Question

Describe the molecular geometry of \(\mathrm{CCl}_{4}\) suggested by each of the following methods: (a) Lewis theory; (b) valence-bond method using simple atomic orbitals; (c) VSEPR theory; (d) valence-bond method using hybridized atomic orbitals.

Short answer

The molecular geometry of \(\mathrm{CCl}_{4}\) is tetrahedral according to all four methods: Lewis theory, valence-bond method using simple atomic orbitals, VSEPR theory, and valence-bond method using hybridized atomic orbitals.

Step-by-step solution

Lewis Theory Analysis

According to the Lewis theory, all atoms achieve a noble gas configuration. The central carbon atom shares its 4 electrons with 4 chlorine atoms, each contributing one electron leading to formation of 4 single covalent bonds. This results in the tetrahedral geometric shape.

Valence-Bond Method Using Simple Atomic Orbitals

In this method, atomic orbitals of the carbon atom overlap with atomic orbitals of the chlorine atom to form covalent bonds. The four 2p orbitals of the carbon overlap individually with the 3p orbitals of the four chlorine atoms. This creates 4 individual bonds resulting in a tetrahedral geometry.

VSEPR Theory Analysis

The Valence Shell Electron Pair Repulsion (VSEPR) theory suggests that electron pairs arranged around the central atom will orient themselves as far apart as possible to minimize repulsion. Carbon has 4 bonding pairs and no lone pairs, so according to VSEPR theory, this leads to a tetrahedral geometry.

Valence-Bond Method Using Hybridized Atomic Orbitals

In this method, carbon's 2s and three 2p orbitals blend together to form four new sp3 hybrid orbitals which are oriented toward the corners of a regular tetrahedron. In CCl4, these hybridized orbitals overlap with chlorine's 3p orbitals, forming the bonds and giving the molecule a tetrahedral geometry.

Key concepts

Lewis Theory

Lewis Theory is a foundational concept in chemistry which helps us understand how molecules form. It uses a simple visual representation to depict valence electrons as dots around atoms. This method highlights how atoms share electrons to achieve a stable electronic configuration, usually akin to that of a noble gas. In the case of carbon tetrachloride (\(\mathrm{CCl}_{4}\)), we imagine the central carbon atom looking to complete its valence electron shell.

• The carbon atom has four valence electrons.
• Each chlorine atom has seven valence electrons and needs one more to complete its outer shell.
• Carbon shares its four electrons with the electrons from four chlorine atoms.

This sharing of electrons forms four single covalent bonds between carbon and each chlorine atom in \(\mathrm{CCl}_{4}\). As a result, each atom achieves a stable configuration, resulting in the molecule adopting a tetrahedral shape to minimize electron repulsion.

Valence-Bond Theory

Valence-Bond Theory provides a different perspective by focusing on the overlaps between atomic orbitals when forming chemical bonds. Originally, this theory considered the use of simple atomic orbitals, such as 2p orbitals of carbon bonding with the 3p orbitals of chlorine.
To understand it more:

• Each 2p orbital of carbon overlaps with one 3p orbital from chlorine.
• This overlap leads to sigma bonds that hold the atoms together.
• The involvement of individual orbital overlaps results in the molecule's tetrahedral structure.

In essence, Valence-Bond Theory illustrates how bonds form through the direct overlap of orbitals, resulting in the formation of a tetrahedral molecule.

VSEPR Theory

The VSEPR Theory, or Valence Shell Electron Pair Repulsion Theory, is a practical model used to predict the shape of molecules by considering the repulsion between electron pairs. Notably, it focuses on minimizing the repulsion between pairs of electrons in the valence shell of the central atom.
In \(\mathrm{CCl}_{4}\):

• Carbon is the central atom with four bonding pairs and no lone pairs.
• The four electron pairs arrange themselves as far apart as possible.
• This results in a tetrahedral molecular shape as it minimizes repulsion.

The VSEPR theory offers a straightforward way to explain why \(\mathrm{CCl}_{4}\) forms a tetrahedral shape, as it is driven by the principle of minimizing electron pair repulsion.

Hybridization

Hybridization is a concept that introduces a more refined view of molecular geometry. It involves the combination of atomic orbitals to create new hybridized orbitals that are better suited for the pairing of electrons in bonds. For carbon in \(\mathrm{CCl}_{4}\), hybridization plays a crucial role.

• Carbon atom undergoes \(\mathrm{sp^3}\) hybridization.
• Its 2s and three 2p orbitals blend to create four equivalent \(\mathrm{sp^3}\) hybrid orbitals.
• The \(\mathrm{sp^3}\) orbitals position themselves towards the corners of a tetrahedron.
• They overlap with chlorine's 3p orbitals to form bonds.

As a result, hybridization not only supports the formation of tetrahedral geometry in \(\mathrm{CCl}_{4}\) but also provides a deeper insight into the bonding process beyond simple orbital overlaps.