Write the molecular orbital configuration `O_(2),O_(2)^(-)and O_(2)^(2-)` Arrange them in increasing order of
(i) Bond order (ii) Bond dissociation energy

Answer

To solve the problem, we need to determine the molecular orbital configurations for \(O_2\), \(O_2^-\), and \(O_2^{2-}\), and then calculate their bond orders and arrange them in increasing order.

### Step 1: Molecular Orbital Configuration of \(O_2\)

1. **Count the total number of electrons**: Oxygen has 8 electrons, so \(O_2\) has \(8 + 8 = 16\) electrons.
2. **Fill the molecular orbitals**:
- \(1s^2\)
- \(1s^{*2}\)
- \(2s^2\)
- \(2s^{*2}\)
- \(2p_z^2\) (sigma)
- \(2p_x^2\) (pi)
- \(2p_y^2\) (pi)
- \(2p_x^{*1}\) (one electron in the antibonding pi)
- \(2p_y^{*1}\) (one electron in the antibonding pi)

Therefore, the configuration is:
\[ O_2: 1s^2 1s^{*2} 2s^2 2s^{*2} 2p_z^2 2p_x^2 2p_y^2 2p_x^{*1} 2p_y^{*1} \]

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

3. **Bond order formula**:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]
4. **Count bonding and antibonding electrons**:
- Bonding electrons = 10 (from \(1s^2, 2s^2, 2p_z^2, 2p_x^2, 2p_y^2\))
- Antibonding electrons = 6 (from \(1s^{*2}, 2s^{*2}, 2p_x^{*1}, 2p_y^{*1}\))

\[ \text{Bond Order} = \frac{(10 - 6)}{2} = 2 \]

### Step 3: Molecular Orbital Configuration of \(O_2^-\)

5. **Count the total number of electrons**: \(O_2^-\) has \(16 + 1 = 17\) electrons.
6. **Fill the molecular orbitals**:
- The configuration will be the same as \(O_2\) but with one additional electron in the antibonding orbitals:
\[ O_2^-: 1s^2 1s^{*2} 2s^2 2s^{*2} 2p_z^2 2p_x^2 2p_y^2 2p_x^{*2} 2p_y^{*1} \]

### Step 4: Calculate Bond Order for \(O_2^-\)

7. **Count bonding and antibonding electrons**:
- Bonding electrons = 10
- Antibonding electrons = 7 (one more than \(O_2\))

\[ \text{Bond Order} = \frac{(10 - 7)}{2} = 1.5 \]

### Step 5: Molecular Orbital Configuration of \(O_2^{2-}\)

8. **Count the total number of electrons**: \(O_2^{2-}\) has \(16 + 2 = 18\) electrons.
9. **Fill the molecular orbitals**:
\[ O_2^{2-}: 1s^2 1s^{*2} 2s^2 2s^{*2} 2p_z^2 2p_x^2 2p_y^2 2p_x^{*2} 2p_y^{*2} \]

### Step 6: Calculate Bond Order for \(O_2^{2-}\)

10. **Count bonding and antibonding electrons**:
- Bonding electrons = 10
- Antibonding electrons = 8

\[ \text{Bond Order} = \frac{(10 - 8)}{2} = 1 \]

### Step 7: Arrange in Increasing Order

11. **Bond Order Summary**:
- \(O_2\): Bond Order = 2
- \(O_2^-\): Bond Order = 1.5
- \(O_2^{2-}\): Bond Order = 1

12. **Increasing order of bond order**:
\[ O_2^{2-} < O_2^- < O_2 \]

### Step 8: Bond Dissociation Energy

Since bond order is directly proportional to bond dissociation energy, the increasing order of bond dissociation energy will be the same as the bond order.

### Final Answer

(i) Increasing order of bond order:
\[ O_2^{2-} < O_2^- < O_2 \]

(ii) Increasing order of bond dissociation energy:
\[ O_2^{2-} < O_2^- < O_2 \]