In terms of the molecular orbital model, which species in each of the following two pairs will most likely be the one to gain an electron? Explain. a. CN or \(\mathrm{NO}\) b. \(\mathrm{O}_{2}^{2+}\) or \(\mathrm{N}_{2}^{2+}\)

In order to determine the species most likely to gain an electron, we must first know the molecular orbital diagrams of each species. These diagrams show the energies of the molecular orbitals and the electrons occupying them. a. CN and NO: For both CN and NO, we can use the molecular orbital diagram for diatomic nitrogen (N2) as a reference because they have similar electronic configurations. The molecular orbital diagram for N2 consists of σ1s, σ*1s, σ2s, σ*2s, π2p_x, π2p_y, σ2p_z, π*2p_x, π*2p_y, σ*2p_z. b. O2^2+ and N2^2+: For both of these species, we can use the molecular orbital diagram for diatomic oxygen (O2) as a reference because they also have similar electronic configurations. The molecular orbital diagram for O2 consists of σ1s, σ*1s, σ2s, σ*2s, σ2p_z, π2p_x, π2p_y, π*2p_x, π*2p_y, σ*2p_z.

The species with the lowest unoccupied molecular orbital (LUMO) is more likely to gain an electron. a. CN and NO: CN has one less electron than NO, so its LUMO (the orbitals where it would put the next electron) is lower in energy than the LUMO for NO. Therefore, CN is more likely to gain an electron. b. O2^2+ and N2^2+: Both O2^2+ and N2^2+ have the same reference molecular orbital diagram as mentioned earlier. O2^2+ has two more electrons in the π*2p orbitals compared to N2^2+. So, the LUMO of O2^2+ is the π*2p_x and π*2p_y orbitals, while the LUMO of N2^2+ is the π2p_x and π2p_y orbitals. Since the energy of the π*2p orbitals is higher than the π2p orbitals, N2^2+ has a lower energy LUMO. Therefore, N2^2+ is more likely to gain an electron. To summarize: a. CN is more likely to gain an electron than NO. b. N2^2+ is more likely to gain an electron than O2^2+.