Bond order of 2.5 is shown by

Options

A. `O_(2)^(2-)`
B. `O_(2)`
C. `O_(2)^(+)`
D. `O_(2)^(-)`

Answer

To find the bond order of the species with a bond order of 2.5, we will analyze the molecular orbital (MO) configuration of the given species, specifically focusing on \( O_2^+ \).

### Step-by-Step Solution:

1. **Identify the species**: We are looking for a species with a bond order of 2.5. The candidates mentioned include \( O_2 \), \( O_2^- \), \( O_2^{2-} \), and \( O_2^+ \).

2. **Determine the number of electrons**:
- For \( O_2 \), there are 16 electrons (8 from each oxygen atom).
- For \( O_2^+ \), we remove one electron from \( O_2 \), resulting in 15 electrons.

3. **Write the molecular orbital configuration**:
- The molecular orbital configuration for \( O_2 \) is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^1 \pi_{2p_y}^1 \]
- For \( O_2^+ \), we remove one electron from the highest energy orbital (which is one of the \( \pi_{2p} \) orbitals):
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^1 \]

4. **Count bonding and anti-bonding electrons**:
- **Bonding electrons**:
- From the configuration, we have:
- \( \sigma_{1s}^2 \) contributes 2
- \( \sigma_{2s}^2 \) contributes 2
- \( \sigma_{2p_z}^2 \) contributes 2
- \( \pi_{2p_x}^2 \) contributes 2
- \( \pi_{2p_y}^1 \) contributes 1
- Total bonding electrons = \( 2 + 2 + 2 + 2 + 1 = 9 \)

- **Anti-bonding electrons**:
- From the configuration, we have:
- \( \sigma_{1s}^*^2 \) contributes 2
- \( \sigma_{2s}^*^2 \) contributes 2
- \( \pi_{2p_x}^0 \) contributes 0
- \( \pi_{2p_y}^0 \) contributes 0
- Total anti-bonding electrons = \( 2 + 2 = 4 \)

5. **Calculate the bond order**:
- The formula for bond order is:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} \]
- Substituting the values:
\[ \text{Bond Order} = \frac{(9 - 4)}{2} = \frac{5}{2} = 2.5 \]

6. **Conclusion**: The species with a bond order of 2.5 is \( O_2^+ \).