Which of the following statements are true about `P_(4)O_(6) and P_(4)O_(10)`?

Options

A. Both these oxides have a closed cage like structure
B. Each oxide requires 6 water molecules for complete hydrolysis to form their respective oxoacids
C. both these oxides contain 12 equivalent P-O bonds
D. `P_(4)O_(6) and P_(4)O_(10)` both contains `p pi-p pi` bonds

Answer

To determine which statements are true about \( P_4O_6 \) and \( P_4O_{10} \), we will analyze each statement one by one based on their structures and properties.

### Step 1: Analyze the structure of \( P_4O_6 \) and \( P_4O_{10} \)

1. **Structure of \( P_4O_6 \)**:
- \( P_4O_6 \) has a closed cage-like structure. Each phosphorus atom is bonded to three oxygen atoms.

2. **Structure of \( P_4O_{10} \)**:
- \( P_4O_{10} \) also has a closed cage-like structure similar to \( P_4O_6 \). It consists of four phosphorus atoms bonded to ten oxygen atoms.

**Conclusion**: Both \( P_4O_6 \) and \( P_4O_{10} \) have closed cage-like structures.

### Step 2: Hydrolysis of \( P_4O_6 \) and \( P_4O_{10} \)

1. **Hydrolysis of \( P_4O_6 \)**:
- When \( P_4O_6 \) reacts with 6 water molecules, it forms \( H_3PO_3 \) (phosphorous acid).
- The balanced equation is:
\[ P_4O_6 + 6H_2O \rightarrow 4H_3PO_3 \]

2. **Hydrolysis of \( P_4O_{10} \)**:
- When \( P_4O_{10} \) reacts with 6 water molecules, it forms \( H_3PO_4 \) (phosphoric acid).
- The balanced equation is:
\[ P_4O_{10} + 6H_2O \rightarrow 4H_3PO_4 \]

**Conclusion**: Both oxides require 6 water molecules for complete hydrolysis to form their respective oxoacids.

### Step 3: Count the phosphorus-oxygen bonds

1. **Phosphorus-oxygen bonds in \( P_4O_6 \) and \( P_4O_{10} \)**:
- Each phosphorus atom in both \( P_4O_6 \) and \( P_4O_{10} \) is bonded to three oxygen atoms.
- With 4 phosphorus atoms, the total number of phosphorus-oxygen bonds is:
\[ 4 \text{ P} \times 3 \text{ O} = 12 \text{ P-O bonds} \]

**Conclusion**: Both oxides contain 12 equivalent phosphorus-oxygen bonds.

### Step 4: Check for π bonds

1. **Bonds in \( P_4O_6 \)**:
- The structure of \( P_4O_6 \) consists entirely of sigma bonds; there are no π bonds present.

2. **Bonds in \( P_4O_{10} \)**:
- The structure of \( P_4O_{10} \) contains Pπ-Dπ bonds, indicating the presence of some π bonding.

**Conclusion**: The statement that both \( P_4O_6 \) and \( P_4O_{10} \) contain π bonds is incorrect.

### Final Summary of Statements

- **Statement 1**: True (both have closed cage-like structures)
- **Statement 2**: True (both require 6 water molecules for hydrolysis)
- **Statement 3**: True (both contain 12 equivalent phosphorus-oxygen bonds)
- **Statement 4**: False (not both contain π bonds)

### Final Answer
The true statements about \( P_4O_6 \) and \( P_4O_{10} \) are statements 1, 2, and 3.