What is the bond order of B2 and B2+? Which of these species has a longer bond? Bond order of B2: Bond order of B2+: Which species has a longer bond
The Correct Answer and Explanation is:
Bond order of B₂: 1
Bond order of B₂⁺: 0.5
Which species has a longer bond? B₂⁺
Explanation:
To determine the bond order and compare bond lengths of diatomic molecules such as B₂ and B₂⁺, we refer to Molecular Orbital (MO) Theory, which describes bonding in terms of molecular orbitals formed from the combination of atomic orbitals. For second-period homonuclear diatomic molecules like boron (B), the molecular orbital energy level diagram is essential.
For elements with atomic numbers less than or equal to 7 (i.e., B, C, N), the order of molecular orbitals is:
σ(1s) < σ*(1s) < σ(2s) < σ*(2s) < π(2p) < σ(2p) < π*(2p) < σ*(2p)
Step 1: Electron configuration of B₂
Each boron atom has 5 electrons, so B₂ has 10 electrons total.
Filling the molecular orbitals:
- σ(1s) → 2 electrons
- σ*(1s) → 2 electrons
- σ(2s) → 2 electrons
- σ*(2s) → 2 electrons
- π(2p_x) and π(2p_y) → 2 electrons (one in each)
Bond order = ½ [(bonding e⁻) − (antibonding e⁻)]
= ½ [(2 in π(2p) + 2 in σ(2s) + 2 in σ(1s)) − (2 in σ*(2s) + 2 in σ*(1s))]
= ½ [(6 bonding) − (4 antibonding)]
= ½ (6 − 4) = 1
Step 2: Electron configuration of B₂⁺
B₂⁺ has 9 electrons (one less than B₂).
Remove one electron from the highest energy occupied MO, which is one of the π(2p) orbitals.
Now, π(2p) contains only 1 electron (unpaired), so:
Bond order = ½ [(5 bonding) − (4 antibonding)] = ½ (1) = 0.5
Step 3: Bond length comparison
The greater the bond order, the stronger and shorter the bond.
Since B₂ has a bond order of 1 and B₂⁺ has a bond order of 0.5, B₂⁺ has a longer bond due to its weaker bonding interaction.
Summary:
- B₂ has a bond order of 1
- B₂⁺ has a bond order of 0.5
- B₂⁺ has the longer bond because lower bond order implies a weaker, longer bond.
