Pick out the incorrect statement ?

Options

A. `N_2` has greater dissociation energy than `N_2^+`
B. `O_2` has lower dissociation energy than `O_2^+`
C. Bond length in `N_2^+` is less than `N_2`
D. Bond length in `NO^+` is less than in NO.

Answer

To solve the question "Pick out the incorrect statement," we need to analyze the statements provided and determine which one is incorrect based on the principles of chemical bonding and molecular orbital theory (MOT).

### Step-by-Step Solution:

1. **Understanding Dissociation Energy**:
- Dissociation energy is the energy required to break one mole of a molecule into its constituent atoms in the gaseous state. It is directly related to the bond order of the molecule.

2. **Analyzing the First Statement**:
- **Statement**: N2 has greater dissociation energy than N2+.
- **Bond Order Calculation**:
- For N2:
- Total electrons = 14 (7 from each nitrogen).
- Bonding electrons = 10 (2 in σ1s, 2 in σ2s, 6 in π2p).
- Anti-bonding electrons = 4 (2 in σ1s*, 2 in σ2s*).
- Bond Order = (Bonding - Anti-bonding) / 2 = (10 - 4) / 2 = 3.
- For N2+:
- Total electrons = 13 (1 electron removed).
- Bonding electrons = 9.
- Anti-bonding electrons = 4.
- Bond Order = (9 - 4) / 2 = 2.5.
- **Conclusion**: N2 has a higher bond order than N2+, hence greater dissociation energy. This statement is correct.

3. **Analyzing the Second Statement**:
- **Statement**: O2 has lower dissociation energy than O2+.
- **Bond Order Calculation**:
- For O2:
- Total electrons = 16.
- Bonding electrons = 10.
- Anti-bonding electrons = 6.
- Bond Order = (10 - 6) / 2 = 2.
- For O2+:
- Total electrons = 15 (1 electron removed).
- Bonding electrons = 10.
- Anti-bonding electrons = 5.
- Bond Order = (10 - 5) / 2 = 2.5.
- **Conclusion**: O2+ has a higher bond order than O2, thus greater dissociation energy. Therefore, this statement is incorrect.

4. **Analyzing the Third Statement**:
- **Statement**: The bond length in NO2 is less than that in N2.
- **Bond Order Analysis**:
- N2 has a bond order of 3, indicating a strong bond and shorter bond length.
- NO2 has a bond order of approximately 1.5 (due to resonance).
- **Conclusion**: Since N2 has a higher bond order than NO2, it has a shorter bond length. This statement is correct.

5. **Final Conclusion**:
- The incorrect statement is: **O2 has lower dissociation energy than O2+**.

### Summary of Incorrect Statement:
- The incorrect statement is that O2 has lower dissociation energy than O2+. In fact, O2+ has higher dissociation energy due to its higher bond order.