Question

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.

Short answer

In both the Localized Electron (LE) and Molecular Orbital (MO) models, the bonding in $N{O}^{+}$ is characterized by the absence of unpaired electrons. For $N{O}^{-}$, both models predict two unpaired electrons. However, for $NO$, the MO model predicts an unpaired electron in the antibonding orbitals, while the LE model suggests an unpaired electron in nitrogen. The MO model provides a more accurate description of the bonding in molecules, as it accounts for the delocalization of electrons, thereby offering a better explanation of their stability.

Step-by-step solution

Determining the total number of valence electrons in each molecule

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: - $\text{N}$ (nitrogen) has 5 valence electrons - $\text{O}$ (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)

Describing bonding with the Localized Electron model

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.

Describing bonding with the Molecular Orbital model

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 $\text{2s}$ and $\text{2p}$ 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: - ${\mathrm{NO}}^{+}$: ${\sigma }_{2s}^2{\sigma }_{2s^{\ast }}^1{\pi }_{2p}^4{\sigma }_{2p}^2{\pi }_{2p^{\ast }}^1$ (10 electrons) - ${\mathrm{NO}}^{-}$: ${\sigma }_{2s}^2{\sigma }_{2s^{\ast }}^1{\pi }_{2p}^4{\sigma }_{2p}^2{\pi }_{2p^{\ast }}^3$ (12 electrons) - $\mathrm{NO}$: ${\sigma }_{2s}^2{\sigma }_{2s^{\ast }}^1{\pi }_{2p}^4{\sigma }_{2p}^2{\pi }_{2p^{\ast }}^2$ (11 electrons)

Comparing the two models and accounting for discrepancies

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.

Key concepts

Localized Electron Model

The Localized Electron Model, often utilizing Lewis structures, is one of the fundamental methods to visualize bond formation between atoms. In this model, electrons are viewed as residing in specific bonds between two atoms, making bonds appear more tangible and easier to understand. For simple molecules, it is especially helpful in mapping out how atoms are connected.
For example, in the case of $obreak{\mathrm{NO}}^{+}obreak$, the Localized Electron Model suggests a triple bond connecting nitrogen and oxygen. This results in a scenario where all electrons are paired, implying a very stable structure with no unpaired electrons.
On the other hand, $obreak{\mathrm{NO}}^{-}obreak$ is portrayed with a double bond, with each atom sporting one lone pair, leading to two unpaired electrons. Meanwhile, $obreak\mathrm{NO}obreak$ is illustrated with a double bond, a lone pair on nitrogen, two on oxygen, and an unpaired electron on nitrogen.
This model provides clear bonds and lone pairs, offering a straightforward visualization. However, it falls short when describing electron movements, such as nontraditional bonding or electron delocalization seen in larger and more complex molecules.

Molecular Orbital Model

The Molecular Orbital Model provides a more sophisticated take on bonding by considering electrons in molecules as delocalized over an entire molecule rather than being confined to a bond between two atoms. In this model, atomic orbitals meld into new orbitals extending over the whole molecule, known as molecular orbitals.
For $obreak{\mathrm{NO}}^{+}obreak$, the electron configuration in the molecular orbital model is $obreak{\sigma }_{2s}^2{\sigma }_{2s^{\ast }}^1{\pi }_{2p}^4{\sigma }_{2p}^2{\pi }_{2p^{\ast }}^{1}obreak$. This configuration highlights the electrons placed in bonding molecular orbitals, maintaining paired spins akin to the localized model, hinting at high stability.
In $obreak{\mathrm{NO}}^{-}obreak$, the electron configuration $obreak{\sigma }_{2s}^2{\sigma }_{2s^{\ast }}^1{\pi }_{2p}^4{\sigma }_{2p}^2{\pi }_{2p^{\ast }}^{3}obreak$ identifies the presence of unpaired electrons in antibonding orbitals. This observation aligns with the localized model, reinforcing the predictions of decreased stability due to increased antibonding character.
The $obreak\mathrm{NO}obreak$ molecule finds its electron configuration as $obreak{\sigma }_{2s}^2{\sigma }_{2s^{\ast }}^1{\pi }_{2p}^4{\sigma }_{2p}^2{\pi }_{2p^{\ast }}^{2}obreak$. The unpaired electron in anti-bonding orbitals reflects the observations from localized analysis but situates it within a complex electron framework.
This model gives a nuanced view of electron interactions and energies, making it indispensable for explaining properties like magnetism and reactivity.

Chemical Bonding Discrepancies

Chemical bonding discrepancies often appear when contrasting the Localized Electron Model and the Molecular Orbital Model. These discrepancies arise largely due to their differing approaches in viewing electron distribution.
While the localized model situates electrons in definitive bonds or lone pairs, offering simplicity in depicting bonding, it inadequately accounts for electron delocalization that becomes increasingly significant in more complex chemical systems. This aspect is pivotal, as delocalization influences stability and spectral properties like absorption and emission of light.
The molecular orbital model then comes into play, showcasing electron distribution across a molecule in molecular orbitals which reflect electron delocalization. In $obreak{\mathrm{NO}}^{+},obreak{\mathrm{NO}}^{-},obreak\mathrm{NO}obreak$, while both models present general congruity, the finer details such as electron position and spin in antibonding orbitals produce slight discrepancies that are better navigated through molecular orbitals.
Consequently, chemical bonding discrepancies between these models primarily lie in the representation and reckoning of electron placement and movement, favoring molecular orbitals for deeper insight into molecular behavior.