Question

Carbon dioxide \(\left(\mathrm{CO}_{2}\right),\) dinitrogen monoxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) the azide ion \(\left(\mathrm{N}_{3}^{-}\right),\) and the cyanate ion (OCN^-) have the same arrangement of atoms and the same number of valence shell electrons. However, there are significant differences in their electronic structures. (a) What hybridization is assigned to the central atom in each species? Which orbitals overlap to form the bonds between atoms in each structure. (b) Evaluate the resonance structures of these four species. Which most closely describe the bonding in these species? Comment on the differences in bond lengths and bond orders that you expect to see based on the resonance structures.

Short answer

For CO₂, N₂O, N₃⁻, and OCN⁻, the central atoms are sp hybridized. Resonance structures reveal bond order variations affecting bond lengths, particularly notable in N₂O and N₃⁻.

Step-by-step solution

Identify the Central Atoms and Their Hybridization

Examine the chemical formula of each species to determine the central atom: - For CO₂, the central atom is Carbon (C). - For N₂O, the central atom is Nitrogen (N). - In N₃⁻ and OCN⁻, the central atom is also Nitrogen (N). Determine hybridization: - CO₂: Carbon forms two double bonds, resulting in sp hybridization. - N₂O: The central Nitrogen forms two double bonds, leading to sp hybridization. - N₃⁻: With two double bonds, the central Nitrogen is sp hybridized. - OCN⁻: The central Nitrogen forms a triple bond with Carbon and a single bond with Oxygen, suggesting sp hybridization.

Determine Orbital Overlap for Bond Formation

Identify which orbitals overlap to form bonds between atoms: - CO₂: The sp orbitals of Carbon overlap with the p orbitals of Oxygen to form σ t}

continued: Determine Orbital Overlap for Bond Formation

bonds, while remaining π bonds are formed by p-p overlap. - N₂O: The sp orbitals of central Nitrogen overlap with the p orbitals of each terminal atom (N and O) to form σ bonds; π bonds result from p-p orbital overlap. - N₃⁻: The central N's sp orbitals bond with the p orbitals of the terminal N atoms (σ bonds), with π bonding through p-p overlap. - OCN⁻: The sp hybrid orbital of N and C forms a σ bond, p-p orbital overlap accounts for π bonds with both O and C.

Evaluate the Resonance Structures

Construct the resonance structures for each molecule/ion: - CO₂ has no significant resonance as it’s a linear molecule primarily described by two double bonds. - N₂O can show resonance with one structure having a triple bond N-N and a single bond N-O, and another with a single bond N-N and a double bond N-O. - N₃⁻ has possible structures depending on where the negative charge resides and how bonds are distributed among the three nitrogen atoms. - OCN⁻ has two resonance structures where the connectivity changes between N-C-O and O-C-N. Evaluate based on formal charges and stability: - The most stable structure of N₂O has a triple bond N-O with less charge on the terminal Oxygen. - For N₃⁻, alternating structures correspond to different bond lengths and stability but share the negative charge across the ions. - In OCN⁻, the more stable structure with negative charge on nitrogen reflects its higher electronegativity.

Analyze Bond Lengths and Bond Orders

Relate bond orders from resonance structures to bond lengths: - CO₂: Expected equal bond lengths with a bond order of 2. - N₂O: Bonds depend on resonance; typically, bond order between N and O varies (~2-3), influencing bond length. - N₃⁻: Resonance gives fractional bond orders (~1.33 per N-N bond), suggesting bond lengths that are consistent yet shorter than single bonds. - OCN⁻: Predominantly triple bonds in stable structures indicate shorter bonds between C-N and longer bonds in the predicted O-C single bond. Bond orders and formal charges lead to predictions: CO₂ and N₂O's bonds display varying lengths due to differing resonance contributions and bond orders.

Key concepts

Resonance Structures

Resonance structures are crucial for illustrating the potential configurations of electron distributions in a molecule. They help us understand how molecules can redefine their bond arrangements without changing overall energy significantly.
For carbon dioxide (\(\text{CO}_{2}\)), resonance isn't prominent as the molecule typically maintains two strong double bonds between carbon and oxygen in a linear formation. This uniformity keeps the molecule stable without resonance alternatives.
In dinitrogen monoxide (\(\text{N}_{2}\text{O}\)), there are notable resonance structures. One possibility includes a triple bond between the two nitrogen atoms, while the other nitrogen-oxygen pair maintains a single bond. The alternative configuration shows a single bond between nitrogens, with a double bond extending to oxygen.
The azide ion (\(\text{N}_{3}^{-}\)) exhibits several resonance forms because the negative charge can be spread over the three nitrogen atoms. This distribution alters the bond orders slightly, resulting in resonance that suggests equal blending of multiple structures rather than a fixed pattern of bonds.
The cyanate ion (OCN^-) can also resonate between distinct structures such as N-C-O and O-C-N, indicating variations in formal charges and stability due to the differing electronegativities of nitrogen and oxygen.

Orbital Overlap

Orbital overlap explains how atomic orbitals come together to form bonds, determining the shape and strength of these connections. Understanding this is fundamental to predicting molecular geometries and bond properties.
In CO₂, the hybrid sp orbitals of carbon precisely overlap with the p orbitals of the oxygen atoms. This leads to the formation of strong sigma (\(\sigma\)) bonds, while remaining parallel p orbitals overlap side-to-side to create pi (\(\pi\)) bonds.
N₂O also showcases sp hybrid orbitals of the central nitrogen atom overlapping with p orbitals of both terminal nitrogen and oxygen to establish sigma (\(\sigma\)) bonds. Meanwhile, pi (\(\pi\)) bonds arise due to additional p-p interactions.
In \(\text{N}_{3}^{-}\), each sp hybridized nitrogen central atom overlaps with terminal nitrogen p orbitals to form sigma (\(\sigma\)) bonds. Pi (\(\pi\)) bonds come from the side-to-side overlap of pure p orbitals.
OCN^- sees sigma bonds arising from the end-to-end overlap of hybrid orbitals between N and C. The pi (\(\pi\)) bonds are formed by p-p overlap, representing the most efficient use of overlapping p orbitals.

Bond Order

Bond order is pivotal for predicting the physical properties of molecules, such as bond strength and bond length. It's a measure of the number of chemical bonds between a pair of atoms.
In CO₂, bond order is straightforward, calculated as a double bond situation where each carbon-oxygen linkage has a bond order of 2. This gives rise to identical bond lengths.
N₂O's bond order varies due to its resonance structures, typically ranging a bit beyond 2 between the nitrogen and oxygen due to the potential for a part-triple bond configuration, causing some variability in bond length.
The azide ion (\(\text{N}_{3}^{-}\)) showcases a fractional bond order, about 1.33 per nitrogen linkage. This results from the resonance averaging across its configurations and suggests intermediate bond lengths often shorter than standard single bonds.
OCN^- exhibits bond orders generally aligning with triple bonds between carbon and nitrogen. Depending on the stable resonance structure, it can suggest single plans for oxygen, leading to differing bond lengths among its atoms.

Valence Electrons

Valence electrons are the outermost electrons of an atom and crucial for understanding how molecules form and react. They determine an atom's bonding potential and are keys to predicting molecular behavior.
For CO₂, each carbon atom utilizes its four valence electrons to form double bonds with oxygen, sharing electrons to fill their octet and stabilize the molecule with a symmetrical distribution.
N₂O displays a more complex scenario where shared valence electrons between nitrogen and oxygen atoms adjust to neutralize charges and maximize stability across possible resonant structures.
With the azide ion (\(\text{N}_{3}^{-}\)), the negative charge reflects extra valence electrons, which distribute over the nitrogen atoms enabling resonance. This shared electric field allows for stable yet dynamic bonding patterns across its structure.
OCN^- shows its adaptability as valence electrons find stability by adhering to parameters of electronegativity and resonance, leading to diverse yet equivalent structures in distributing electronegativity and charge among oxygen, carbon, and nitrogen.