Question

Determine the electron configurations for \(\mathrm{CN}^{+}, \mathrm{CN}\), and \(\mathrm{CN}^{-}\). (a) Which species has the strongest \(\mathrm{C}-\mathrm{N}\) bond? (b) Which species, if any, has unpaired electrons?

Short answer

(a) The strongest C-N bond is present in CN⁺, as it has the least number of antibonding electrons (4) compared to CN (5) and CN⁻ (6). (b) Out of the three species, only CN has unpaired electrons, with one unpaired electron in the π*(2py) orbital. CN⁺ and CN⁻ have no unpaired electrons.

Step-by-step solution

Determine the total number of electrons for each ion

The number of electrons for each ion is determined by considering the atomic number of each element and their charge. Carbon (C) has 6 electrons and nitrogen (N) has 7 electrons. CN⁺: Carbon (6) + Nitrogen (7) - 1 (positive charge) = 12 electrons CN: Carbon (6) + Nitrogen (7) = 13 electrons CN⁻: Carbon (6) + Nitrogen (7) + 1 (negative charge) = 14 electrons

Determine the electron configuration using the molecular orbital theory

The molecular orbital theory uses atomic orbitals from the elements to create molecular orbitals. There are five molecular orbitals: σ(2s), σ*(2s), σ(2pz), π(2px), and π(2py). The order of these orbitals in terms of their energy is: σ(2s) < σ*(2s) < π(2px) = π(2py) < σ(2pz) Now, we fill these orbitals with the electrons of CN⁺, CN, and CN⁻ to find their electron configurations.

Electron configurations of CN⁺, CN, and CN⁻

Using the molecular orbitals, we fill the electrons from the lowest energy level up. CN⁺ (12 electrons): σ(2s)², σ*(2s)², π(2px)², π(2py)², σ(2pz)², π*(2px)² CN (13 electrons): σ(2s)², σ*(2s)², π(2px)², π(2py)², σ(2pz)², π*(2px)², π*(2py)¹ CN⁻ (14 electrons): σ(2s)², σ*(2s)², π(2px)², π(2py)², σ(2pz)², π*(2px)², π*(2py)²

Identify the species with the strongest C-N bond

The bond strength is determined by the difference between bonding and antibonding electrons. The fewer antibonding electrons and the greater bonding electrons, the stronger the bond. From the electron configurations: CN⁺: Bonding electrons = 8 (σ(2s)², π(2px)², π(2py)², σ(2pz)²) Antibonding electrons = 4 (σ*(2s)², π*(2px)²) CN: Bonding electrons = 8 (σ(2s)², π(2px)², π(2py)², σ(2pz)²) Antibonding electrons = 5 (σ*(2s)², π*(2px)², π*(2py)¹) CN⁻: Bonding electrons = 8 (σ(2s)², π(2px)², π(2py)², σ(2pz)²) Antibonding electrons = 6 (σ*(2s)², π*(2px)², π*(2py)²) Among the three species, CN⁺ has the strongest C-N bond as it has the least number of antibonding electrons.

Determine which species has unpaired electrons

The species with unpaired electrons should have an odd number of electrons in its antibonding orbitals. From the electron configurations: CN⁺: All electrons are paired (none unpaired) CN: One unpaired electron in the π*(2py) orbital CN⁻: All electrons are paired (none unpaired) Hence, the CN species has one unpaired electron.