HSC Exam Practice

Sample response. A random error is an unpredictable variation in measurements that can be higher or lower than the true value; it primarily affects reliability (precision/reproducibility) and can be reduced by repeating trials and averaging. A systematic error always shifts results in the same direction (consistently too high or too low), does not vary between measurements, and primarily affects validity (accuracy); it cannot be fixed by repeating trials.

Marking notes. 1 mark for a correct definition of random error (unpredictable, varies both directions); 1 mark for stating random error affects reliability; 1 mark for a correct definition of systematic error (consistent direction, cannot be reduced by repeating); 1 mark for stating systematic error affects validity.

Sample response. “Human error” is not an acceptable answer because it does not identify the specific source of the error, explain its mechanism, or indicate its direction of effect on the result. Examiners require students to name the specific procedural error (e.g. “parallax error when reading the burette meniscus because the student’s eye was above the meniscus level”), state whether it causes an over- or underestimate, and explain the consequence for the calculated concentration.

Marking notes. 1 mark for explaining that “human error” is too vague (doesn’t name the specific source); 1 mark for stating what is required instead (specific source, direction of effect, consequence for calculated result).

Sample response. Validity refers to how well an experiment measures what it is intended to measure — a valid result is free from systematic error and uses appropriate equipment and methodology. In a titration, rinsing the burette with the titrant before filling improves validity by ensuring the titrant concentration is not diluted by residual water. Reliability refers to the reproducibility of results — whether repeated measurements give consistent values. Repeating titrations to obtain three concordant titres and averaging them improves reliability by reducing the influence of random variation.

Marking notes. 1 mark for correct definition of validity (free from systematic error / measures what it is intended to); 1 mark for a specific procedure that improves validity (e.g. rinsing burette; using calibrated volumetric glassware; flushing air bubbles); 1 mark for correct definition of reliability (reproducibility / consistency of repeated measurements); 1 mark for a specific procedure that improves reliability (e.g. obtaining concordant titres; repeating and averaging; performing rough titre first).

Sample response (a). Random error. Reading the burette above the meniscus sometimes overestimates the volume and sometimes underestimates it; the effect on the titre varies unpredictably between readings. This means calculated concentration is sometimes too high and sometimes too low, reducing the precision (reliability) of results but not causing a consistent bias.

Sample response (b). Systematic error. Because the air bubble is expelled during every titration, the recorded volume always includes the air volume as if it were solution. The titre is consistently larger than the actual volume of NaOH dispensed. This leads to n(HCl) being calculated as too large every time; via the stoichiometric ratio, n(NaOH) appears too large, and c(NaOH) = n/V is a systematic overestimate across all trials.

Marking notes. 1 mark for correctly classifying each scenario (random for (a); systematic for (b)); 1 mark for correctly explaining the effect on the calculated concentration for each (unpredictable variation / systematic overestimate). 2 marks total per sub-part.

Sample response. A measuring cylinder has a precision of ±0.5 mL, which introduces an uncertainty of at least 1 mL in the analyte volume. This would introduce a systematic or significant random error into the calculated concentration because the volume of analyte (25.0 mL) is a key term in c = n/V. A calibrated 25 mL pipette (±0.05 mL) is the correct choice because it delivers an exact volume with ten times greater precision.

Marking notes. 1 mark for explaining why a measuring cylinder is unsuitable (large uncertainty / unsuitable precision for volumetric analysis); 1 mark for naming the calibrated 25 mL pipette as the appropriate piece of equipment.

Sample response. If the BaSO₄ precipitate is not fully dried, it retains water molecules within the solid. The mass recorded on the balance is therefore higher than the true mass of pure BaSO₄ [1]. A higher recorded mass leads to a higher calculated n(BaSO₄) = m/M [1]. Via the 1:1 stoichiometric ratio (Ba²⁺ : BaSO₄), the calculated n(Ba²⁺) also appears too large, and therefore c(Ba²⁺) = n/V is an overestimate. Because the same residual moisture is present in every trial (the drying step was consistently insufficient), the overestimate is systematic — it appears in the same direction in every repeat [1].

Marking notes. 1 mark for identifying that retained water increases the recorded mass above the true BaSO₄ mass; 1 mark for the stoichiometric chain (mass too high → n(BaSO₄) too high → n(Ba²⁺) too high → c(Ba²⁺) overestimated); 1 mark for classifying the error as systematic and explaining why (consistent direction across all trials because same procedure used each time).

Sample response (a). Priya’s five titres (approximately 23.9–24.1 mL) are tightly clustered within a range of only ~0.2 mL, indicating high precision [1]. Lachlan’s five titres (approximately 19.8–23.5 mL) are widely scattered over a range of ~3.7 mL, indicating low precision [1]. Priya’s results are therefore considerably more precise than Lachlan’s, even though both sets are centred around different values [1].

Sample response (b). The error is a systematic error because all five of Priya’s results are consistently ~2 mL above the true value in the same direction; it is not random variation [1]. One specific procedural error: the burette was not rinsed with the titrant (HCl) before filling. Residual distilled water from the last wash dilutes the HCl solution inside the burette, lowering [HCl] below 0.200 mol/L. A larger volume of HCl is therefore required to neutralise the 25.0 mL NaOH aliquot, producing a consistently larger titre than the true value [1]. This mechanism operates identically in every titration, explaining the consistent overestimate of ~2 mL [1]. (Accept also: air bubble present in every titration; consistently overshooting the endpoint each trial.)

Sample response (c). Averaging five titres that are all ~2 mL above the true value gives a mean that is still ~2 mL too high [1]. Repeating and averaging cannot fix a systematic error because the same bias (e.g. diluted titrant) affects every trial equally and in the same direction. To fix the error, the source must be identified and eliminated — in this case, rinsing the burette three times with the titrant solution before filling [1].

Marking notes. Part (a): 1 mark for commenting on Priya’s precision with values; 1 mark for commenting on Lachlan’s precision with values; 1 mark for a valid comparison statement. Part (b): 1 mark for classifying as systematic with justification; 1 mark for naming a specific procedure (unrinsed burette / air bubble / consistent overshoot); 1 mark for correct mechanism explanation. Part (c): 1 mark for explaining that all five values carry the same bias so the mean is still biased; 1 mark for stating what is needed to fix it (identify and remove the source of error).

Sample response. Performing more trials and averaging is an effective strategy for improving reliability when the dominant sources of error are random in nature — that is, when errors vary unpredictably between measurements and are equally likely to be too high or too low. For example, parallax error when reading the burette meniscus (reading from slightly different angles on different occasions) is a random error: sometimes the reading is too high, sometimes too low. Repeating five titrations and averaging the concordant results allows these over- and under-readings to partially cancel each other, bringing the mean closer to the true volume. Similarly, small variations in endpoint detection — stopping the titration when the colour is slightly more or less pink on different trials — are random errors that averaging can reduce. In these cases, more trials genuinely improve both precision and the closeness of the mean to the true value. However, repeating trials does not improve validity and does not correct systematic errors. A systematic error shifts every trial in the same direction by a consistent amount. Three well-known examples from titration: (i) an air bubble trapped in the burette tip that is expelled during every titration makes the recorded volume larger than the true volume of solution dispensed in every trial; (ii) a burette that was not rinsed with the titrant before filling has diluted HCl inside, requiring more volume to neutralise the same amount of NaOH, and this overestimate occurs consistently across all trials; (iii) in gravimetric analysis, an incompletely dried BaSO₄ precipitate retains water, causing the recorded mass to exceed the true precipitate mass in every weighing. In each of these three cases, averaging five results still gives an answer biased in the same direction as each individual result, because the bias is identical in every trial. The mean is precise (tight cluster) but inaccurate (systematically shifted from the true value). Repeating only improves the estimate of the biased mean — it does not bring the result closer to the truth. The fundamental distinction is therefore: averaging reduces random errors and improves reliability; it does not fix systematic errors and does not improve validity. For validity, the source of the systematic error must be identified and eliminated before the experiment begins (e.g. flushing the burette, rinsing with titrant, drying the precipitate to constant mass). The statement in the question is therefore partially correct only: repeating trials is sufficient to improve reliability when errors are random, but it is insufficient to produce a valid outcome when systematic errors are present.

Marking criteria (7 marks). 1 = correctly explains when repeating/averaging is effective — for reducing random errors (with example: parallax, endpoint variation). 1 = identifies that averaging does not fix systematic errors, with reference to a specific named example (air bubble, unrinsed burette, or incomplete drying). 1 = correctly defines or applies the distinction between validity (freedom from systematic error) and reliability (reproducibility). 1 = second named systematic error from titration or gravimetric analysis with mechanistic explanation of why averaging does not fix it. 1 = explains the outcome when averaging a set of systematically biased values (mean is still biased; precision high but accuracy low). 1 = identifies the correct remedy for systematic errors (find and eliminate the source; not repetition). 1 = reaches an explicit evaluative judgement: the statement is only partially correct — it applies to random errors but not systematic errors.