Question

What is the state of hybridisation of carbon in (a) ${\mathrm{CO}}_3^{2-}$ (b) diamond (c) graphite?

Short answer

(a) ${\mathrm{sp}}^2$; (b) ${\mathrm{sp}}^3$; (c) ${\mathrm{sp}}^2$.

Step-by-step solution

Understand Hybridization

Hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals, which in turn form chemical bonds. In carbon compounds, the hybridization state of carbon influences the structure and bonding properties of the compound.

Identify Hybridization in ${\mathrm{CO}}_3^{2-}$

In carbonate ion ${\mathrm{CO}}_3^{2-}$, carbon is bonded to three oxygen atoms with resonance structures showing a single and two double bonds. Each C-O bond requires a set of hybrid orbitals. Carbon here undergoes ${\mathrm{sp}}^2$ hybridization, forming three ${\mathrm{sp}}^2$ hybrid orbitals to bond with each oxygen atom, leaving a p-orbital for $\pi$-bonding across all the oxygens.

Identify Hybridization in Diamond

In diamond, each carbon atom forms four single bonds with other carbon atoms, arranged in a tetrahedral structure. This geometry is indicative of ${\mathrm{sp}}^3$ hybridization. Each carbon atom uses four ${\mathrm{sp}}^3$ hybrid orbitals to form four sigma bonds with other carbon atoms.

Identify Hybridization in Graphite

Graphite consists of layers of carbon atoms arranged in a hexagonal lattice. Each carbon atom forms three sigma bonds with three other carbon atoms in the plane. This arrangement is due to the ${\mathrm{sp}}^2$ hybridization, with the carbon also contributing one electron to a delocalized $\pi$-bonding network above and below the plane.

Key concepts

sp2 hybridization

The concept of sp2 hybridization is fundamental for understanding certain carbon compounds. Carbon atoms in the sp2 hybridization state will utilize three atomic orbitals (one s and two p) to form three equivalent sp2 hybrid orbitals. This geometry is commonly found in structures where carbon forms double bonds, such as in alkenes or planar arrangements like benzene.

In the case of the carbonate ion (${\mathrm{CO}}_3^{2-}$), carbon undergoes sp2 hybridization to bond with three oxygen atoms. This allows it to form three sigma ($\sigma$) bonds, which are strong covalent bonds, one with each oxygen, while one unhybridized p-orbital remains for creating pi ($\pi$) bonds. The resonance within ${\mathrm{CO}}_3^{2-}$ distributes the double bond character among all carbon-oxygen bonds, providing stability and an equal bond length throughout the structure.

This type of hybridization results in a planar triangular shape of the molecule with 120-degree bond angles, allowing for efficient overlap of orbitals, thereby strengthening the chemical bonding.

sp3 hybridization

In sp3 hybridization, a single s and all three p orbitals of carbon mix to create four equivalent sp3 hybrid orbitals. This type of hybridization is characteristic of carbon in compounds where it forms four single bonds, adopting a tetrahedral geometry.

Diamond is a classic example of sp3 hybridization where each carbon atom is bonded to four other carbon atoms in a network, creating a rigid three-dimensional structure. This is due to the unique overlap of the sp3 hybrid orbitals, leading to sigma bonds that are very strong and account for the extreme hardness of diamond.

The tetrahedral angle, approximately 109.5 degrees, maximizes the distance between electrons, minimizing electron repulsion and resulting in a stable structure. This geometry serves as a foundation for many organic molecules, influencing both physical properties and reactivity.

chemical bonding

Chemical bonding is the force that holds atoms together in compounds. Broadly, it can be categorized into ionic, covalent, and metallic bonds, with covalent bonding being prominent in organic compounds like those of carbon.

Covalent bonds involve the sharing of electron pairs between atoms, usually between nonmetals. For example, carbon, with its four valence electrons, achieves stability by forming four covalent bonds in compounds like methane or diamond, allowing it to complete an octet.

The type of hybridization in carbon determines the nature of these covalent bonds. In sp2 hybridization, such as with graphite, carbon forms three sigma bonds and partakes in a system of delocalized electrons, contributing to graphite's conductivity and lubricative properties. Meanwhile, in sp3 hybridization like in diamond, the resulting single covalent bonds lead to strong, stable structures.

Understanding chemical bonding and hybridization provides insight into the diverse properties and functions of carbon compounds, influencing everything from material strength to reactivity and electrical conductivity.