Describe the bonding in the C2 2- ion in terms of molecular orbital theory and compare the bond order to that of C2.

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 can be explained using molecular orbital theory. In this theory, atomic orbitals combine to form molecular orbitals, which are filled according to the Pauli Exclusion Principle and Hund’s Rule.

1. Atomic Orbitals: Carbon (C) has an atomic number of 6, meaning its electrons are arranged as 1s² 2s² 2p². For the C₂ molecule, each carbon atom contributes two 2s and two 2p orbitals.
2. Molecular Orbitals: When two carbon atoms bond, their atomic orbitals combine to form molecular orbitals. The bonding orbitals are called σ and π orbitals. The molecular orbitals for the C₂²⁻ ion are:
   • From the two 2s orbitals: one σ(2s) (bonding), one σ*(2s) (antibonding).
   • From the two 2p orbitals: one σ(2p) (bonding), two π(2p) (bonding), and one π*(2p) (antibonding).
   In the case of the C₂²⁻ ion, there are two additional electrons compared to the neutral C₂ molecule. These electrons occupy the antibonding π*(2p) orbitals, which lowers the bond order.
3. Bond Order Calculation: The bond order is given by the formula: Bond Order=12(Bonding Electrons−Antibonding Electrons)\text{Bond Order} = \frac{1}{2} (\text{Bonding Electrons} – \text{Antibonding Electrons})Bond Order=21​(Bonding Electrons−Antibonding Electrons) For C₂²⁻:
   • Bonding electrons: 2 (σ(2s)) + 2 (π(2p)) = 4.
   • Antibonding electrons: 2 (σ*(2s)) + 2 (π*(2p)) = 4.
   • Bond order = ½(4 – 4) = 0.
4. Comparison with C₂: In the neutral C₂ molecule, the bond order is calculated as: Bond Order=12(8−4)=2.\text{Bond Order} = \frac{1}{2} (8 – 4) = 2.Bond Order=21​(8−4)=2. Therefore, the bond order in C₂²⁻ is 0, indicating no net bonding between the carbon atoms, while the bond order in C₂ is 2, suggesting a stable double bond between the carbon atoms.