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.
- 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.
- 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).
- 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.
- 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.
