To determine the increasing order of bond strengths among the given species (O2+, O2, O2-, and O2 2-), we need to calculate the bond order for each species using Molecular Orbital Theory (MOT). The bond order is directly related to bond strength, with higher bond orders corresponding to stronger bonds.
### Step-by-Step Solution:
1. **Understanding Bond Order**:
The bond order can be calculated using the formula:
\[
\text{Bond Order} = \frac{(\text{Number of electrons in bonding orbitals}) - (\text{Number of electrons in antibonding orbitals})}{2}
\]
A higher bond order indicates a stronger bond.
2. **Calculate Bond Order for O2+**:
- O2+ has 15 electrons.
- The electron configuration in molecular orbitals is:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y¹
- Bonding electrons: 10 (σ1s, σ2s, σ2p_z, π2p_x, π2p_y)
- Antibonding electrons: 5 (σ*1s, σ*2s, π*2p_x, π*2p_y)
- Bond Order = (10 - 5) / 2 = 2.5
3. **Calculate Bond Order for O2**:
- O2 has 16 electrons.
- The electron configuration in molecular orbitals is:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y²
- Bonding electrons: 10
- Antibonding electrons: 6 (σ*1s, σ*2s, π*2p_x, π*2p_y)
- Bond Order = (10 - 6) / 2 = 2
4. **Calculate Bond Order for O2-**:
- O2- has 17 electrons.
- The electron configuration in molecular orbitals is:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y² π*2p_x¹
- Bonding electrons: 10
- Antibonding electrons: 7 (σ*1s, σ*2s, π*2p_x, π*2p_y, π*2p_x)
- Bond Order = (10 - 7) / 2 = 1.5
5. **Calculate Bond Order for O2 2-**:
- O2 2- has 18 electrons.
- The electron configuration in molecular orbitals is:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y² π*2p_x²
- Bonding electrons: 10
- Antibonding electrons: 8 (σ*1s, σ*2s, π*2p_x, π*2p_y, π*2p_x, π*2p_y)
- Bond Order = (10 - 8) / 2 = 1
6. **Summarizing Bond Orders**:
- O2+: Bond Order = 2.5
- O2: Bond Order = 2
- O2-: Bond Order = 1.5
- O2 2-: Bond Order = 1
7. **Increasing Order of Bond Strength**:
- Since bond strength is directly proportional to bond order, the increasing order of bond strengths is:
\[
\text{O2 2-} < \text{O2-} < \text{O2} < \text{O2+}
\]
### Final Answer:
The increasing order of bond strengths is:
O2 2- < O2- < O2 < O2+
