Reaction of hydrated ferric chloride `(FeCl_(3).6H_(2)O)` with thionyl chloride gives anhydrous ferric chloride with evolution of hydrochloric acid `(HCl)` and sulphur dioxide `(SO_(2))` gases. The number of sulphur dioxide `(SO_(2))` molecules involved in the balanced chemical equation is `:`

Options

A. 6
B. 4
C. 5
D. 3

Explanation

To solve the problem, we need to write and balance the chemical equation for the reaction of hydrated ferric chloride \((FeCl_3 \cdot 6H_2O)\) with thionyl chloride \((SOCl_2)\). The products of this reaction are anhydrous ferric chloride \((FeCl_3)\), hydrochloric acid \((HCl)\), and sulfur dioxide \((SO_2)\).

### Step-by-Step Solution:

1. **Write the Unbalanced Equation:**
The unbalanced reaction can be written as:
\[ FeCl_3 \cdot 6H_2O + SOCl_2 \rightarrow FeCl_3 + HCl + SO_2 \]

2. **Identify the Components:**
- Reactants: Hydrated ferric chloride \((FeCl_3 \cdot 6H_2O)\) and thionyl chloride \((SOCl_2)\)
- Products: Anhydrous ferric chloride \((FeCl_3)\), hydrochloric acid \((HCl)\), and sulfur dioxide \((SO_2)\)

3. **Balance the Equation:**
- Start with the iron (Fe) atoms: There is 1 Fe on both sides, so it is balanced.
- Next, balance the chlorine (Cl) atoms. In the reactants, we have 3 Cl from \(FeCl_3\) and 2 Cl from \(SOCl_2\) (total 5 Cl). In the products, we have 3 Cl from \(FeCl_3\) and need to add \(HCl\) to balance the remaining 2 Cl. Thus, we need 2 \(HCl\):
\[ FeCl_3 \cdot 6H_2O + SOCl_2 \rightarrow FeCl_3 + 2HCl + SO_2 \]
- Now, we have 5 Cl on both sides (3 from \(FeCl_3\) and 2 from \(HCl\)).
- Next, balance the sulfur (S) atoms: We have 1 S from \(SOCl_2\) and 1 S from \(SO_2\), which is balanced.
- Finally, balance the oxygen (O) atoms: In the reactants, we have 6 O from \(6H_2O\) and 2 O from \(SOCl_2\) (total 8 O). In the products, we have 2 O from \(SO_2\) and 6 O from \(6H_2O\) (total 8 O), which is also balanced.

4. **Final Balanced Equation:**
The balanced equation is:
\[ FeCl_3 \cdot 6H_2O + 6SOCl_2 \rightarrow FeCl_3 + 6HCl + 6SO_2 \]

5. **Determine the Number of \(SO_2\) Molecules:**
From the balanced equation, we see that 6 molecules of \(SO_2\) are produced.

### Final Answer:
The number of sulfur dioxide \((SO_2)\) molecules involved in the balanced chemical equation is **6**.

---