To determine which molecule has the strongest O-O bond, we need to calculate the bond order for each of the given molecules: O2, O2+, O2-, and O2^2-. The bond order is a measure of the strength of a bond, and it can be calculated using molecular orbital theory.
### Step-by-Step Solution:
1. **Understanding Bond Order**:
- Bond order is defined as the difference between the number of bonding electrons and the number of anti-bonding electrons, divided by two.
- The formula is:
\[
\text{Bond Order} = \frac{(N_b - N_a)}{2}
\]
where \(N_b\) is the number of bonding electrons and \(N_a\) is the number of anti-bonding electrons.
2. **Determine the Electron Configuration**:
- For O2, there are 16 electrons (8 from each oxygen atom). The molecular orbital filling for O2 is:
- \(\sigma_{1s}^2\), \(\sigma_{1s}^*\), \(\sigma_{2s}^2\), \(\sigma_{2s}^*\), \(\sigma_{2p_z}^2\), \(\pi_{2p_x}^2\), \(\pi_{2p_y}^2\), \(\pi_{2p_x}^*\), \(\pi_{2p_y}^*\).
- The filling results in 10 bonding electrons and 6 anti-bonding electrons.
3. **Calculate Bond Order for O2**:
- Bond order for O2:
\[
\text{Bond Order} = \frac{(10 - 6)}{2} = \frac{4}{2} = 2
\]
4. **Calculate Bond Order for O2+**:
- O2+ has 15 electrons (one electron removed). The electron configuration will be:
- \(\sigma_{1s}^2\), \(\sigma_{1s}^*\), \(\sigma_{2s}^2\), \(\sigma_{2s}^*\), \(\sigma_{2p_z}^2\), \(\pi_{2p_x}^2\), \(\pi_{2p_y}^1\).
- Bond order for O2+:
\[
\text{Bond Order} = \frac{(10 - 5)}{2} = \frac{5}{2} = 2.5
\]
5. **Calculate Bond Order for O2-**:
- O2- has 17 electrons (one extra electron added). The electron configuration will be:
- \(\sigma_{1s}^2\), \(\sigma_{1s}^*\), \(\sigma_{2s}^2\), \(\sigma_{2s}^*\), \(\sigma_{2p_z}^2\), \(\pi_{2p_x}^2\), \(\pi_{2p_y}^2\), \(\pi_{2p_x}^*\).
- Bond order for O2-:
\[
\text{Bond Order} = \frac{(10 - 7)}{2} = \frac{3}{2} = 1.5
\]
6. **Calculate Bond Order for O2^2-**:
- O2^2- has 18 electrons (two extra electrons added). The electron configuration will be:
- \(\sigma_{1s}^2\), \(\sigma_{1s}^*\), \(\sigma_{2s}^2\), \(\sigma_{2s}^*\), \(\sigma_{2p_z}^2\), \(\pi_{2p_x}^2\), \(\pi_{2p_y}^2\), \(\pi_{2p_x}^*\), \(\pi_{2p_y}^*\).
- Bond order for O2^2-:
\[
\text{Bond Order} = \frac{(10 - 8)}{2} = \frac{2}{2} = 1
\]
7. **Comparison of Bond Orders**:
- O2: Bond Order = 2
- O2+: Bond Order = 2.5
- O2-: Bond Order = 1.5
- O2^2-: Bond Order = 1
8. **Conclusion**:
- The molecule with the strongest O-O bond is O2+ with a bond order of 2.5, which is the highest among the given options.
