Acid-Base Titrations & Indicators

Q1 — Sample Band 6 response (8 marks), annotated

Primary standard definition and Na₂CO₃ suitability: A primary standard is a highly pure, chemically stable solid with a known molar mass that can be accurately weighed to prepare or verify a standard solution of precisely known concentration. Anhydrous Na₂CO₃ is suitable because it is non-hygroscopic under normal storage, has a reasonably high molar mass (105.99 g mol⁻¹) that reduces the relative error in weighing, and reacts completely and stoichiometrically with HCl (and indirectly validates the NaOH used in subsequent titrations). [2 marks: 1 definition; 1 Na₂CO₃ justification with at least two properties]

Calculation: Average concordant titre = (17.90 + 17.85 + 17.92) / 3 = 17.89 mL = 0.01789 L. n(NaOH) = 0.2000 × 0.01789 = 0.003578 mol. Mole ratio H₂SO₄ : NaOH = 1:2, so n(H₂SO₄) = 0.003578 / 2 = 0.001789 mol. This is in the 1.00 mL diluted aliquot, so c(diluted) = 0.001789 / 0.001000 = 1.789 mol L⁻¹. Multiply by dilution factor 1000: c(undiluted H₂SO₄) = 1.789 × 1000 = 17.9 mol L⁻¹. [2 marks: 1 correct mole calculation with ratio applied; 1 correct application of dilution factor]

Evaluation against specification: The calculated concentration of 17.9 mol L⁻¹ is below the 18.0 mol L⁻¹ specification. Percentage difference = |(17.9 − 18.0)| / 18.0 × 100 = 0.56%. While this is a small discrepancy, in an industrial context it means the batch is slightly below specification and would need to be flagged for review. [1 mark]

Systematic error: One systematic error would be using a burette with a calibration error (e.g. scale displaced by 0.1 mL throughout), which would consistently produce titres that are slightly too large or too small in every trial, shifting the calculated concentration in one direction. Another example: if the NaOH solution absorbed CO₂ from the air, forming Na₂CO₃, the effective NaOH concentration would be lower than assumed, causing the calculated H₂SO₄ concentration to be underestimated (since less NaOH reacts per mole than expected). [1 mark: identified error + direction of effect]

Primary standard vs reagent bottle label: The labelled concentration on a reagent bottle is often nominal or reflects the manufactured concentration at the time of production, not the actual concentration at time of use. NaOH solutions in particular absorb CO₂ and water vapour from the air over time, reducing their effective concentration. Standardising against a primary standard ensures that the concentration used in calculations is verified experimentally rather than assumed, which is a fundamental requirement in accredited laboratories where results must be traceable to a known measurement standard. [2 marks]

Marking criteria summary:

• 1 mark — Correct definition of primary standard (pure, stable, known molar mass, accurately weighed).
• 1 mark — Explains why Na₂CO₃ is suitable (at least two properties: non-hygroscopic, high molar mass, stoichiometric reaction).
• 1 mark — Correct average titre and mole calculation with 1:2 ratio applied.
• 1 mark — Correct application of the 1000× dilution factor to give 17.9 mol L⁻¹.
• 1 mark — Evaluates result against 18.0 mol L⁻¹ specification with percentage difference or clear comparison.
• 1 mark — Identifies a named systematic error and correctly states the direction of its effect on the result.
• 2 marks — Explains why standardisation against a primary standard is essential for reliable results (distinguishes from nominal bottle label; links to traceability or absorptive degradation of NaOH).

Q2 — Sample Band 6 response (7 marks), annotated

Calculation: n(NaOH) = 0.2000 × 0.02840 = 0.005680 mol. HCl + NaOH react 1:1, so n(excess HCl) = 0.005680 mol. n(initial HCl) = 0.5000 × 0.05000 = 0.02500 mol. n(HCl reacted with CaCO₃) = 0.02500 − 0.005680 = 0.01932 mol. CaCO₃ : HCl = 1:2, so n(CaCO₃) = 0.01932 / 2 = 0.009660 mol. m(CaCO₃) = 0.009660 × 100.09 = 0.967 g. [2 marks: 1 for correctly subtracting excess; 1 for correct 1:2 ratio and mass]

Why back titration is more appropriate: CaCO₃ is an insoluble solid that cannot be dissolved and directly pipetted as a precise aliquot, making direct titration impractical. Additionally, the reaction of CaCO₃ with HCl produces CO₂ gas which can cause bubbling that makes it difficult to detect a precise endpoint directly. Back titration avoids both problems by adding a known excess of HCl to dissolve the solid and allow complete reaction, then measuring only the remaining excess acid in a clear, CO₂-free solution. [2 marks: 1 per distinct chemical reason]

Indicator choice evaluation: At the equivalence point of the second titration (HCl + NaOH), the solution contains NaCl(aq), a neutral salt that produces a solution at approximately pH 7. Phenolphthalein transitions between pH 8.2 and 10.0, which is above pH 7. For a strong acid (excess HCl) being titrated by a strong base (NaOH), the equivalence point is at pH 7, so the steep pH jump spans from about pH 4 to pH 10. Phenolphthalein’s transition range (pH 8.2–10.0) falls within this steep region, so it is an acceptable indicator, though bromothymol blue (pH 6.0–7.6) would also work and would give an endpoint closer to pH 7. [2 marks: 1 for identifying equivalence pH; 1 for evaluating whether phenolphthalein is within the steep jump]

Modification to improve reliability: Stir the mixture for longer (e.g. 15–20 minutes) or gently heat the mixture after adding HCl to ensure the CaCO₃ reacts completely before filtering. If any CaCO₃ remains unreacted, the calculated amount of acid consumed will be too low, leading to an underestimate of the CaCO₃ content in the tablet. Complete reaction is the most critical validity requirement for back titration. [1 mark]

Marking criteria summary:

• 1 mark — Correctly calculates n(excess HCl) using 1:1 NaOH:HCl ratio.
• 1 mark — Correctly subtracts excess HCl, applies 1:2 CaCO₃:HCl ratio, and calculates mass of CaCO₃ as 0.967 g.
• 1 mark — Explains one chemical reason why back titration is preferred (insoluble solid or CO₂ gas production).
• 1 mark — Explains a second distinct chemical reason.
• 1 mark — Identifies that the equivalence point in step 3 is at pH ≈ 7 (strong acid + strong base).
• 1 mark — Evaluates phenolphthalein against the steep jump and states whether it is acceptable (yes, falls within the steep region; alternative indicators also acceptable).
• 1 mark — Identifies a specific modification to improve reliability with a valid justification (e.g. longer stirring/heating to ensure complete reaction of CaCO₃; conducting multiple trials and averaging; filtering carefully to prevent any CaCO₃ passing into the filtrate).