Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy. a. \(\mathrm{CO}\) b. \(\mathrm{CO}^{+}\) c. \(\mathrm{CO}^{2+}\)

We need to find how many total electrons are present in each diatomic species. For CO, there are 6 valence electrons from C (Carbon) and 8 from O (Oxygen), totaling 14 electrons. For CO+, one electron is removed, resulting in 13 electrons. Lastly, for CO2+, two electrons are removed, leaving 12 electrons.

Using the aufbau principle, we will put the electrons into the molecular orbitals in the order: σ1s, σ*1s, σ2s, σ*2s, π2px, π2py, σ2pz, π*2px, π*2py, σ*2pz. - For \(\mathrm{CO}\) (14 electrons): σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz², π*2px¹, π*2py¹ - For \(\mathrm{CO}^+\) (13 electrons): σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz², π*2px¹ - For \(\mathrm{CO}^{2+}\) (12 electrons): σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz²

To find the bond order, use the formula: Bond Order = (Number of electrons in bonding orbitals - Number of electrons in anti-bonding orbitals) / 2. - Bond Order for \(\mathrm{CO}\): (10 - 4) / 2 = 3 - Bond Order for \(\mathrm{CO}^+\): (9 - 3) / 2 = 3 - Bond Order for \(\mathrm{CO}^{2+}\): (8 - 2) / 2 = 3

A species is paramagnetic if it has one or more unpaired electrons. Examine the electron configurations: - \(\mathrm{CO}\) has two unpaired electrons (in π*2px¹ and π*2py¹ orbitals), so it is paramagnetic. - \(\mathrm{CO}^+\) has one unpaired electron (in π*2px¹ orbital), so it is also paramagnetic. - \(\mathrm{CO}^{2+}\) has no unpaired electrons, so it is diamagnetic.

As the bond order increases, bond energy increases, and bond length decreases. All the species have the same bond order (3), so we can rank them as follows: - Bond Length: \(\mathrm{CO} \approx \mathrm{CO}^+ \approx \mathrm{CO}^{2+}\) - Bond Energy: \(\mathrm{CO} \approx \mathrm{CO}^+ \approx \mathrm{CO}^{2+}\) In conclusion, the electron configurations for each species are: a. \(\mathrm{CO}\): σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz², π*2px¹, π*2py¹ (paramagnetic) b. \(\mathrm{CO}^+\): σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz², π*2px¹ (paramagnetic) c. \(\mathrm{CO}^{2+}\): σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz² (diamagnetic) Bond lengths and energies are approximately equal for all three species since they all have a bond order of 3.