Problem 119 - Chemistry: The Central Science

Question

(a) What are the \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in diamond? (b) What are they in graphite (in one sheet)? (c) What atomic orbitals are involved in the stacking of graphite sheets with each other?

Step-by-Step Solution

Answer

(a) In diamond, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles are \(109.5^\circ\) due to the tetrahedral arrangement of carbon atoms with sp3 hybridization. (b) Within one sheet of graphite, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles are \(120^\circ\), as carbon atoms have a planar arrangement with sp2 hybridization in hexagonal rings. (c) The stacking of graphite sheets involves the perpendicular p-orbitals, which form weak van der Waals forces between the layers.

Step 1: Understand the structure of diamond

Diamond has a three-dimensional network structure in which each carbon atom is covalently bonded to four other carbon atoms in a tetrahedral arrangement. This means the carbon atoms are in a sp3 hybridization state.

Step 2: Determine the bond angle in diamond

Since the carbon atoms in diamond have a tetrahedral arrangement, the bond angle in diamond can be determined using the tetrahedral angle formula. The angle between any two bonds in a tetrahedron is given as the "tetrahedral angle". This is an angle of \(109.5^\circ\). Therefore, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in diamond are \(109.5^\circ\).

Step 3: Understand the structure of graphite

Graphite consists of layers of carbon atoms arranged in hexagonal rings. Each carbon atom in a graphite layer forms three covalent bonds with three other carbon atoms in a planar arrangement, with one electron left unpaired in a perpendicular p-orbital. This means the carbon atoms are in a sp2 hybridization state.

Step 4: Determine the bond angle in graphite

Because each carbon atom in graphite is bonded to three other carbon atoms in a planar arrangement, the bond angle can be determined by considering the angles of a regular hexagon. Each interior angle of a regular hexagon is \(120^\circ\). Therefore, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in graphite (within one sheet) are \(120^\circ\).

Step 5: Identify the atomic orbitals involved in the stacking of graphite sheets

In graphite, each carbon atom has one electron left unpaired in a perpendicular p-orbital. When sheets of graphite are stacked together, these p-orbitals can overlap and interact, forming weak van der Waals forces between the layers. These forces are responsible for the stacking of graphite sheets. In summary: (a) The \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in diamond are \(109.5^\circ\). (b) Within one sheet, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in graphite are \(120^\circ\). (c) The atomic orbitals involved in the stacking of graphite sheets are the perpendicular p-orbitals.

Key Concepts

sp3 Hybridization

Atoms with sp3 hybridization have their valence electrons rearranged into four equivalent sp3 hybrid orbitals. This happens when one s orbital mixes with three p orbitals, creating four hybrid orbitals. Each of these orbitals points to a corner of a tetrahedron, resulting in bond angles of approximately 109.5 degrees.

• This is typical for carbon atoms in alkanes, like in a diamond structure.
• The characteristic tetrahedral shape minimizes electron-pair repulsion, maximizing stability.

Understanding this hybridization provides insights into the three-dimensional shapes and bond angles of molecules.

sp2 Hybridization

In sp2 hybridization, one s orbital combines with two p orbitals to form three sp2 hybrid orbitals. These lie in a single plane, leaving one p orbital unhybridized. The unhybridized p orbital stands perpendicular to the plane of the hybridized orbitals.

• This configuration is common in molecules with double bonds, such as the carbon atoms in graphite or ethene.
• The unhybridized p orbitals overlap, leading to pi bonds.
• sp2 hybridization results in a planar structure with bond angles of 120 degrees.

This arrangement allows for the formation of strong covalent bonds and gives materials like graphite their unique properties.

Tetrahedral Angle

The term tetrahedral angle refers to the angle formed between any two bonds in a tetrahedral molecule. This angle is approximately 109.5 degrees, crucial in understanding the shape of tetrahedrally coordinated complexes.

• For carbon compounds like in diamond, each carbon atom forms bonds at a tetrahedral angle.
• The tetrahedral angle ensures that molecules have optimal geometry to reduce repulsion between electron pairs.

Recognizing the tetrahedral angle is key to predicting and visualizing the shape of many organic molecules.

Diamond Structure

Diamond displays a distinctive three-dimensional network structure. In this arrangement, each carbon atom is bonded covalently to four other carbon atoms, creating a robust lattice. This structure is due to the sp3 hybridization of carbon:

• Each carbon atom in diamond shares electrons in four sp3 hybrid orbitals.
• This configuration forms a heavily interconnected structure that contributes to diamond's exceptional hardness.

Understanding this structure explains why diamond is one of the hardest natural materials known and has a high melting point.

Graphite Structure

Graphite is composed of layers of carbon atoms arranged in hexagonal rings. In these rings, each carbon atom connects to three others through covalent bonds, forming extensive planar layers.
The property of these layers is primarily due to sp2 hybridization:

• The p orbitals of adjacent atoms overlap, creating a network of pi bonds across the layers.
• The layers can slide over one another easily due to weak van der Waals forces between them.

These characteristics make graphite an excellent lubricant and conductor of electricity, showcasing its unique properties compared to diamond.