How To Make Hard Water Soft

Soap Scum On A Bathtub

(Source: Wikimedia Commons)

Soap contains salts such as sodium stearate.

When Ca²⁺ in hard water mixes with soap, a precipitate of calcium stearate, a.k.a. scum, is formed. This is the scaly deposit one observes on bathtubs and sinks.

(Molecular Sructures From Wikimedia Commons — sodium stearate; calcium stearate)

To minimise scum formation, hard water is ‘softened’ by removing Ca²⁺ ions. This can be achieved by adding washing soda (i.e. Na₂CO₃) into the water. The Ca²⁺ ions in solution then precipitates out as CaCO₃, leaving Na⁺ ions in their place in the ‘softened’ water.

Ca²⁺(aq) + Na₂CO₃(aq) → CaCO₃(s) + Na⁺(aq)

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Worked example

When the concentration of Ca²⁺ ions in water is greater than 10^–5 mol dm^–3, an insoluble scum would be formed with soap.

To prevent scum formation, what is the minimum mass of sodium carbonate that should be added to 1 dm³ of water? [K_sp of CaCO₃ = 5.0 × 10^–9 mol² dm^–6]

Suggested Solution

To prevent scum formation, less than 10^–5 mol dm^–3 of Ca²⁺ ions must be present.

This means that we need to calculate the minimum [CO₃^2–] that will cause precipitation of CaCO₃ when [Ca²⁺] = 10^–5 mol dm^–3.

Precipitation of CaCO₃ occurs when

∴ Minimum mass of Na₂CO₃ that should be added
= (5 × 10^–4) × Molar mass of Na₂CO₃
= (5 × 10^–4) × [2(23.0) + 12.0 + 3(16.0)] = 0.053 g