The number of `sigma` bonds in `P_(4)O_(10)` is

Options

A. `6`
B. `7`
C. `17`
D. `16`

Answer

To determine the number of sigma bonds in \( P_4O_{10} \), we can follow these steps:

### Step 1: Understand the Structure of \( P_4O_{10} \)
- \( P_4O_{10} \) consists of four phosphorus (P) atoms and ten oxygen (O) atoms.
- The oxidation state of phosphorus in \( P_4O_{10} \) is +5, which is equal to its maximum oxidation state.

### Step 2: Identify the Type of Linkages
- Since the oxidation state of phosphorus is equal to its maximum oxidation state, the structure will have oxy linkages (P-O-P linkages).
- Each phosphorus atom will be connected to oxygen atoms through single bonds (sigma bonds) and double bonds.

### Step 3: Draw the Structure
- The structure of \( P_4O_{10} \) can be visualized as a tetrahedral arrangement of the phosphorus atoms, with each phosphorus atom bonded to oxygen atoms.
- Each phosphorus atom forms one double bond with an oxygen atom and two single bonds with other oxygen atoms.

### Step 4: Count the Sigma Bonds
- Each P-O single bond counts as one sigma bond.
- Each P=O double bond consists of one sigma bond and one pi bond, but we only count the sigma bond for this question.
- For each phosphorus atom:
- It forms 4 sigma bonds (2 with O and 2 with other P atoms).
- Since there are 4 phosphorus atoms, the total number of sigma bonds contributed by phosphorus is:
\[ 4 \text{ P atoms} \times 4 \text{ sigma bonds per P} = 16 \text{ sigma bonds} \]

### Step 5: Include the Sigma Bonds from Oxygen
- Each oxygen atom in \( P_4O_{10} \) that is involved in a single bond will also contribute to the sigma bond count.
- There are 10 oxygen atoms, and since each oxygen atom forms a single bond with phosphorus, we can count these as well.

### Final Count of Sigma Bonds
- Total sigma bonds from phosphorus: 16
- Total sigma bonds from oxygen: 10
- Therefore, the total number of sigma bonds in \( P_4O_{10} \) is:
\[ 16 + 10 = 26 \text{ sigma bonds} \]

### Conclusion
The total number of sigma bonds in \( P_4O_{10} \) is **26**.

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