The unbalanced equation for the reaction of `P_(4)S_(3)` with nitrate in aqueous acidic medium is given below :
`P_(4)S_(3)+NO_(3)^(-)rarrH_(3)PO_(4)+SO_(4)^(2-)+NO`
the number of moles of water reuired per mole of `P_(4)S_(3)` is :

Options

A. 18
B. `8//3`
C. 8
D. 28

Answer

To solve the problem of determining the number of moles of water required per mole of \( P_4S_3 \) in the given reaction, we will follow these steps:

### Step-by-Step Solution:

1. **Write the Unbalanced Reaction**:
The unbalanced reaction is given as:
\[ P_4S_3 + NO_3^- \rightarrow H_3PO_4 + SO_4^{2-} + NO \]

2. **Identify Oxidation and Reduction Half-Reactions**:
- **Oxidation Half-Reaction**: The phosphorus in \( P_4S_3 \) is oxidized to phosphoric acid \( H_3PO_4 \) and sulfur is oxidized to sulfate \( SO_4^{2-} \).
- **Reduction Half-Reaction**: The nitrate ion \( NO_3^- \) is reduced to nitric oxide \( NO \).

3. **Balance the Oxidation Half-Reaction**:
The balanced oxidation half-reaction can be written as:
\[ P_4S_3 + 28 H_2O \rightarrow 4 H_3PO_4 + 3 SO_4^{2-} + 34 H^+ + 38 e^- \]

4. **Balance the Reduction Half-Reaction**:
The balanced reduction half-reaction can be written as:
\[ NO_3^- + 4 H^+ + 38 e^- \rightarrow NO + 2 H_2O \]

5. **Combine the Half-Reactions**:
To find the overall balanced equation, we need to multiply the oxidation half-reaction by 3 and the reduction half-reaction by 38 to equalize the number of electrons:
- Oxidation (multiplied by 3):
\[ 3 P_4S_3 + 84 H_2O \rightarrow 12 H_3PO_4 + 9 SO_4^{2-} + 102 H^+ + 114 e^- \]
- Reduction (multiplied by 38):
\[ 38 NO_3^- + 152 H^+ + 114 e^- \rightarrow 38 NO + 76 H_2O \]

6. **Add the Balanced Half-Reactions**:
Combine the two balanced half-reactions:
\[ 3 P_4S_3 + 38 NO_3^- + 8 H_2O \rightarrow 12 H_3PO_4 + 38 NO + 9 SO_4^{2-} \]

7. **Determine Moles of Water per Mole of \( P_4S_3 \)**:
From the balanced equation, we see that for 3 moles of \( P_4S_3 \), 8 moles of water are required. Therefore, for 1 mole of \( P_4S_3 \):
\[ \text{Moles of water} = \frac{8}{3} \]

### Final Answer:
Thus, the number of moles of water required per mole of \( P_4S_3 \) is:
\[ \frac{8}{3} \]