The correct bond order in the following species is:

Options

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

Explanation

To determine the bond order of the species O2+, O2-, and O2^2+, we will follow these steps:

### Step 1: Determine the number of electrons in each species
- **O2+**: Oxygen has 8 electrons, so O2 has 16 electrons. O2+ has 15 electrons (16 - 1).
- **O2-**: O2- has 17 electrons (16 + 1).
- **O2^2+**: O2^2+ has 14 electrons (16 - 2).

### Step 2: Write the molecular orbital (MO) configuration for each species
1. **For O2+ (15 electrons)**:
- MO configuration:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y² π*2p_x¹

2. **For O2- (17 electrons)**:
- MO configuration:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y² π*2p_x² π*2p_y¹

3. **For O2^2+ (14 electrons)**:
- MO configuration:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y²

### Step 3: Count the number of bonding and anti-bonding electrons
- **O2+**:
- Bonding electrons: 10 (σ1s² + σ2s² + σ2p_z² + π2p_x² + π2p_y²)
- Anti-bonding electrons: 5 (σ*1s² + σ*2s² + π*2p_x¹)

- **O2-**:
- Bonding electrons: 10 (same as above)
- Anti-bonding electrons: 7 (σ*1s² + σ*2s² + π*2p_x² + π*2p_y¹)

- **O2^2+**:
- Bonding electrons: 10 (same as above)
- Anti-bonding electrons: 4 (σ*1s² + σ*2s²)

### Step 4: Calculate the bond order for each species
The bond order formula is given by:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} \]

1. **For O2+**:
\[ \text{Bond Order} = \frac{(10 - 5)}{2} = \frac{5}{2} = 2.5 \]

2. **For O2-**:
\[ \text{Bond Order} = \frac{(10 - 7)}{2} = \frac{3}{2} = 1.5 \]

3. **For O2^2+**:
\[ \text{Bond Order} = \frac{(10 - 4)}{2} = \frac{6}{2} = 3 \]

### Conclusion
- The bond orders are:
- O2+: 2.5
- O2-: 1.5
- O2^2+: 3

The species with the highest bond order is O2^2+, which has a bond order of 3.