Water Chemistry and Hardness

Water Chemistry and Hardness

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Hardness measures how much soap-destroying calcium (Ca²⁺) and magnesium (Mg²⁺) water carries in solution, expressed as the mass of calcium carbonate (CaCO₃) equivalent in mg/L (ppm). Two types exist: temporary hardness from bicarbonates — Ca(HCO₃)₂ and Mg(HCO₃)₂ — removable by boiling because they decompose to insoluble carbonates, and permanent hardness from chlorides and sulphates (CaCl₂, MgSO₄, CaSO₄) that survive boiling. The conversion formula every NECO candidate must memorise: Hardness as CaCO₃ = (2.5 × Ca²⁺ mg/L) + (4.1 × Mg²⁺ mg/L). The factors 2.5 and 4.1 come from the molar-mass ratio 100/40 and 100/24.3 respectively. Soap (sodium stearate) forms an insoluble scum with these ions, wasting soap before a stable lather forms. High-yield exam pointers: distinguish the two hardness types, write the boiling reaction, name Clark’s process (slaked lime), and use the 2.5 / 4.1 factors confidently.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Sources of Hardness

Rainwater dissolves Ca²⁺ and Mg²⁺ ions as it percolates through limestone (CaCO₃), dolomite (CaCO₃·MgCO₃), and gypsum (CaSO₄·2H₂O) in soils and rock strata. Groundwater from chalky regions therefore becomes hard, while rainwater is naturally soft because it lacks dissolved mineral ions.

Temporary vs Permanent Hardness

Temporary hardness is caused by the hydrogencarbonates Ca(HCO₃)₂ and Mg(HCO₃)₂. On boiling, the unstable bicarbonate decomposes: Ca(HCO₃)₂ —Δ→ CaCO₃(s)↓ + H₂O(l) + CO₂(g) The white scale (fur or boiler scale) you see in a kettle is exactly this CaCO₃ precipitate.

Permanent hardness is caused by the chlorides and sulphates of calcium and magnesium — CaCl₂, MgCl₂, CaSO₄, MgSO₄. These salts are heat-stable, so boiling has no effect. Distinguishing the two is a regular NECO Paper 2 question.

Expressing Hardness Numerically

Hardness is reported in mg/L of CaCO₃ equivalent even when the actual ion is Mg²⁺. Using CaCO₃ (M = 100 g/mol) as a reference:

Ion	Molar mass	Factor to convert mg/L → mg/L CaCO₃
Ca²⁺	40	× 100/40 = 2.5
Mg²⁺	24.3	× 100/24.3 = 4.1

A water sample containing 80 mg/L Ca²⁺ and 24.3 mg/L Mg²⁺ has a total hardness of (2.5 × 80) + (4.1 × 24.3) = 200 + 99.6 ≈ 299.6 mg/L CaCO₃, classed as very hard.

Softening Methods

• Boiling — only removes temporary hardness.
• Washing soda (Na₂CO₃) — precipitates both types: CaSO₄ + Na₂CO₃ → CaCO₃(s) + Na₂SO₄.
• Caustic soda (NaOH) — removes Mg(HCO₃)₂ as Mg(OH)₂.
• Clark’s process (lime softening) — uses Ca(OH)₂ to precipitate temporary hardness: Ca(HCO₃)₂ + Ca(OH)₂ → 2CaCO₃(s) + 2H₂O.
• Ion-exchange resins — replace Ca²⁺/Mg²⁺ with Na⁺ or H⁺.
• EDTA (sequestration) — forms soluble complexes; 1 mol EDTA binds 1 mol of M²⁺, the basis of complexometric titration of total hardness.

Soap and Scum

Sodium stearate C₁₇H₃₅COONa reacts: 2C₁₇H₃₅COONa + Ca²⁺ → (C₁₇H₃₅COO)₂Ca(s) + 2Na⁺. The calcium stearate floats as a grey scum; only after all hardness ions are precipitated does the water lather.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases and Exam Traps

A frequent NECO trap is the statement “boiling removes all hardness.” The correct answer is only temporary (carbonate) hardness is removed; permanent (non-carbonate) hardness from chlorides and sulphates needs chemical softening or ion exchange. Another trap involves the 2.5 and 4.1 factors: students sometimes divide instead of multiply, or use 24 instead of 24.3 for Mg. Memorise that Mg²⁺ is lighter, so the same mass contributes more CaCO₃-equivalent hardness — that is why the factor 4.1 is larger than 2.5.

Hardness above 180 mg/L CaCO₃ is generally classified as hard in WHO guidelines; below 60 mg/L is soft. NECO numerical problems usually give you Ca²⁺ and Mg²⁺ concentrations and ask for total hardness — work in mg/L throughout, do not switch to mol/L mid-calculation.

Industrial and Health Implications

Hard water forms boiler scale (CaCO₃ + MgCO₃) on heat-exchange surfaces, insulating the metal, causing overheating and fuel wastage. Soap wastage in textile and laundry industries made softening economically critical before detergents. Conversely, soft acidic water aggressively leaches Pb²⁺ and Cu²⁺ from pipes — the Flint, Michigan crisis (2014) showed the health cost of over-softening. Ca²⁺ and Mg²⁺ also contribute to dietary mineral intake, so complete demineralisation is undesirable for drinking water.

Worked Micro-Example

A borehole water analysis reports 120 mg/L Ca²⁺ and 48.6 mg/L Mg²⁺. Total hardness = (2.5 × 120) + (4.1 × 48.6) = 300 + 199.26 = 499.3 mg/L CaCO₃ → very hard. To soften 1 L using Na₂CO₃, you need to precipitate the equivalent moles of Ca²⁺ and Mg²⁺. Moles of Ca²⁺ = 120/40 = 3.0 mmol; moles of Mg²⁺ = 48.6/24.3 = 2.0 mmol; Na₂CO₃ required = 5.0 mmol = 0.530 g per litre (M Na₂CO₃ = 106 g/mol).

Practice Prompts

1. State two reasons why a solution containing 200 mg/L Ca²⁺ is classified as hard, and write the equation for its removal by washing soda.
2. A sample has 50 mg/L Ca²⁺ and 12.15 mg/L Mg²⁺. Calculate the total hardness in mg/L CaCO₃ and state whether Clark’s process alone would soften it completely. Justify your answer with one balanced equation.

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