Which of the following show maximum bond-order?

Options

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

Explanation

To determine which of the given molecules shows the maximum bond order, we need to calculate the bond order for each molecule using the molecular orbital theory. The bond order can be calculated using the formula:

\[ \text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2} \]

Let's analyze the bond order for \(O_2\), \(O_2^+\), and \(O_2^-\).

### Step 1: Calculate Bond Order for \(O_2\)

1. **Total Electrons**: Oxygen has 8 electrons, so \(O_2\) has a total of 16 electrons.
2. **Molecular Orbital Configuration**:
- \(\sigma_{1s}^2\)
- \(\sigma^*_{1s}^2\)
- \(\sigma_{2s}^2\)
- \(\sigma^*_{2s}^2\)
- \(\sigma_{2p_z}^2\)
- \(\pi_{2p_x}^2\)
- \(\pi_{2p_y}^2\)
- \(\pi^*_{2p_x}^1\)
- \(\pi^*_{2p_y}^0\)

3. **Count Electrons**:
- Bonding Electrons: \(2 (1s) + 2 (2s) + 2 (2p_z) + 2 (2p_x) + 2 (2p_y) = 10\)
- Antibonding Electrons: \(2 (1s) + 2 (2s) + 1 (2p_x) + 0 (2p_y) = 4\)

4. **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 4}{2} = \frac{6}{2} = 3 \]

### Step 2: Calculate Bond Order for \(O_2^+\)

1. **Total Electrons**: \(O_2^+\) has 15 electrons.
2. **Molecular Orbital Configuration**:
- The same as \(O_2\) but one electron is removed from the antibonding orbital.
- \(\sigma_{1s}^2\)
- \(\sigma^*_{1s}^2\)
- \(\sigma_{2s}^2\)
- \(\sigma^*_{2s}^2\)
- \(\sigma_{2p_z}^2\)
- \(\pi_{2p_x}^2\)
- \(\pi_{2p_y}^2\)
- \(\pi^*_{2p_x}^1\)

3. **Count Electrons**:
- Bonding Electrons: \(10\)
- Antibonding Electrons: \(3\)

4. **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 3}{2} = \frac{7}{2} = 3.5 \]

### Step 3: Calculate Bond Order for \(O_2^-\)

1. **Total Electrons**: \(O_2^-\) has 17 electrons.
2. **Molecular Orbital Configuration**:
- The same as \(O_2\) but two electrons are added to the antibonding orbital.
- \(\sigma_{1s}^2\)
- \(\sigma^*_{1s}^2\)
- \(\sigma_{2s}^2\)
- \(\sigma^*_{2s}^2\)
- \(\sigma_{2p_z}^2\)
- \(\pi_{2p_x}^2\)
- \(\pi_{2p_y}^2\)
- \(\pi^*_{2p_x}^2\)

3. **Count Electrons**:
- Bonding Electrons: \(10\)
- Antibonding Electrons: \(5\)

4. **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 5}{2} = \frac{5}{2} = 2.5 \]

### Conclusion

Now we can summarize the bond orders:
- \(O_2\): Bond Order = 2
- \(O_2^+\): Bond Order = 2.5
- \(O_2^-\): Bond Order = 1.5

The molecule with the maximum bond order is \(O_2^+\) with a bond order of 2.5.