Using molecular orbital theory predict the correct decreasing bond order of the following species
1. `O_(2)^(+)` 2. `O_(2)^(-)` 3. `O_(2)^(2-)` 4. `O_(2)^(2+)`

Options

A. `1 gt 2 gt 3 gt 4`
B. `4 gt 1 gt 2 gt 3`
C. `4 gt 1 gt 3 gt 2`
D. `1 gt 4 gt 2 gt 3`

Answer

To determine the bond order of the given species using molecular orbital theory, we will follow these steps:

### Step 1: Determine the number of electrons for each species
1. **O2+**: Oxygen has 8 electrons, so O2 has 16 electrons. O2+ has 15 electrons (16 - 1).
2. **O2-**: O2- has 17 electrons (16 + 1).
3. **O2^2-**: O2^2- has 18 electrons (16 + 2).
4. **O2^2+**: O2^2+ has 14 electrons (16 - 2).

### Step 2: Write the molecular orbital configurations
1. **O2+ (15 electrons)**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_x² π2p_y² π2p_z¹
- Bonding electrons: 10
- Antibonding electrons: 5
- Bond order = (Bonding - Antibonding) / 2 = (10 - 5) / 2 = **2.5**

2. **O2- (17 electrons)**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_x² π2p_y² π2p_z²
- Bonding electrons: 10
- Antibonding electrons: 6
- Bond order = (10 - 6) / 2 = **2.0**

3. **O2^2- (18 electrons)**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_x² π2p_y² π2p_z² π*2p_y² π*2p_z²
- Bonding electrons: 10
- Antibonding electrons: 8
- Bond order = (10 - 8) / 2 = **1.0**

4. **O2^2+ (14 electrons)**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_x² π2p_y²
- Bonding electrons: 8
- Antibonding electrons: 6
- Bond order = (8 - 6) / 2 = **1.0**

### Step 3: Compare the bond orders
Now we can summarize the bond orders:
- O2+ = 2.5
- O2- = 2.0
- O2^2- = 1.0
- O2^2+ = 1.0

### Step 4: Write the decreasing order of bond orders
The correct decreasing order of bond order is:
1. O2+ (2.5)
2. O2- (2.0)
3. O2^2- (1.0)
4. O2^2+ (1.0)

### Final Answer
**Decreasing bond order: O2+ > O2- > O2^2- = O2^2+**

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