Question

(a) What are the \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) 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?

Short answer

(a) The \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in diamond is approximately 109.47 degrees. (b) The \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in one graphite sheet is 120 degrees. (c) The atomic orbitals involved in the stacking of graphite sheets are the unhybridized p-orbitals (2pz orbitals) that form weak van der Waals forces between the sheets.

Step-by-step solution

Understanding the structure of diamond

The carbon atoms in diamond are arranged in a tetrahedral structure, where each carbon atom is bonded to four other carbon atoms. This arrangement results in a three-dimensional network with each bond having equal length and bond angle.

Calculating the diamond bond angle

In diamond, the bond angle can be calculated using the tetrahedral angle formula. The tetrahedral angle is given by: \[\cos^{-1}\left(\frac{-1}{3}\right) \approx 109.47^{\circ}\] So, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in diamond is approximately 109.47 degrees.

Understanding the structure of graphite

Graphite has a layered structure, where carbon atoms are arranged in a hexagonal pattern within each sheet, and these sheets are stacked on top of each other. Each carbon atom in the sheet is bonded to three other carbon atoms within the same sheet, and these bonds create a planar structure.

Calculating graphite bond angle in one sheet

As the carbon atoms in graphite sheets are arranged in a hexagonal pattern, the bond angle between them can be calculated using the hexagonal angle formula. The hexagonal angle is given by: \[180^{\circ} - \frac{360^{\circ}}{6} = 120^{\circ}\] So, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in one graphite sheet is 120 degrees.

Identifying the atomic orbitals involved in graphite sheets stacking

The atomic orbitals involved in the bonding within a single graphite sheet are sp2 hybridized orbitals, as each carbon atom forms three sigma bonds with its neighboring carbon atoms. The remaining unhybridized p-orbitals (2pz orbitals) are responsible for the weak interactions between graphite sheets. These interactions are known as van der Waals forces or London dispersion forces. In summary: (a) The \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in diamond is approximately 109.47 degrees. (b) The \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in one graphite sheet is 120 degrees. (c) The atomic orbitals involved in the stacking of graphite sheets are the unhybridized p-orbitals (2pz orbitals) that form weak van der Waals forces between the sheets.

Key concepts

Diamond Structure

Diamond is why your engagement ring sparkles! It's made up entirely of carbon atoms that form a perfect, three-dimensional lattice. Each carbon atom connects to four other carbon atoms through strong covalent bonds. This forms a repeating, tetrahedral structure—a symmetric and stable configuration. Here are key characteristics of diamond's structure:

• Every carbon atom is equidistant from its four neighbors.
• The entire network creates a strongly interconnected, hard structure.
• Unlike other forms, diamond lacks free electrons, making it an electrical insulator.

The carbon connections result in the maximum possible number of covalent bonds for a carbon atom, explaining diamond’s renowned hardness.

Graphite Structure

Graphite, another allotrope of carbon, writes your notes. Unlike diamond, graphite consists of layers of carbon atoms arranged in hexagonal patterns. Each layer forms a two-dimensional plane of covalent bonds while being weakly held to adjacent layers through van der Waals forces.

• Graphite layers can slide over each other, making it ideal for lubricants and pencils.
• Its hexagonal arrangement gives it a unique electrical conductivity along the planes.
• Each carbon atom creates three sigma bonds with neighboring atoms.

This structure contrasts with diamond because graphite's layers provide a different type of stability—flexibility and electrical conductivity, without three-dimensional hardness.

Hybridization

Hybridization is the secret behind diverse atomic bonding like a swiss army knife! It’s a process by which atomic orbitals mix to form new hybrid orbitals, ideal for specific molecular shapes. In carbon, this process results in different bonding configurations depending on the element's environment:

• sp³ Hybridization: Occurs in diamond; each carbon atom fuses one s and three p orbitals to form four equivalent sp³ hybrid orbitals, resulting in a tetrahedral shape.
• sp² Hybridization: Found in graphite; each carbon atom mixes one s and two p orbitals to create three sp² hybrid orbitals used to form sigma bonds, leaving an unhybridized p orbital for pi-bonding.

Understanding hybridization allows chemists to predict how atoms bond and the resulting molecular geometry.

Tetrahedral Angle

The tetrahedral angle is a fundamental concept in molecular geometry, especially in chemistry's understanding of carbon structures like diamond. This angle arises from sp³ hybridization:

• In a perfect tetrahedron, the angle between any two bonds originating from a central atom is \(109.47^\circ\).
• This specific angle ensures maximum separation between electron pairs, minimizing repulsion.
• The result is a stable, evenly spaced structure, explaining the uniformity of diamond's carbon network.

The tetrahedral angle is more than a number; it's a geometric solution for optimal atomic separation.

Hexagonal Angle

Hexagonal angles contribute to graphite's layered beauty and versatility. This is a different kind of angle formed between bonds in a plane, typical of sp² hybridized structures:

• In graphite, the carbon atoms are arranged in a planar hexagon, giving rise to bond angles of\(120^\circ\).
• The flat arrangement allows graphite's layers to stack loosely.
• These layers slide over one another due to weak van der Waals forces, making graphite excellent for applications requiring lubricity.

Understanding the hexagonal angle is crucial for comprehending graphite's function in various products.