Question

Specify which hybrid orbitals are used by carbon atoms in these species: (a) \(\mathrm{CO},\) (b) \(\mathrm{CO}_{2},\) (c) \(\mathrm{CN}^{-}\).

Short answer

The carbon atom in each molecule uses the following hybrid orbitals: (a) CO uses sp hybrid orbitals, (b) CO2 also uses sp hybrid orbitals, and (c) CN- uses sp2 hybrid orbitals.

Step-by-step solution

Determine Electron Domains for CO

For molecule CO, Carbon is bonded to a single Oxygen atom and has one lone pair. This means that Carbon has two electron domains.

Identify Hybridization for CO

Since there are two electron domains surrounding Carbon in CO, it implies that Carbon uses sp hybrid orbitals.

Determine Electron Domains for CO2

For molecule CO2, Carbon is bonded to two Oxygen atoms and carries no lone pairs. This means that Carbon has two electron domains.

Identify Hybridization for CO2

Since there are two electron domains surrounding Carbon in CO2, it implies that Carbon uses sp hybrid orbitals.

Determine Electron Domains for CN-

For molecule CN-, Carbon is bonded to one Nitrogen atom and has no lone pairs but has a triple bond with nitrogen. It has three electron domains.

Identify Hybridization for CN-

Since there are three electron domains around Carbon in CN-, it implies that Carbon uses sp2 hybrid orbitals.

Key concepts

Electron Domains

Understanding electron domains is the first step in determining the type of hybrid orbitals an atom will use in a molecular structure. Electron domains are regions around a central atom where electrons are likely to be found. These regions can include:

• Bonds to other atoms, whether they are single, double, or triple bonds
• Lone pairs of electrons that are not shared with other atoms

Each of these is considered one electron domain. For example, in a molecule like carbon monoxide (CO), carbon is bonded once to oxygen and has one lone pair, resulting in two electron domains. On the other hand, in the cyanide ion (CN^-), carbon is triple-bonded to nitrogen, which counts as one bond, but is still considered as having one electron domain due to the bond's nature. By counting these domains, we can predict the kind of hybridization occurring in the atom.

sp Hybrid Orbitals

sp hybrid orbitals arise when an atom mixes one s orbital with one p orbital to form two new equivalent orbitals. This type of hybridization usually occurs in linear geometries. A classic example of this is carbon in carbon dioxide (CO₂), where carbon forms two double bonds with oxygen atoms.
In this context, carbon makes use of sp hybrid orbitals because it has two electron domains, indicating that two orbitals rearrange to accommodate bonding.

• This process gives rise to two equivalent sp hybrid orbitals, oriented 180 degrees apart.
• This orientation results in the linear shape observed in CO₂ and similar molecules.
• Each sp hybrid can form σ (sigma) bonds, typically resulting from head-on overlapping with orbitals of other atoms.

These key characteristics help predict the linear structure and bonding properties of the molecule.

sp2 Hybrid Orbitals

sp² hybrid orbitals result from the mixing of one s orbital and two p orbitals to create three equivalent orbitals. These are often found in planar triangular geometry, such as in carbonate ions. In the case of the cyanide ion (CN^-), where carbon forms a triple bond with nitrogen, it uses sp² hybridization due to the electron domain arrangements.
Here's how sp² hybridization fits in:

• It involves three sp² orbitals arranged 120 degrees apart, maintaining a planar shape.
• One remaining p orbital can participate in forming π (pi) bonds, which occur from side-to-side overlap.
• This configuration allows for both the necessary σ bonds and additional π bonds to form multiple bonds, as seen in CN^-.

The arrangement of these hybrid orbitals is crucial in explaining the molecule's bonding characteristics and its overall geometry.