student A’s results are highly precise (tightly clustered, range ≤ 0.3 mL) but inaccurate (all ~2 mL above the true value of 20.0 mL). Student B’s results are imprecise (widely scattered, range ~3.0 mL) but more accurate on average (scattered around the true value of 20.0 mL).
Q3.2 — Systematic error causing ~2 mL overestimate (3 marks)
Accept any one of: (i) Air bubble in burette: if an air bubble of ~2 mL was consistently present in the burette tip and expelled during every titration, the volume of solution recorded would be ~2 mL too large every time, producing a consistently high titre (systematic, same direction, all trials). (ii) Burette not rinsed with titrant: residual water in the burette dilutes the HCl, so more HCl volume is required to neutralise the NaOH, producing a consistently larger titre. (iii) Consistently overshooting the endpoint by the same amount due to adding too much titrant past the colour change every trial. Award 1 mark for naming the specific source, 1 mark for explaining the mechanism, 1 mark for explaining why it produces a systematic overestimate.
Q3.3 — Can repeating fix the systematic error? (2 marks)
No. Repeating does not fix a systematic error because the same source of error (e.g. the air bubble or unrinsed burette) affects every trial equally and in the same direction. Averaging five titres that are all ~2 mL too large gives a mean that is still ~2 mL too large. To fix it, the source of the systematic error must be identified and removed (e.g. flushing the burette tip or rinsing it with titrant before filling).
Q4 — Systematic vs random comparison table
Direction of effect: Random: varies unpredictably, sometimes too high, sometimes too low. Systematic: always the same direction (consistently too high or consistently too low).
Property affected: Random: precision/reliability (reproducibility). Systematic: accuracy/validity (closeness to true value).
Effect of repeating: Random: can be reduced by averaging many trials — random errors partially cancel. Systematic: NOT reduced by repeating — every trial is biased equally.
Named titration example: Random: parallax error when reading the burette (angle varies between readings). Systematic: air bubble in burette tip expelled during every titration; overshooting the endpoint every time.
How to fix/reduce: Random: repeat trials and average concordant results. Systematic: identify and eliminate the specific source (e.g. flush burette, rinse with titrant, perform rough titre first).