Which of the following will have highest bond energy ?

Options

A. `F_2`
B. `N_2`
C. `F_2^-`
D. `O_2^-`

Answer

To determine which of the given molecules has the highest bond energy, we will analyze the bond orders of each molecule using Molecular Orbital Theory (MOT). The bond energy is directly related to the bond order: the higher the bond order, the higher the bond energy.

### Step-by-Step Solution:

1. **Identify the Molecules**: The molecules we need to analyze are F2, N2, F2-, and O2-.

2. **Calculate the Total Electrons**:
- **F2**: Each fluorine atom has 7 valence electrons, so F2 has 14 valence electrons.
- **N2**: Each nitrogen atom has 5 valence electrons, so N2 has 10 valence electrons.
- **F2-**: F2 has 14 electrons, and with one additional electron, F2- has 15 electrons.
- **O2-**: O2 has 16 electrons, and with one additional electron, O2- has 17 electrons.

3. **Construct Molecular Orbital Diagrams**:
- **F2**: The order of molecular orbitals is:
- σ1s, σ*1s, σ2s, σ*2s, σ2p_z, π2p_y, π2p_x, π*2p_x, π*2p_y
- Fill the 14 electrons:
- σ1s (2), σ*1s (2), σ2s (2), σ*2s (2), σ2p_z (2), π2p_y (2), π2p_x (2)
- Bond Order = (Number of bonding electrons - Number of antibonding electrons)/2 = (8 - 6)/2 = 1.

- **N2**: The order of molecular orbitals is:
- σ1s, σ*1s, σ2s, σ*2s, π2p_x, π2p_y, σ2p_z, π*2p_x, π*2p_y
- Fill the 10 electrons:
- σ1s (2), σ*1s (2), σ2s (2), σ*2s (2), π2p_x (2), π2p_y (2)
- Bond Order = (Number of bonding electrons - Number of antibonding electrons)/2 = (10 - 4)/2 = 3.

- **F2-**: The order of molecular orbitals remains the same, but we add one more electron:
- Fill the 15 electrons:
- σ1s (2), σ*1s (2), σ2s (2), σ*2s (2), σ2p_z (2), π2p_y (2), π2p_x (2), π*2p_x (1)
- Bond Order = (8 - 7)/2 = 0.5.

- **O2-**: The order of molecular orbitals is:
- σ1s, σ*1s, σ2s, σ*2s, π2p_x, π2p_y, σ2p_z, π*2p_x, π*2p_y
- Fill the 17 electrons:
- σ1s (2), σ*1s (2), σ2s (2), σ*2s (2), π2p_x (2), π2p_y (2), σ2p_z (2), π*2p_x (1), π*2p_y (1)
- Bond Order = (10 - 7)/2 = 1.5.

4. **Compare Bond Orders**:
- F2: Bond Order = 1
- N2: Bond Order = 3
- F2-: Bond Order = 0.5
- O2-: Bond Order = 1.5

5. **Conclusion**: The molecule with the highest bond energy is N2, as it has the highest bond order of 3.

### Final Answer:
**N2 has the highest bond energy.**