Which of the following species contains equal number of pi and pi bonds ?

Options

A. `X_eO_4`
B. `(CN)_2`
C. `CH_2(CN)_2`
D. `HCO_3^-`

Answer

To determine which of the given species contains an equal number of sigma (σ) and pi (π) bonds, we will analyze each option step by step.

### Step 1: Analyze the first species, Xenon (XeO4)

1. **Structure**: The structure of XeO4 can be represented as:
```
O
||
O = Xe = O
||
O
```
2. **Count the Bonds**:
- **Sigma Bonds**: Each double bond consists of one sigma bond. There are 4 double bonds, so:
- 4 sigma bonds.
- **Pi Bonds**: Each double bond also consists of one pi bond. Thus:
- 4 pi bonds.
3. **Conclusion**: XeO4 has 4 sigma bonds and 4 pi bonds.

### Step 2: Analyze the second species, Cyanogen (C2N2)

1. **Structure**: The structure of C2N2 can be represented as:
```
C ≡ N - C ≡ N
```
2. **Count the Bonds**:
- **Sigma Bonds**: Each triple bond consists of one sigma bond. There are 2 triple bonds, so:
- 2 sigma bonds.
- **Pi Bonds**: Each triple bond consists of two pi bonds. Thus:
- 2 triple bonds × 2 pi bonds = 4 pi bonds.
3. **Conclusion**: C2N2 has 2 sigma bonds and 4 pi bonds.

### Step 3: Analyze the third species, CH2(CN)2

1. **Structure**: The structure can be represented as:
```
H
|
H - C ≡ N
|
C ≡ N
```
2. **Count the Bonds**:
- **Sigma Bonds**:
- 1 for each C-H bond (2 total).
- 1 for each C-C bond (1 total).
- 1 for each C≡N bond (2 total).
- Total: 2 + 1 + 2 = 5 sigma bonds.
- **Pi Bonds**: Each triple bond has 2 pi bonds:
- 2 triple bonds × 2 pi bonds = 4 pi bonds.
3. **Conclusion**: CH2(CN)2 has 5 sigma bonds and 4 pi bonds.

### Step 4: Analyze the fourth species, Bicarbonate (HCO3^-)

1. **Structure**: The structure can be represented as:
```
O
||
H - C - O^-
|
O
```
2. **Count the Bonds**:
- **Sigma Bonds**:
- 1 for each C-H bond (1 total).
- 1 for each C=O bond (1 total).
- 1 for each C-O^- bond (1 total).
- Total: 1 + 1 + 1 + 1 = 4 sigma bonds.
- **Pi Bonds**: There is 1 double bond (C=O) which contributes 1 pi bond.
3. **Conclusion**: HCO3^- has 4 sigma bonds and 1 pi bond.

### Final Conclusion

After analyzing all the species:
- **XeO4**: 4 sigma, 4 pi (Equal)
- **C2N2**: 2 sigma, 4 pi (Not Equal)
- **CH2(CN)2**: 5 sigma, 4 pi (Not Equal)
- **HCO3^-**: 4 sigma, 1 pi (Not Equal)

Thus, the species that contains an equal number of sigma and pi bonds is **XeO4**.