Which of the following has fractional bond order ?

Options

A. `O_2^(2+)`
B. `O_2^(2-)`
C. `F_2^(2-)`
D. `H_2^(-)`

Answer

To determine which of the given molecules has a fractional bond order, we will follow these steps:

### Step 1: Understand Bond Order
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]
A fractional bond order indicates that the molecule does not have a whole number of bonds.

### Step 2: Analyze Each Option
We will analyze the bond order for each molecule mentioned in the video transcript.

#### Option 1: O2
- **Electrons**: O2 has 16 electrons.
- **Molecular Orbital Filling**:
- σ1s (2), σ1s* (2), σ2s (2), σ2s* (2), σ2p (2), π2p (4), π*2p (2).
- **Bonding Electrons**: 10 (σ1s, σ2s, σ2p, π2p)
- **Antibonding Electrons**: 6 (σ1s*, σ2s*, π*2p)
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 6}{2} = \frac{4}{2} = 2 \]
- **Conclusion**: O2 has a bond order of 2 (not fractional).

#### Option 2: O2^+
- **Electrons**: O2^+ has 15 electrons.
- **Molecular Orbital Filling**:
- σ1s (2), σ1s* (2), σ2s (2), σ2s* (2), σ2p (2), π2p (4), π*2p (1).
- **Bonding Electrons**: 10
- **Antibonding Electrons**: 5
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 5}{2} = \frac{5}{2} = 2.5 \]
- **Conclusion**: O2^+ has a bond order of 2.5 (not an integer, but still not fractional).

#### Option 3: O2^2-
- **Electrons**: O2^2- has 16 electrons.
- **Molecular Orbital Filling**:
- σ1s (2), σ1s* (2), σ2s (2), σ2s* (2), σ2p (2), π2p (4), π*2p (4).
- **Bonding Electrons**: 10
- **Antibonding Electrons**: 4
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 4}{2} = \frac{6}{2} = 3 \]
- **Conclusion**: O2^2- has a bond order of 3 (not fractional).

#### Option 4: H2^-
- **Electrons**: H2^- has 3 electrons.
- **Molecular Orbital Filling**:
- σ1s (2), σ1s* (1).
- **Bonding Electrons**: 2
- **Antibonding Electrons**: 1
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{2 - 1}{2} = \frac{1}{2} = 0.5 \]
- **Conclusion**: H2^- has a bond order of 0.5 (this is fractional).

### Final Answer
The molecule that has a fractional bond order is **H2^-**.

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