Chemistry • Year 12 • Module 5 • Lesson 16

Solubility Rules & Precipitation

Two extended-response tasks at Band 5–6 level: synthesise solubility data, evaluate a water-treatment decision, and critique a source claim about precipitation chemistry.

Master • Extended Response

1. Evaluate a water treatment decision for Broken Hill lead contamination

Scenario: In 2016, water quality researchers sampling drinking water in Broken Hill (NSW) reported elevated dissolved lead concentrations in several older neighbourhoods, attributed to the corrosion of lead-lined service pipes installed before 1970. The water in these areas had a pH of 6.2 and relatively low total dissolved solids (TDS). A team of environmental engineers evaluated three candidate precipitants to lower dissolved Pb²⁺ below the Australian Drinking Water Guidelines limit of 0.01 mg/L: (i) Na₂CO₃ (sodium carbonate), (ii) Na₃PO₄ (sodium phosphate), and (iii) Na₂SO₄ (sodium sulfate).

Table 1. Key data for candidate precipitants of Pb²⁺
Precipitant	Precipitate formed	K_sp (25°C)	Other ions introduced	Cost index
Na₂CO₃	PbCO₃	7.4×10⁻¹⁴	Na⁺, CO₃²⁻	Low
Na₃PO₄	Pb₃(PO₄)₂	8.0×10⁻⁴³	Na⁺, PO₄³⁻	Moderate
Na₂SO₄	PbSO₄	2.5×10⁻⁸	Na⁺, SO₄²⁻	Low

Source: K_sp values adapted from CRC Handbook of Chemistry and Physics (2022). Australian Drinking Water Guidelines (NHMRC, 2022) limit for Pb: 0.01 mg/L.

Question (8 marks): Evaluate which of the three candidate precipitants is most appropriate for treating the Broken Hill drinking water supply. In your response you must:

Define solubility product (K_sp) and explain what a lower K_sp means for the effectiveness of precipitation treatment;
Apply NAGSAG to verify that each precipitate is predicted to be insoluble;
Compare all three precipitants on at least three criteria (e.g. precipitation completeness, effect on other water quality parameters, cost);
Consider whether the dissolved CO₃²⁻ or PO₄³⁻ introduced could affect other common ions in the water supply (Na⁺, Ca²⁺, Mg²⁺);
Reach an evidence-based judgement identifying the preferred precipitant with justification.

Your response (approximately 15 lines):

Plan your response: define K_sp first, then check NAGSAG for all three, then build a comparison table mentally across three criteria, then evaluate and conclude.

2. Source critique — a media article on water hardness removal

Read the following excerpt, then answer the question below. 8 marks

Source excerpt (simulated media article)

“Engineers at a Queensland water utility have solved the local hard-water problem by adding table salt (NaCl) to the supply. The sodium ions displace calcium and magnesium ions from the water, causing them to fall out as insoluble precipitates. Because both calcium chloride and magnesium chloride are insoluble, the hardness ions are permanently removed. The sodium left behind is completely harmless and makes the water taste slightly better. The process works for any ionic compound since all dissolved ions will eventually form precipitates when another ion is added.”

— Adapted from a hypothetical regional news article, 2024.

Question (8 marks): The article contains multiple scientific errors related to solubility rules and precipitation chemistry. Identify at least three distinct errors, explain the correct chemistry for each, and describe how the actual process of water softening by precipitation works. Your response must apply NAGSAG explicitly where relevant.

Your response (approximately 15 lines):

Work through the claims one by one: (1) Does NaCl cause precipitation of Ca²⁺/Mg²⁺? (2) Are CaCl₂ and MgCl₂ insoluble? (3) Is it true that any ion will eventually precipitate another? Identify what is actually used for lime softening.

Answers — Do not peek before attempting

Q1 — Marking criteria (8 marks)

1 mark — K_sp defined correctly: K_sp is the equilibrium constant for the dissolution of a sparingly soluble ionic compound; K_sp = [cation]^a[anion]^b at saturation. A lower K_sp means the equilibrium lies further to the left (less dissolution), so less Pb²⁺ remains dissolved after precipitation.

1 mark — NAGSAG verification (all three): PbCO₃: carbonates generally insoluble, Pb²⁺ not Group 1 → insoluble ✓. Pb₃(PO₄)₂: phosphates generally insoluble, Pb²⁺ not Group 1 → insoluble ✓. PbSO₄: Pb²⁺ is a named exception to the sulfate rule → insoluble ✓. [Award 1 mark for all three correctly identified; partial if two of three correct.]

1 mark — Precipitation completeness (K_sp comparison): K_sp order: Pb₃(PO₄)₂ (8×10⁻⁴³) << PbCO₃ (7.4×10⁻¹⁴) << PbSO₄ (2.5×10⁻⁸). Na₃PO₄ gives the most complete precipitation by many orders of magnitude, reducing Pb²⁺ to far below the 0.01 mg/L guideline. Na₂SO₄ is least effective.

1 mark — Effect on other water ions: CO₃²⁻ (from Na₂CO₃) would also precipitate Ca²⁺ as CaCO₃ (NAGSAG: carbonates + non-Group-1 cation → insoluble). PO₄³⁻ (from Na₃PO₄) would also precipitate Ca²⁺ as Ca₃(PO₄)₂ (insoluble). SO₄²⁻ (from Na₂SO₄) at high concentration might partially precipitate Ca²⁺ as CaSO₄ (sparingly soluble). If Ca²⁺ removal is undesirable (e.g. nutritional), this is a disadvantage of Na₂CO₃ and Na₃PO₄.

1 mark — Cost consideration: Na₂CO₃ and Na₂SO₄ have low cost index; Na₃PO₄ is moderate cost. For a large-scale utility, cost is significant.

1 mark — Low pH context: At pH 6.2, CO₃²⁻ would be partially protonated to HCO₃⁻ and H₂CO₃, reducing its effectiveness as a precipitant. PO₄³⁻ is similarly affected by pH (pKa of HPO₄²⁻ ~ 12), though orthophosphate treatment is still used at slightly acidic pH. This is a practical consideration that favours adjusting pH before adding precipitant.

1 mark — Evidence-based judgement: Na₃PO₄ is most effective due to the extremely low K_sp of Pb₃(PO₄)₂, ensuring Pb²⁺ is reduced to concentrations orders of magnitude below the guideline. Despite moderate cost, the public health imperative justifies it. Na₂CO₃ is a reasonable second choice if cost is the primary constraint and Ca²⁺ co-precipitation is acceptable. Na₂SO₄ should not be used — K_sp of PbSO₄ is too high to guarantee compliance with the 0.01 mg/L limit. [Award 1 mark for a clear reasoned conclusion naming the preferred option with justification referencing at least one quantitative comparison.]

1 mark — Net ionic equations: PbCO₃: Pb²⁺(aq) + CO₃²⁻(aq) → PbCO₃(s); Pb₃(PO₄)₂: 3Pb²⁺(aq) + 2PO₄³⁻(aq) → Pb₃(PO₄)₂(s); PbSO₄: Pb²⁺(aq) + SO₄²⁻(aq) → PbSO₄(s). Award 1 mark for all three net ionic equations with correct charge balance shown.

Q2 — Marking criteria (8 marks)

Error 1 (2 marks) — NaCl does not cause Ca²⁺/Mg²⁺ precipitation: Adding NaCl introduces Na⁺ and Cl⁻. From NAGSAG: Na⁺ is Group 1 → all Na salts soluble. Cl⁻ is a halide → generally soluble; exceptions are Ag⁺ and Pb²⁺, not Ca²⁺ or Mg²⁺. CaCl₂ and MgCl₂ are both soluble. Therefore NaCl cannot precipitate hardness ions. [1 mark for identifying the error; 1 mark for NAGSAG application showing CaCl₂/MgCl₂ are soluble]

Error 2 (2 marks) — CaCl₂ and MgCl₂ are NOT insoluble: The article claims these compounds are insoluble. This is incorrect. By NAGSAG, Cl⁻ salts are generally soluble, and neither Ca²⁺ nor Mg²⁺ are listed exceptions. Both CaCl₂ and MgCl₂ are highly soluble and routinely dissolved in solution. [1 mark for identifying; 1 mark for citing NAGSAG correctly]

Error 3 (2 marks) — It is not true that any dissolved ion will eventually precipitate: Precipitation only occurs when the ion product Q exceeds K_sp for a specific combination. Na⁺ and K⁺ (Group 1) form no common insoluble salts. Many combinations remain dissolved indefinitely regardless of concentration. The general claim that “any dissolved ion will eventually precipitate when another ion is added” is incorrect. [1 mark for identifying; 1 mark for explaining ion product / K_sp condition]

Correct process (2 marks) — Lime softening: Actual lime softening adds Ca(OH)₂ (lime) to raise pH, causing Ca²⁺ to precipitate as CaCO₃ in the presence of carbonate ions (added or naturally present): Ca²⁺(aq) + CO₃²⁻(aq) → CaCO₃(s). Mg²⁺ precipitates as Mg(OH)₂(s) at high pH: Mg²⁺(aq) + 2OH⁻(aq) → Mg(OH)₂(s). The precipitates are filtered off, removing the hardness ions. [1 mark for identifying correct reagents and precipitates; 1 mark for writing correct net ionic equation(s)]