Describe the bonding in \(\mathrm{NO}^{+}, \mathrm{NO}^{-},\) and \(\mathrm{NO},\) using both the localized electron and molecular orbital models. Account for any discrepancies between the two models.

First, we need to determine the total number of valence electrons in each molecule. For \(\mathrm{NO}^{+}, \mathrm{NO}^{-},\) and \(\mathrm{NO},\) we have the following: - \(\textrm{N}\) (nitrogen) has 5 valence electrons - \(\textrm{O}\) (oxygen) has 6 valence electrons - \(\mathrm{NO}^{+}\) has 10 valence electrons (11 electrons from N and O minus 1 electron for the +1 charge) - \(\mathrm{NO}^{-}\) has 12 valence electrons (11 electrons from N and O plus 1 electron for the -1 charge) - \(\mathrm{NO}\) has 11 valence electrons (5 from N and 6 from O)

In the LE model, electrons are localized between adjacent atoms in individual bonds. Using the Lewis structure, we can describe the bonding as follows: - \(\mathrm{NO}^{+}\): triple bond between nitrogen and oxygen, resulting in no unpaired electrons - \(\mathrm{NO}^{-}\): double bond between nitrogen and oxygen with one lone pair on each atom, resulting in two unpaired electrons - \(\mathrm{NO}\): double bond between nitrogen and oxygen with one lone pair on N and two lone pairs on O, 1 unpaired electron on N.

In the MO model, electrons reside in molecular orbitals formed from atomic orbitals of individual atoms. The atomic orbitals used for \(\mathrm{NO}^{+}, \mathrm{NO}^{-},\) and \(\mathrm{NO}\) are the \(\textrm{2s}\) and \(\textrm{2p}\) orbitals of nitrogen and oxygen. These orbitals combine to form bonding and antibonding molecular orbitals. For simplicity, we will describe the molecular orbital using the electron configuration: - \(\mathrm{NO}^{+}\): \(\sigma_{2s}^{2}\sigma_{2s^{*}}^{1}\pi_{2p}^{4}\sigma_{2p}^{2}\pi_{2p^{*}}^{1}\) (10 electrons) - \(\mathrm{NO}^{-}\): \(\sigma_{2s}^{2}\sigma_{2s^{*}}^{1}\pi_{2p}^{4}\sigma_{2p}^{2}\pi_{2p^{*}}^{3}\) (12 electrons) - \(\mathrm{NO}\): \(\sigma_{2s}^{2}\sigma_{2s^{*}}^{1}\pi_{2p}^{4}\sigma_{2p}^{2}\pi_{2p^{*}}^{2}\) (11 electrons)

Both the LE and MO models explain the bonding in \(\mathrm{NO}^{+}, \mathrm{NO}^{-},\) and \(\mathrm{NO},\) but there are some differences between them. - For \(\mathrm{NO}^{+}\), the MO model predicts a more stable ion with no unpaired electrons, while the LE model predicts no unpaired electrons, both models match. - For \(\mathrm{NO}^{-}\), the MO model predicts two unpaired electrons in the antibonding orbitals, agreeing with the LE model's description of two unpaired electrons. - For \(\mathrm{NO}\), the MO model predicts an unpaired electron in the antibonding orbitals while the localized model suggests an unpaired electron in nitrogen. The discrepancies observed between the two models arises from their representation of chemical bonding. The molecular orbital model gives a more accurate description of the bonding in molecules, as it accounts for the delocalization of electrons, thereby providing a better explanation of the stability of these species.