Out of the following bond order of oxygen species identify the correct answer

Options

A. `O_2^(-)gtO_2gtO_2^+`
B. `O_2^(-)ltO_2ltO_2^+`
C. `O_2^(-)gtO_2ltO_2^+`
D. `O_2^(-)ltO_2gtO_2^+`

Answer

To determine the bond order of the oxygen species \( O_2^- \), \( O_2 \), and \( O_2^+ \), we will follow these steps:

### Step 1: Determine the Total Number of Electrons
- **For \( O_2^- \)**: Oxygen has 8 electrons, and since there are 2 oxygen atoms, that gives us \( 8 + 8 = 16 \) electrons. The extra negative charge adds 1 more electron, resulting in a total of **17 electrons**.
- **For \( O_2 \)**: As calculated earlier, \( O_2 \) has **16 electrons**.
- **For \( O_2^+ \)**: The positive charge means we remove one electron from \( O_2 \), resulting in **15 electrons**.

### Step 2: Apply the Bond Order Formula
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2} \]

### Step 3: Determine the Electron Configuration
Using the molecular orbital theory, we can fill the molecular orbitals for each species:

1. **For \( O_2^- \)** (17 electrons):
- The configuration is: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \)
- Bonding electrons: 10 (from \( \sigma_{1s}, \sigma_{2s}, \sigma_{2p_z}, \pi_{2p_x}, \pi_{2p_y} \))
- Antibonding electrons: 3 (from \( \sigma_{1s}^*, \sigma_{2s}^*, \pi_{2p_x}^* \))
- Bond Order:
\[ \text{Bond Order} = \frac{10 - 3}{2} = \frac{7}{2} = 3.5 \]

2. **For \( O_2 \)** (16 electrons):
- The configuration is: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \)
- Bonding electrons: 10
- Antibonding electrons: 2
- Bond Order:
\[ \text{Bond Order} = \frac{10 - 2}{2} = \frac{8}{2} = 4 \]

3. **For \( O_2^+ \)** (15 electrons):
- The configuration is: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^1 \)
- Bonding electrons: 9
- Antibonding electrons: 2
- Bond Order:
\[ \text{Bond Order} = \frac{9 - 2}{2} = \frac{7}{2} = 3.5 \]

### Step 4: Compare the Bond Orders
- \( O_2^- \): Bond Order = 3.5
- \( O_2 \): Bond Order = 4
- \( O_2^+ \): Bond Order = 3.5

### Conclusion
The bond order for \( O_2 \) is the highest, followed by \( O_2^- \) and \( O_2^+ \) having the same bond order.

### Final Answer
The correct order of bond orders is:
1. \( O_2 \) (4)
2. \( O_2^- \) (3.5)
3. \( O_2^+ \) (3.5)