Part 2: Uncertainty, conclusions and improvements

Distinguish repeatability from accuracy and connect each experimental limitation to a realistic improvement.

Calculate uncertainty in the quantity actually measured

Use the uncertainty given for the apparatus or question. For an analogue reading a common estimate is half the smallest division, but a stated tolerance takes priority. When a measurement is a difference, include both readings.

Worked example: two burette readings each have ±0.05 cm³ uncertainty. The titre has ±0.10 cm³ uncertainty. For a 20.00 cm³ titre, percentage uncertainty = 0.10/20.00 × 100 = 0.50%. Increasing the titre reduces this percentage without changing the burette.

For school-level maximum uncertainty estimates, add absolute uncertainties for sums/differences; add percentage uncertainties for products/quotients. This is a worst-case estimate, not a statistical confidence interval.

Find which measurement dominates the uncertainty

Constructed standard-solution example: mass delivered by difference is 2.000 g from two readings each ±0.001 g. Maximum absolute uncertainty is ±0.002 g, or 0.100%. A 250.0 cm³ flask has stated uncertainty ±0.2 cm³, or 0.080%. For c = m/(MV), treating M as exact for this exercise, maximum percentage uncertainty is approximately 0.180%.

For a 0.100 mol dm⁻³ solution, 0.180% corresponds to about ±0.00018 mol dm⁻³. This simple addition is a worst-case school estimate, not a statistical confidence interval. Use uncertainty values supplied for the actual apparatus; printed decimal places alone do not establish every instrument’s tolerance.

If a temperature rise is 2.0 K and each temperature reading is ±0.1 K, the difference uncertainty is ±0.2 K, or 10%. A more precise balance would do little to resolve that dominant temperature uncertainty. Choose the improvement that addresses the largest relevant limitation.

Precision, accuracy and errors

Precision describes how closely repeated measurements agree; accuracy describes closeness to the accepted or true value. Concordant titres show repeatability, but a consistently diluted burette solution can still make every result inaccurate.

Random variation produces scatter; repeated measurements and a mean reduce its effect. A systematic bias shifts results consistently and is not removed by repetition. Investigate an anomalous result and repeat it where possible; do not delete data merely because it disagrees with a prediction.

A conclusion should state the pattern, cite numerical evidence, explain the chemistry and recognise the tested range. Correlation over three concentrations does not establish a rate law beyond those conditions.

Keep significant figures through intermediate calculations and round at the end to a precision justified by the data or explicitly requested. For multiplication/division, the least precise measured input usually limits significant figures. 0.0050 has two significant figures and is 5.0 × 10⁻³; changing units must not invent precision. Interpolation estimates within the measured range; extrapolation extends beyond it and needs a justified model.

Separate agreement, bias and a justified conclusion

Illustrative repeats 19.90, 20.00 and 20.10 cm³ cluster closely, suggesting good repeatability. They may all still be displaced by a common calibration or dilution error. A mean reduces random scatter under suitable conditions; it does not restore a lost reagent concentration or recover gas that escaped on every run.

If a measured result is 84.0 and a reference is 80.0 in the same units, percentage difference relative to the reference is |84.0 − 80.0|/80.0 × 100 = 5.0%. This is a comparison with a reference, not the apparatus uncertainty calculated from instrument tolerances.

A discrepancy larger than an estimated uncertainty deserves investigation of assumptions, calibration and method. Agreement within an estimated uncertainty does not prove that all systematic effects are absent; opposing biases can also cancel. State the evidence and limitation without claiming more than the experiment establishes.

Match the improvement to the limitation

For a gas experiment, gas lost while fitting the bung makes the measured volume too small. Start mixing inside a closed apparatus using a dropping device or separate internal container. A syringe avoids collection through water, but CO₂ can still dissolve in the reaction mixture. Record temperature and pressure when using gas volumes quantitatively.

For a titration, rinse the burette with its reagent to avoid dilution. Rinse the conical flask with distilled water; extra water does not change the moles of analyte. “Use better apparatus” is weaker than naming a smaller uncertainty and explaining its effect.

Build an evaluation as limitation → effect → improvement

For gas loss before the bung is fitted: the measured volume is too small, which underestimates product amount and can distort the early-time gradient. Arrange controlled mixing after the gas path is closed, with a freely moving syringe or other suitable outlet. Do not solve the leak problem by heating a sealed rigid vessel.

For heat loss in an exothermic cup reaction: the measured temperature rise is too small and the calculated molar ΔH is less negative. An insulated cup and lid reduce loss; time-resolved measurement with justified extrapolation estimates its effect. Repeats alone do not correct it.

For an overshot titration end point: the recorded titre is too large. In the standard-base/unknown-acid arrangement this overestimates the acid amount. Add dropwise while swirling near the end point and use a rough run to locate it. A smaller burette division addresses reading uncertainty but does not by itself prevent careless overshooting.

Use the skills throughout the course

Return to these ideas in amount of substance (mass and gas measurements), acids (standard solutions and titration), enthalpy (calorimetry), qualitative analysis (test sequence), rates (graphs) and organic synthesis (reflux, distillation and purification). These connect respectively to relevant PAG 1, 2, 3, 4, 9 and 5 opportunities in the full A-level practical programme.

For an extended response, organise method → measurement → processing → limitation → improvement. OCR level-of-response questions judge the connected, relevant reasoning as a whole; five disconnected facts do not automatically mean five marks.

Quick checks

Original Finesse questions. Reveal the indicative worked solutions after attempting each question; these are not official OCR A mark allocations.

Sources