HSC Exam Practice

Sample response. Calibration is the process of establishing the relationship between the voltage measured by the pH probe and the true pH of a solution, using buffer solutions of precisely known pH. It must be performed before each use because the properties of the glass membrane change over time (electrode aging) and because temperature changes alter the Nernst slope — calibration corrects for both types of drift simultaneously, ensuring the measured pH is accurate.

Marking notes. 1 mark for defining calibration as using known-pH buffer solutions to establish the voltage–pH relationship. 1 mark for a valid reason it must be done before each use (electrode aging / Nernst slope temperature dependence / reference electrode drift). Accept any one valid reason for 1 mark.

Sample response. The glass membrane of a pH electrode is selectively permeable to H⁺ ions. When the electrode is placed in an acidic solution, H⁺ ions from the test solution exchange into the outer hydrated gel layer of the glass membrane, while H⁺ ions from the inner reference solution (of fixed, known [H⁺]) occupy the inner gel layer. Because [H⁺] is different on the two sides of the membrane, a potential difference (voltage) develops across the glass membrane. This voltage is proportional to the difference in [H⁺] and is described by the Nernst equation: at 25 °C, E ≈ E° − 0.0592 × pH. The meter's electronics measure this voltage and convert it to a pH value using the calibrated relationship.

Marking notes. 1 mark — glass membrane is selectively permeable to H⁺ ions; H⁺ ions exchange into the gel layers. 1 mark — different [H⁺] on each side of the membrane creates a potential difference (voltage) across the membrane. 1 mark — the voltage is related to pH by the Nernst equation and is converted to pH by the meter electronics (via calibration).

Sample response. A direct pH probe reading gives the pH of the solution (typically to ±0.01 pH units). To obtain concentration, the pH must be converted to [H⁺] and then used in a reverse Ka calculation, which introduces uncertainty from the Ka value (~5–10% in concentration, due to temperature and ionic strength variation in Ka). A volumetric titration with NaOH directly measures the moles of acetic acid that react stoichiometrically with NaOH (1:1), giving concentration to ±0.1–0.3% uncertainty (from concordant titres to ±0.05 mL). The titration is far more precise for determining concentration than the pH probe + Ka method.

Marking notes. 1 mark — pH probe gives pH directly; concentration requires Ka-based calculation. 1 mark — pH probe method has ~5–10% concentration uncertainty due to Ka uncertainty. 1 mark — titration gives concentration directly with ~0.1–0.3% uncertainty from burette readings; is more precise for concentration measurement.

Sample response. (a) Continuous glass electrode pH monitoring (direct pH probe). Reason: continuous monitoring detects rapid pH changes in real time, enabling immediate automated correction; a titration cannot be performed continuously. (b) Conductometric titration or automated potentiometric titration (pH probe detects EP from inflection of pH vs volume curve). Reason: the dark colour of red wine masks the phenolphthalein colour change at the equivalence point — indicator titration is unreliable; conductometric/potentiometric detection is unaffected by colour. (c) Back titration. Reason: CaCO₃ is insoluble in water and reacts slowly with HCl — a direct titration cannot detect a clean equivalence point; back titration allows the solid to dissolve completely in excess HCl before the unreacted excess is back-titrated with standard NaOH.

Marking notes. 2 marks per part (a)–(c): 1 mark for correct method, 1 mark for a valid reason linked to a specific property of the sample or measurement requirement.

Sample response. In two-point calibration, the first calibration point (pH 7.00) sets the intercept (the absolute offset) of the linear voltage–pH relationship — it positions the line at the correct pH for that voltage. The second calibration point (pH 4.00) sets the slope (sensitivity: mV per pH unit) of the line — it corrects for any change in the Nernst slope due to electrode aging or temperature. A one-point calibration with only pH 7.00 sets the intercept but cannot correct for errors in the slope — if the slope has drifted, the pH readings will be increasingly inaccurate as the sample pH moves away from pH 7.00, even though the reading is correct exactly at pH 7.00.

Marking notes. 1 mark — identifies that the first calibration point sets the intercept. 1 mark — identifies that the second calibration point sets the slope (sensitivity/mV per pH unit). 1 mark — explains that single-point calibration cannot correct for slope errors, causing inaccuracy at pH values far from the single calibration point.

Sample response (a) — calibration slope. Slope = (V₂ − V₁)/(pH₂ − pH₁) = (−332 − (−155))/(7.00 − 4.00) = −177/3.00 = −59.0 mV/pH. This is very close to the theoretical Nernst slope of −59.2 mV/pH at 25 °C — a difference of only 0.2 mV/pH (0.3%), within normal experimental variation due to small temperature deviations or slight electrode aging. [2 marks: 1 for correct calculation; 1 for comparison to Nernst value]

Sample response (b) — pH of vinegar sample. Using calibration line from pH 4.00, −155 mV, slope −59.0 mV/pH: pH = 4.00 + (−155 − (−214))/59.0 = 4.00 + 59/59.0 = 4.00 + 1.00 = pH 5.00. [2 marks: 1 for correct formula/method; 1 for correct answer pH 5.00 ± 0.05]

Sample response (c) — Ka-based concentration vs titration. [H⁺] = 10⁻⁵·⁰⁰ = 1.00 × 10⁻⁵ mol/L. Ka = [H⁺]²/(c − [H⁺]) ≈ [H⁺]²/c for weak acid (since c ≫ [H⁺]): c ≈ [H⁺]²/Ka = (1.00 × 10⁻⁵)²/(1.8 × 10⁻⁵) = 1.00 × 10⁻¹⁰/1.8 × 10⁻⁵ = 5.6 × 10⁻⁶ mol/L. This value appears unrealistically low for vinegar (expected ~0.8–1.0 mol/L); this illustrates the unreliability of the Ka method at pH 5.00 which is far from a typical vinegar pH. Precision comment: Ka method introduces ~7–10% uncertainty; titration gives n(NaOH) = 0.5000 × 0.01860 = 9.30 × 10⁻³ mol → c(CH₃COOH) = 9.30 × 10⁻³/0.01000 = 0.930 mol/L with titre uncertainty of 0.05/18.60 ≈ 0.27% — far more precise. [3 marks: 1 for Ka calculation attempt; 1 for identifying the high uncertainty of Ka method; 1 for quantitative precision comparison with titration]

Sample response (a) — pH probe uncertainty. Although a calibrated pH probe measures voltage to ±0.1 mV (±0.002 pH units), the conversion from pH to concentration uses the Ka value in the reverse equilibrium calculation: c ≈ [H⁺]²/Ka. The Ka for aspirin (Ka = 3.0 × 10⁻⁴) is an average literature value that varies with temperature and ionic strength by ±10–15%. This Ka uncertainty propagates directly into the calculated concentration — a 10% error in Ka gives a ~10% error in c, producing 7–12% overall concentration uncertainty. The 0.01 pH precision of the probe is thus irrelevant for concentration precision: the Ka uncertainty dominates. [2 marks: 1 for identifying Ka uncertainty as the dominant source; 1 for explaining propagation from Ka error to concentration error]

Sample response (b) — why choose direct titration over conductometric for pharmaceutical QC. Both direct titration (~0.3%) and conductometric titration (~0.8%) have uncertainties well below 1%, and both are suitable in principle for ≥99.0% purity certification. However, direct NaOH titration has three advantages for pharmaceutical QC: (1) substantially lower uncertainty (0.3% vs 0.8%), making it more appropriate for the stringent ≥99.0% specification where a 0.8% error could cause a non-compliant sample to pass; (2) direct NaOH titration is the pharmacopoeial (BP/USP) standard method for aspirin purity — regulatory inspectors and certification bodies accept it without question; (3) aspirin in ethanol–water forms a turbid solution at higher concentrations, but the turbidity is moderate and sufficient dilution makes phenolphthalein visible; if this is a concern, conductometric titration could be used as an alternative, but regulatory compliance favours the established pharmacopoeial method. [3 marks: 1 for lower uncertainty of direct titration numerically justified; 1 for regulatory/pharmacopoeial acceptance; 1 for applicability consideration (turbidity management or regulatory compliance argument)]

Sample response. The glass electrode pH probe is a precision electrochemical instrument that converts the concentration of H⁺ ions in a solution into a measurable voltage via the Nernst equation. Its glass membrane — rich in SiO₂, Na₂O, and CaO — is selectively permeable to H⁺ ions. When the electrode is immersed in a solution, H⁺ ions exchange into the outer hydrated gel layer of the membrane, while the inner gel layer is in contact with an internal reference solution of fixed [H⁺]. The difference in [H⁺] across the membrane creates a potential difference described at 25 °C by E ≈ E° − 0.0592 × pH. The meter's electronics convert this voltage to a pH reading using the calibrated Nernst relationship. Before each use, two-point calibration with buffer solutions (e.g. pH 4.00 and 7.00) is mandatory: the first buffer sets the intercept (offset) and the second sets the slope (sensitivity in mV/pH), correcting for electrode aging and temperature drift simultaneously.

The glass electrode's primary advantage is its ability to measure pH rapidly (in seconds), continuously, and for any solution type — coloured, turbid, or clear. In the NSW EPA water monitoring network, calibrated glass electrode probes are installed at river monitoring stations and industrial discharge points to continuously measure pH and alert authorities when values fall outside the 6.5–8.5 regulatory range. A single probe can monitor 24 hours per day without analyst intervention — a task that is impossible for manual titration. This makes continuous pH monitoring the only feasible method for real-time environmental compliance.

However, the glass electrode has a critical limitation for concentration determination: it measures pH, not concentration. Converting pH to concentration requires the Ka of the acid — a step that introduces 5–10% uncertainty from Ka temperature and ionic-strength dependence, compared with 0.1–0.3% for volumetric titration. For determining the acetic acid content of vinegar for FSANZ food labelling compliance — where the Australian vinegar standard requires reporting % w/v acetic acid to ±0.1% — the glass electrode + Ka method is not acceptable; a direct NaOH titration with phenolphthalein (or automated potentiometric titration) is mandated. Similarly, the Australian Wine Research Institute (AWRI) uses automated potentiometric NaOH titration (equivalence point from the pH-curve inflection) for titratable acidity certification of wines — not a direct pH reading — because only the titration directly measures moles of acid reacted.

In summary, the glass electrode excels at continuous, rapid, solution-type-independent pH monitoring (environmental compliance, process control) but is insufficiently precise for quantitative concentration determination in regulatory contexts. Volumetric titration is more precise for concentration (~0.3% vs ~7%), and is the required standard for food and pharmaceutical certification, but cannot be performed continuously or rapidly at scale. The two techniques are complementary, not competitive: each is optimal for a different analytical purpose.

Marking criteria.

• 1 mark — Describes the physical basis of the glass electrode: glass membrane selectively permeable to H⁺; H⁺ exchange at gel layers creates potential difference; Nernst equation relates voltage to pH.
• 1 mark — Explains the role of calibration: two-point calibration with buffer solutions sets both the intercept and slope; corrects for electrode aging and temperature drift.
• 1 mark — Identifies a specific advantage of the glass electrode with a named Australian industrial application (e.g. NSW EPA continuous pH monitoring, industrial discharge compliance, AWRI pH measurement).
• 1 mark — Identifies the precision limitation of the glass electrode for concentration: ~5–10% from Ka propagation, compared with ~0.1–0.3% for titration; explains the source of the Ka uncertainty.
• 1 mark — Identifies a specific application where volumetric titration is required (FSANZ vinegar certification, AWRI titratable acidity, pharmaceutical purity) with a named Australian context.
• 1 mark — Explains why volumetric titration is more appropriate for that application (directly measures moles; precision meets regulatory standard; no Ka dependence).
• 1 mark — Reaches an explicit, evidence-based evaluative judgement that frames the two techniques as complementary — each optimal for a different analytical purpose — not as a ranking of one over the other.