Which of the following options represents the correct bond order?
Thinking process
To calcualte bond order, write the molecular orbital configuration of particular species and afterwards using the formula.
Bond order =`1/2` [Number of bonding `(N_(6))` - Number of anti-bonding electrons `(N_(a))`]

Options

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

Explanation

To find the bond order of the oxygen molecule (O2) and its ions (O2+ and O2-), we will follow these steps:

### Step 1: Determine the total number of electrons
Oxygen (O) has an atomic number of 8, so O2 has a total of:
\[ 8 + 8 = 16 \text{ electrons} \]
- For O2+, we remove one electron: \( 16 - 1 = 15 \text{ electrons} \)
- For O2-, we add one electron: \( 16 + 1 = 17 \text{ electrons} \)

### Step 2: Write the molecular orbital (MO) configuration for O2
The molecular orbital configuration for O2 is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \pi_{2p_y}^*^1 \]
This can be summarized as:
- Bonding electrons: \( \sigma_{1s}^2, \sigma_{2s}^2, \sigma_{2p_z}^2, \pi_{2p_x}^2, \pi_{2p_y}^2 \) = 10 electrons
- Antibonding electrons: \( \sigma_{1s}^*^2, \sigma_{2s}^*^2, \pi_{2p_x}^*^0, \pi_{2p_y}^*^0 \) = 6 electrons

### Step 3: Calculate the bond order for O2
Using the formula:
\[ \text{Bond order} = \frac{1}{2} \left( \text{Number of bonding electrons} - \text{Number of antibonding electrons} \right) \]
For O2:
\[ \text{Bond order} = \frac{1}{2} (10 - 6) = \frac{4}{2} = 2 \]

### Step 4: Calculate the bond order for O2-
For O2-, we add one more electron to the antibonding orbitals:
- New configuration: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \pi_{2p_y}^*^2 \)
- Bonding electrons: 10
- Antibonding electrons: 7

Calculating bond order:
\[ \text{Bond order} = \frac{1}{2} (10 - 7) = \frac{3}{2} = 1.5 \]

### Step 5: Calculate the bond order for O2+
For O2+, we remove one electron from the antibonding orbitals:
- New configuration: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^0 \pi_{2p_y}^*^2 \)
- Bonding electrons: 10
- Antibonding electrons: 5

Calculating bond order:
\[ \text{Bond order} = \frac{1}{2} (10 - 5) = \frac{5}{2} = 2.5 \]

### Step 6: Compare the bond orders
- O2+: Bond order = 2.5
- O2: Bond order = 2
- O2-: Bond order = 1.5

### Conclusion
The order of bond strength is:
\[ \text{O2+} > \text{O2} > \text{O2-} \]
Thus, the correct option representing the highest bond order is O2+.