Bond length in nitric oxide (NO) is 115 pm. Molecular nitrogen (N2) and nitrosyl ion (NO + ) display bonds that are substantially shorter (109.4 and 106 pm, respectively). Use molecular orbital theory to explain these differences.
The Correct Answer and Explanation is:
The bond length differences between nitric oxide (NO), molecular nitrogen (N₂), and the nitrosyl ion (NO⁺) can be explained using molecular orbital (MO) theory, which considers the behavior of electrons in molecular orbitals formed by the combination of atomic orbitals.
Molecular Orbital Configuration and Bond Order:
1. Molecular nitrogen (N₂):
N₂ has 14 total electrons (7 from each nitrogen atom). Its molecular orbital configuration is:
σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁴, σ(2p_z)²
To find the bond order, we use the formula:
Bond order = (Number of bonding electrons – Number of antibonding electrons) / 2
For N₂:
(10 bonding electrons – 4 antibonding electrons) / 2 = 3
So, N₂ has a bond order of 3, indicating a triple bond. This results in a short bond length of 109.4 pm, because stronger bonds are shorter.
2. Nitric oxide (NO):
NO has 15 electrons (7 from N and 8 from O). The MO configuration is similar to N₂, but with an extra electron placed in the π*(2p) antibonding orbital:
σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁴, σ(2p_z)², π*(2p)¹
Bond order:
(10 bonding – 5 antibonding) / 2 = 2.5
This bond order of 2.5 results in a bond that is weaker than a triple bond, making the bond length longer (115 pm) than in N₂.
3. Nitrosyl ion (NO⁺):
NO⁺ has 14 electrons (one less than NO). The electron removed is from the π*(2p) antibonding orbital:
σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁴, σ(2p_z)²
Bond order:
(10 bonding – 4 antibonding) / 2 = 3
So, NO⁺ also has a bond order of 3, like N₂, leading to a shorter bond length (106 pm).
Conclusion:
The differences in bond length are due to the number of electrons in antibonding orbitals. More electrons in antibonding orbitals lower bond order and increase bond length. Thus:
- NO⁺: bond order 3 → shortest bond (106 pm)
- N₂: bond order 3 → short bond (109.4 pm)
- NO: bond order 2.5 → longer bond (115 pm)
