Remember the unique precipitation product for Magnesium temporary hardness on boiling: it forms \(\text{Mg(OH)}_2\), not \(\text{MgCO}_3\), due to solubility product differences (\(K_{sp}\) of \(\text{Mg(OH)}_2<\text{MgCO}_3\)).
Step 1: Understanding the Question:
The question asks to match reactions involved in removing hardness of water with the specific methods used.
Step 2: Understanding the Each Reaction:
\begin{enumerate}
\item Reaction A: \(\text{Mg(HCO}_3)_2 \xrightarrow{\Delta} \text{Mg(OH)}_2 \downarrow + 2\text{CO}_2 \uparrow\).
This reaction represents the removal of temporary hardness caused by magnesium bicarbonate by Boiling. Note that unlike calcium bicarbonate which forms carbonate, magnesium bicarbonate precipitates as hydroxide because \(\text{Mg(OH)}_2\) is less soluble than \(\text{MgCO}_3\). (Matches with III).
\item Reaction B: \(\text{M}^{2+} + \text{Na}_6\text{P}_6\text{O}_{18}^{2-} \rightarrow [\text{Na}_2\text{MP}_6\text{O}_{18}]^{2-} + 2\text{Na}^+\).
The compound \(\text{Na}_6\text{P}_6\text{O}_{18}\) is commercially known as Calgon (Sodium hexametaphosphate). It complexes with metal ions like \(\text{Ca}^{2+}\) and \(\text{Mg}^{2+}\) to keep them in solution but inactive. This is Calgon's method. (Matches with IV).
\item Reaction C: \(\text{Ca(HCO}_3)_2 + \text{Ca(OH)}_2 \rightarrow 2\text{CaCO}_3 \downarrow + 2\text{H}_2\text{O}\).
This involves adding Calculation Processd amounts of lime (\(\text{Ca(OH)}_2\)) to precipitate out calcium carbonate. This is known as Clark's method. (Matches with I).
\item Reaction D: \(2\text{NaZ} + \text{Ca}^{2+} \rightarrow \text{CaZ}_2 + 2\text{Na}^+\).
Here, Z represents Zeolite (hydrated sodium aluminium silicate). The exchange of sodium ions for calcium/magnesium ions on the zeolite surface is characteristic of the Ion exchange method (specifically Permutit/Zeolite process). (Matches with II).
\end{enumerate}
Step 3: Matching:
A \(\rightarrow\) III, B \(\rightarrow\) IV, C \(\rightarrow\) I, D \(\rightarrow\) II.
Required Answer: Option (A).
