In `P_(4)O_(10)` molecule, bridging P - O bond length is

Options

A. Larger than that of in `P_4O_6`
B. Lesser than that of in `P_4O_6`
C. Equal to that of in `P_4O_6`
D. Cannot be compared

Answer

To determine the bridging P-O bond length in the molecule \( P_4O_{10} \), we can follow these steps:

### Step 1: Understand the Structures of \( P_4O_{10} \) and \( P_4O_{6} \)
- **\( P_4O_{10} \)** has a structure where phosphorus atoms are connected by bridging oxygen atoms. It contains both single and double bonded oxygen atoms.
- **\( P_4O_{6} \)** has a simpler structure with only single bonded oxygen atoms connecting the phosphorus atoms.

**Hint:** Draw the Lewis structures of both molecules to visualize the bonding.

### Step 2: Identify the Types of Bonds
- In \( P_4O_{10} \), there are double bonds between phosphorus and oxygen (P=O) along with bridging bonds (P-O-P).
- In \( P_4O_{6} \), all bonds between phosphorus and oxygen are single bonds (P-O-P).

**Hint:** Look for the presence of double bonds in the structure as they influence bond lengths.

### Step 3: Analyze the Effect of Double Bonds on Bond Length
- The presence of double bonds in \( P_4O_{10} \) creates a partial positive charge on the phosphorus atoms. This increases the attraction between phosphorus and the bridging oxygen atoms.
- In \( P_4O_{6} \), the absence of double bonds means less attraction and longer bond lengths.

**Hint:** Consider how the charge distribution affects the bond lengths.

### Step 4: Compare the Bond Lengths
- The bridging P-O bond length in \( P_4O_{10} \) is approximately **143 picometers**.
- The bridging P-O bond length in \( P_4O_{6} \) is approximately **166 picometers**.

**Hint:** Use the bond lengths to conclude which molecule has shorter bridging bonds.

### Step 5: Conclusion
- The bridging P-O bond length in \( P_4O_{10} \) is shorter than that in \( P_4O_{6} \) due to the presence of double bonds in \( P_4O_{10} \), which increases the effective attraction between phosphorus and oxygen.

**Final Answer:** The bridging P-O bond length in \( P_4O_{10} \) is **143 picometers**.

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