Describe the bonding in the C2 2- ion in terms of molecular orbital theory and compare the bond order to that of C2.
The Correct Answer and Explanation is:
The bonding in the C₂²⁻ ion (C₂ with two extra electrons) can be explained using molecular orbital theory, which describes bonding in terms of the combination of atomic orbitals from the individual atoms to form molecular orbitals. The two carbon atoms in C₂²⁻ are held together by molecular orbitals that result from the combination of the atomic orbitals of each carbon.
Electron Configuration in Molecular Orbitals
In molecular orbital theory, the atomic orbitals combine to form bonding and antibonding molecular orbitals. The molecular orbitals for diatomic molecules like C₂ are:
- σ(1s) and σ(1s)* (bonding and antibonding orbitals from the 1s orbitals)
- σ(2s) and σ(2s)* (bonding and antibonding orbitals from the 2s orbitals)
- π(2px) and π(2py) (bonding orbitals from the 2p orbitals)
- π(2px)* and π(2py)* (antibonding orbitals from the 2p orbitals)
- σ(2pz) (bonding orbital from the 2p orbitals)
- σ(2pz)* (antibonding orbital from the 2p orbitals)
For C₂ (the neutral molecule), each carbon atom has 4 valence electrons, so in C₂, there are a total of 8 electrons to distribute in the molecular orbitals.
The electron configuration for C₂ is:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2px)², π(2py)² (6 bonding electrons)
- π*(2px)¹, π*(2py)¹ (2 antibonding electrons)
The bond order for C₂ is calculated as:Bond Order=(Number of bonding electrons) – (Number of antibonding electrons)2\text{Bond Order} = \frac{\text{(Number of bonding electrons) – (Number of antibonding electrons)}}{2}Bond Order=2(Number of bonding electrons) – (Number of antibonding electrons)Bond Order for C₂=8−42=2\text{Bond Order for C₂} = \frac{8 – 4}{2} = 2Bond Order for C₂=28−4=2
Bonding in C₂²⁻
For C₂²⁻, there are two extra electrons, so the electron configuration becomes:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2px)², π(2py)² (6 bonding electrons)
- π*(2px)², π*(2py)² (4 antibonding electrons)
Now, the bond order for C₂²⁻ is:Bond Order for C₂²⁻=8−62=1\text{Bond Order for C₂²⁻} = \frac{8 – 6}{2} = 1Bond Order for C₂²⁻=28−6=1
Comparison of Bond Orders
- C₂ has a bond order of 2, indicating a relatively strong bond between the two carbon atoms.
- C₂²⁻ has a bond order of 1, which indicates a weaker bond due to the additional electrons that fill antibonding orbitals, reducing the overall bonding strength.
Thus, the bond in C₂²⁻ is weaker compared to the bond in C₂, as the extra electrons in antibonding orbitals result in a lower bond order and, consequently, a less stable molecule.
