To determine which of the two species, \( O_2^+ \) or \( O_2^- \), is more stable based on bond order calculations, we can follow these steps:
### Step 1: Determine the number of electrons in each species
- For \( O_2 \), the total number of electrons is 16 (8 from each oxygen atom).
- For \( O_2^+ \) (which has lost one electron), the total number of electrons is 15.
- For \( O_2^- \) (which has gained one electron), the total number of electrons is 17.
### Step 2: Write the molecular orbital configuration for \( O_2^+ \)
- The molecular orbital configuration for \( O_2^+ \) (15 electrons) is:
\[
\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1
\]
### Step 3: Count the bonding and antibonding electrons in \( O_2^+ \)
- **Bonding Electrons**: \( \sigma_{1s}^2, \sigma_{2s}^2, \sigma_{2p_z}^2, \pi_{2p_x}^2, \pi_{2p_y}^2 \) = 10 bonding electrons.
- **Antibonding Electrons**: \( \sigma^*_{1s}^2, \sigma^*_{2s}^2, \pi^*_{2p_x}^1 \) = 5 antibonding electrons.
### Step 4: Calculate the bond order for \( O_2^+ \)
- Bond order is calculated using the formula:
\[
\text{Bond Order} = \frac{(\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons})}{2}
\]
- For \( O_2^+ \):
\[
\text{Bond Order} = \frac{(10 - 5)}{2} = 2.5
\]
### Step 5: Write the molecular orbital configuration for \( O_2^- \)
- The molecular orbital configuration for \( O_2^- \) (17 electrons) is:
\[
\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^2 \pi^*_{2p_y}^1
\]
### Step 6: Count the bonding and antibonding electrons in \( O_2^- \)
- **Bonding Electrons**: \( \sigma_{1s}^2, \sigma_{2s}^2, \sigma_{2p_z}^2, \pi_{2p_x}^2, \pi_{2p_y}^2 \) = 10 bonding electrons.
- **Antibonding Electrons**: \( \sigma^*_{1s}^2, \sigma^*_{2s}^2, \pi^*_{2p_x}^2, \pi^*_{2p_y}^1 \) = 7 antibonding electrons.
### Step 7: Calculate the bond order for \( O_2^- \)
- For \( O_2^- \):
\[
\text{Bond Order} = \frac{(10 - 7)}{2} = 1.5
\]
### Step 8: Compare the bond orders
- \( O_2^+ \) has a bond order of 2.5.
- \( O_2^- \) has a bond order of 1.5.
### Conclusion
Since bond order is directly proportional to stability, \( O_2^+ \) is more stable than \( O_2^- \).
---
