### Correct Option: D. Adding sodium carbonate #### Detailed Explanation: **Understanding Hard Water:** Hard water contains dissolved minerals, primarily calcium (Ca²⁺) and magnesium (Mg²⁺) ions. The two main types of hardness are: 1. **Temporary Hardness:** Caused by bicarbonates (like calcium hydrogen carbonate, Ca(HCO₃)₂) that can be removed by boiling. 2. **Permanent Hardness:** Caused by sulfates (like calcium sulfate, CaSO₄) and cannot be removed by boiling. In this case, the sample contains both calcium sulfate (CaSO₄) and calcium hydrogen carbonate (Ca(HCO₃)₂). **Removing Hardness:** 1. **Boiling the Water (Option A):** - Boiling is effective for removing temporary hardness (like calcium hydrogen carbonate) because it converts bicarbonates into insoluble carbonates, which precipitate out. However, it does not affect permanent hardness (like calcium sulfate), which remains in solution. Therefore, this option is not suitable for completely removing hardness. 2. **Adding Excess Calcium Hydroxide (Option B):** - Calcium hydroxide (Ca(OH)₂) can react with calcium hydrogen carbonate to form calcium carbonate (CaCO₃), which precipitates out, thus removing temporary hardness. However, adding excess calcium hydroxide does not address the calcium sulfate, which remains soluble. Therefore, this option is also inadequate for total hardness removal. 3. **Adding a Calculated Amount of Calcium Hydroxide (Option C):** - Similar to option B, adding a calculated amount of calcium hydroxide can precipitate calcium carbonate from calcium hydrogen carbonate. However, it does not affect calcium sulfate, which means it cannot remove all hardness. Thus, this option is also not effective for total hardness removal. 4. **Adding Sodium Carbonate (Option D):** - Sodium carbonate (Na₂CO₃) reacts with both calcium hydrogen carbonate and calcium sulfate. - For calcium hydrogen carbonate: \[ \text{Ca(HCO}_3\text{)}_2 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 \downarrow + 2 \text{NaHCO}_3 \] This reaction precipitates calcium carbonate, effectively removing temporary hardness. - For calcium sulfate: \[ \text{CaSO}_4 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 \downarrow + \text{Na}_2\text{SO}_4 \] This reaction also leads to the precipitation of calcium carbonate, thus addressing the permanent hardness as well. By adding sodium carbonate, both types of hardness can be effectively removed, making this the correct option. #### Summary of Incorrect Options: - **Option A (Boiling the Water):** Only removes temporary hardness; does not affect permanent hardness. - **Option B (Adding Excess Calcium Hydroxide):** Removes temporary hardness but does not address permanent hardness. - **Option C (Adding a Calculated Amount of Calcium Hydroxide):** Similar to option B; only partially effective. ### Revision Summary: - Hard water contains calcium and magnesium ions, leading to temporary and permanent hardness. - Boiling removes temporary hardness but not permanent hardness. - Calcium hydroxide can remove temporary hardness but not permanent hardness. - Sodium carbonate effectively removes both types of hardness by precipitating calcium carbonate.