A sample of hard water contains some calcium sulphate and calcium hydrogen carbonate. The total hardness may therefore be removed by

1. Analyze the Question

The question asks for a method to remove the total hardness of water that contains both calcium sulphate ($CaSO_4$) and calcium hydrogen carbonate ($Ca(HCO_3)_2$).

2. Explain the Concept

• Temporary Hardness: Caused by calcium hydrogen carbonate ($Ca(HCO_3)_2$) or magnesium hydrogen carbonate. This can be removed by boiling.
• Permanent Hardness: Caused by the presence of calcium sulphate ($CaSO_4$) or magnesium sulphate. Boiling cannot remove this.
• Total Hardness: The sum of both temporary and permanent hardness. To remove total hardness, you need a method that precipitates both the calcium ions ($Ca^{2+}$) and the sulphate/carbonate ions effectively.
• Chemical Precipitation: Adding sodium carbonate ($Na_2CO_3$), also known as washing soda, is the standard industrial and laboratory method for removing total hardness. It reacts with both types of hardness to form insoluble calcium carbonate ($CaCO_3$), which can be filtered out.

3. Show the Solution

• Reaction with Temporary Hardness: $Ca(HCO_3)_2 + Na_2CO_3 \rightarrow CaCO_3(s) + 2NaHCO_3$
• Reaction with Permanent Hardness: $CaSO_4 + Na_2CO_3 \rightarrow CaCO_3(s) + Na_2SO_4$

In both cases, the calcium ions are removed from the water as a solid precipitate ($CaCO_3$), effectively softening the water. While calcium hydroxide (Option C) can remove temporary hardness and some permanent hardness (if magnesium is present), sodium carbonate is the universal reagent used to treat total hardness because it works efficiently for both types of calcium salts present in the sample.

4. Identify the Answer

Adding sodium carbonate is the most effective way to remove both temporary and permanent hardness simultaneously.

5. Exam Tip

Remember the "Carbonate Rule": If you see "hardness of water" in a JAMB question, look for sodium carbonate ($Na_2CO_3$) or washing soda. It is the "magic" chemical that precipitates calcium and magnesium ions regardless of whether the hardness is temporary or permanent.