Precipitation & Solubility Rules

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

All three reagents can remove Pb²⁺ via precipitation. Na₂SO₄: Pb²⁺ is an exception to the sulfate rule, so PbSO₄(s) forms. Net ionic: Pb²⁺(aq) + SO₄²⁻(aq) → PbSO₄(s). Na₂CO₃: Pb²⁺ is not Group 1 or ammonium, so PbCO₃(s) forms. Net ionic: Pb²⁺(aq) + CO₃²⁻(aq) → PbCO₃(s). Na₂S: PbS is a sulfide with a non-Group 1 cation — insoluble. Net ionic: Pb²⁺(aq) + S²⁻(aq) → PbS(s). [1 — NAGSAG confirmation + 2 net ionic equations with state symbols]

A lower Ksp means the equilibrium lies further to the right — more ions leave solution as precipitate, leaving a lower equilibrium [Pb²⁺]. Ranking by removal efficiency: Na₂S (Ksp ≈ 9×10⁻²⁹) >> Na₂CO₃ (Ksp ≈ 7.4×10⁻¹⁴) > Na₂SO₄ (Ksp ≈ 1.6×10⁻⁸). [1 — correct rank + Ksp interpretation]

Secondary contamination risk: Na₂SO₄ adds Na⁺ and SO₄²⁻ — sulfate at the concentrations used is generally within guidelines and is far less toxic than sulfide [1]. Na₂CO₃ raises pH; excess carbonate could push pH above 8.5, violating the drinking-water guideline, and CO₃²⁻ may precipitate other ions (Ca²⁺, Mg²⁺) present in river water [1]. Na₂S is the most efficient precipitant but excess S²⁻ is acutely toxic at concentrations >0.05 mg/L, introducing a serious secondary hazard that would require careful stoichiometric control [1].

Practical limitation common to all three: precipitation is not perfectly complete (residual [Pb²⁺] governed by Ksp); excess reagent causes secondary contamination; precise stoichiometry is required, meaning the exact [Pb²⁺] must first be determined. The process also requires filtering and disposal of the solid precipitate waste. [1]

Recommendation: Na₂CO₃ is the best choice at carefully controlled stoichiometric quantities. Its Ksp is low enough to reduce [Pb²⁺] from 0.022 to below 0.01 mg/L, the carbonate ion does not introduce a toxic secondary hazard (unlike S²⁻), and its cost index is low (unlike Na₂S). Careful dose control prevents pH elevation beyond 8.5. Na₂S would be preferred only if even stricter removal is needed in an emergency, with post-treatment steps to remove excess sulfide. [1 — justified, context-specific recommendation referencing Ksp + safety + cost]

Marking criteria:

• 1 mark — Uses NAGSAG to confirm all three precipitates form and writes two correct net ionic equations with state symbols.
• 1 mark — Correctly ranks reagents by Ksp and explains that lower Ksp corresponds to lower equilibrium [Pb²⁺].
• 1 mark — Evaluates secondary risk of Na₂SO₄ (low).
• 1 mark — Evaluates secondary risk of Na₂CO₃ (pH elevation / co-precipitation).
• 1 mark — Evaluates secondary risk of Na₂S (sulfide toxicity).
• 1 mark — Identifies a practical limitation common to all strategies (residual Pb²⁺ governed by Ksp; excess reagent creates new contamination; precise dosing required).
• 1 mark — Reaches a justified recommendation that balances removal efficiency, secondary contamination risk, and cost, using lesson/table data explicitly.
• 1 mark — Uses precise chemical language throughout (net ionic equation format, state symbols, Ksp, spectator ions).

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

Research question: What is the concentration of Ag⁺ in the unknown AgNO₃(aq) solution? Hypothesis: Adding excess NaCl(aq) to 50.00 mL of the unknown will precipitate all Ag⁺ as AgCl(s); the mass of collected, dried AgCl can be used to calculate [Ag⁺] via mole ratios. [1]

Variables: Independent: amount of AgNO₃ sample used (50.00 mL). Dependent: mass of AgCl(s) collected after drying. Controlled: volume of sample (pipetted accurately), drying temperature and duration, same balance used throughout. [1]

Method: (1) Pipette exactly 50.00 mL of unknown AgNO₃(aq) into a 250 mL beaker. (2) Slowly add excess NaCl(aq) with stirring until no further precipitate forms (test by adding a drop and observing no cloudiness). (3) Weigh a dry filter paper and record mass. (4) Filter the mixture through the pre-weighed filter paper into a 250 mL flask. (5) Wash the precipitate with a small volume of distilled water to remove soluble impurities (NaNO₃ spectator). (6) Dry the filter paper plus precipitate in an oven at 110°C for at least 2 hours. (7) Cool in a desiccator and reweigh. Record mass of AgCl = (total mass) − (filter paper mass). Repeat three times for precision. [1]

Net ionic equation: Ag⁺(aq) + Cl⁻(aq) → AgCl(s). Spectator ions are Na⁺ and NO₃⁻. [1]

Calculation: Mole ratio Ag⁺ : AgCl = 1:1. n(AgCl) = mass(AgCl) / 143.3 g mol⁻¹. Therefore n(Ag⁺) = n(AgCl). [Ag⁺] = n(Ag⁺) / 0.05000 L (mol L⁻¹). [1]

Errors: (1) Incomplete drying: if the precipitate retains moisture, the recorded mass is higher than the true mass of AgCl → calculated n(AgCl) is overestimated → [Ag⁺] is reported as higher than actual (positive error). (2) Incomplete precipitation: if insufficient NaCl is added, some Ag⁺ remains in solution, reducing the mass of AgCl collected → n(Ag⁺) and [Ag⁺] are underestimated (negative error). [1 per error + direction of effect, max 2]

Marking criteria:

• 1 mark — States a clear research question and hypothesis linking Ag⁺ to precipitate mass via mole ratios.
• 1 mark — Correctly identifies independent, dependent, and two controlled variables.
• 1 mark — Describes a logically sequenced method: addition of excess NaCl, filtration, washing, drying at a defined temperature, reweighing.
• 1 mark — Writes the correct net ionic equation with state symbols and identifies spectator ions.
• 1 mark — Shows the correct mole-ratio calculation chain with units (g → mol → mol L⁻¹).
• 1 mark — Identifies first specific error (incomplete drying) and correctly states the direction of its effect on [Ag⁺].
• 1 mark — Identifies second specific error (incomplete precipitation) and correctly states direction of effect. Accept also: loss of precipitate through filter paper (overestimates precipitation efficiency → underestimates [Ag⁺]).