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
- **O2** has 16 electrons.
- **O2+** has 15 electrons (1 electron removed).
- **O2-** has 17 electrons (1 electron added).
- **O2²-** has 18 electrons (2 electrons added).
- **O2²+** has 14 electrons (2 electrons removed).

### Step 2: Write the molecular orbital configuration for each species
1. **O2+ (15 electrons)**:
- Configuration: σ1s², σ*1s², σ2s², σ*2s², σ2p_z², π2p_x², π2p_y¹
- Bonding electrons = 10, Anti-bonding electrons = 5
- Bond order = (Bonding - Anti-bonding) / 2 = (10 - 5) / 2 = 2.5

2. **O2- (17 electrons)**:
- Configuration: σ1s², σ*1s², σ2s², σ*2s², σ2p_z², π2p_x², π2p_y², π*2p_x¹
- Bonding electrons = 10, Anti-bonding electrons = 6
- Bond order = (10 - 6) / 2 = 2.0

3. **O2²- (18 electrons)**:
- Configuration: σ1s², σ*1s², σ2s², σ*2s², σ2p_z², π2p_x², π2p_y², π*2p_x², π*2p_y¹
- Bonding electrons = 10, Anti-bonding electrons = 7
- Bond order = (10 - 7) / 2 = 1.5

4. **O2²+ (14 electrons)**:
- Configuration: σ1s², σ*1s², σ2s², σ*2s², σ2p_z², π2p_x², π2p_y²
- Bonding electrons = 10, Anti-bonding electrons = 4
- Bond order = (10 - 4) / 2 = 3.0

### Step 3: Arrange the bond orders in decreasing order
- O2²+ (Bond order = 3.0)
- O2+ (Bond order = 2.5)
- O2- (Bond order = 2.0)
- O2²- (Bond order = 1.5)

### Final Answer:
The correct decreasing order of bond order is:
1. O2²+
2. O2+
3. O2-
4. O2²-