To find the bond order of the molecules O2, O2^-, and O2^+, we will use molecular orbital theory. Here’s a step-by-step breakdown of the solution:
### Step 1: Determine the Number of Electrons
- **O2** has 16 electrons (8 from each oxygen atom).
- **O2^+** has 15 electrons (one electron is removed).
- **O2^-** has 17 electrons (one electron is added).
### Step 2: Fill the Molecular Orbitals
We will fill the molecular orbitals according to the Aufbau principle, starting from the lowest energy level.
1. **For O2^+ (15 Electrons)**:
- Fill the 1s and 2s orbitals:
- 1s: 2 electrons
- 2s: 2 electrons
- Fill the 2p orbitals:
- 2p: 3 electrons (since one electron is removed from O2)
- The filling order will be:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)², π*(2p)¹
- **Bonding Electrons**: 6 (σ(1s) + σ(2s) + σ(2p) + π(2p))
- **Anti-bonding Electrons**: 1 (π*(2p))
- **Bond Order Calculation**:
\[
\text{Bond Order} = \frac{\text{Bonding Electrons} - \text{Anti-bonding Electrons}}{2} = \frac{6 - 1}{2} = \frac{5}{2} = 2.5
\]
2. **For O2 (16 Electrons)**:
- The filling will be the same as above, but with one additional electron in the π*(2p) orbital:
- The filling order will be:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)², π*(2p)²
- **Bonding Electrons**: 6
- **Anti-bonding Electrons**: 2 (π*(2p))
- **Bond Order Calculation**:
\[
\text{Bond Order} = \frac{6 - 2}{2} = \frac{4}{2} = 2
\]
3. **For O2^- (17 Electrons)**:
- The filling will be the same as O2, but with one more electron in the π*(2p) orbital:
- The filling order will be:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p)², π(2p)², π*(2p)³
- **Bonding Electrons**: 6
- **Anti-bonding Electrons**: 3 (π*(2p))
- **Bond Order Calculation**:
\[
\text{Bond Order} = \frac{6 - 3}{2} = \frac{3}{2} = 1.5
\]
### Conclusion
- **O2^+** has a bond order of **2.5**.
- **O2** has a bond order of **2**.
- **O2^-** has a bond order of **1.5**.
The correct order of bond order from highest to lowest is:
- O2^+ > O2 > O2^-
