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?

First, we need to determine the electron configurations for Carbon (C) and Nitrogen (N). Carbon (C) has 6 electrons, so its electron configuration is: \(1s^2 2s^2 2p^2\) Nitrogen (N) has 7 electrons, so its electron configuration is: \(1s^2 2s^2 2p^3\)

Now, we will determine the molecular orbital (MO) configurations for CN⁺, CN, and CN⁻. CN⁺ has 12 electrons (6 from C and 7 from N minus 1): MO configuration: \(\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p}^2 \pi_{2p}^4\) CN has 13 electrons (6 from C and 7 from N): MO configuration: \(\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p}^2 \pi_{2p}^5\) CN⁻ has 14 electrons (6 from C and 7 from N and one additional electron): MO configuration: \(\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p}^2 \pi_{2p}^6\) Next, we will use the bond order formula to determine the strength of the C-N bond in each species: \(Bond\:Order = \frac{1}{2} (Electrons\:in\:bonding\:orbitals - Electrons\:in\:antibonding\:orbitals)\) Bond order for CN⁺: \(= \frac{1}{2}(6 - 4) = 1\) Bond order for CN: \(= \frac{1}{2}(6.5 - 4) = 1.25\) Bond order for CN⁻: \(= \frac{1}{2}(7 - 4) = 1.5\) A higher bond order indicates a stronger bond.

We will now identify species having unpaired electrons by examining their molecular orbital configurations: CN⁺: \(\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p}^2 \pi_{2p}^4\) - No unpaired electrons. CN: \(\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p}^2 \pi_{2p}^5\) - One unpaired electron. CN⁻: \(\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p}^2 \pi_{2p}^6\) - No unpaired electrons. a) The strongest C-N bond is in CN⁻, as it has the highest bond order of 1.5. b) Among the given species, only CN has unpaired electrons.