Which molecules are described by molecular orbital theory as having a bond order of 2.0?
The correct answer and explanation is:
The correct answer is O₂ (Oxygen molecule).
Explanation:
Molecular orbital (MO) theory provides a way to describe the bonding in molecules by combining atomic orbitals to form molecular orbitals. These molecular orbitals can be classified into bonding, anti-bonding, and non-bonding orbitals. The bond order in MO theory is determined by the difference between the number of electrons in bonding and anti-bonding molecular orbitals, divided by two.
The bond order (BO) is calculated using the formula: Bond order=12(Number of electrons in bonding orbitals−Number of electrons in anti-bonding orbitals)\text{Bond order} = \frac{1}{2} \left( \text{Number of electrons in bonding orbitals} – \text{Number of electrons in anti-bonding orbitals} \right)
For the O₂ molecule, the molecular orbitals are filled with electrons as follows:
- The O₂ molecule has a total of 16 electrons (8 from each oxygen atom).
- These electrons fill the molecular orbitals in order of increasing energy: σ(1s), σ*(1s), σ(2s), σ*(2s), π(2p), π*(2p).
- Oxygen’s molecular orbitals are filled as: σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁴, π*(2p)².
- There are 10 electrons in bonding molecular orbitals (2 from σ(2s)², 2 from σ*(2s)², 4 from π(2p)⁴) and 6 electrons in anti-bonding molecular orbitals (2 from π*(2p)²).
Now, the bond order calculation: Bond order=12(10−6)=12×4=2\text{Bond order} = \frac{1}{2} \left( 10 – 6 \right) = \frac{1}{2} \times 4 = 2
Thus, O₂ has a bond order of 2. This means that the oxygen molecule has a double bond between the two oxygen atoms.
The bond order of 2 is common in molecules that have a similar electron configuration, such as O₂, and it indicates that there are two bonding electron pairs in the molecule, leading to a relatively strong and stable bond.