### How To Make Hard Water Soft

Soap Scum On A Bathtub

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)

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? [Ksp 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 [CO32–] 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