Problem 112 - 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?

Step-by-Step Solution

Answer

In diamond, carbon atoms are arranged in a tetrahedral structure, resulting in C-C-C bond angles of approximately 109.471°. In graphite, carbon atoms are arranged in a hexagonal structure, resulting in C-C-C bond angles of 120°.

Step 1: 1: Understanding the structure of diamond

Diamond consists of carbon atoms bonded to four other carbon atoms in a tetrahedral arrangement. In other words, each carbon atom forms single covalent bonds with four other carbon atoms nearby, ultimately creating a regular and repeating lattice.

Step 2: 2: Finding the bond angles in diamond

Since the carbon atoms in the diamond structure form tetrahedral arrangements in which all four bonding pairs are at equal distances from each other, the bond angles are determined by the tetrahedral geometry. The C-C-C bond angle in a tetrahedral carbon structure can be found using the formula: \(angle = cos^{-1}(-\frac{1}{3})\) angle = 109.471 ° (approximately) So, the C-C-C bond angles in diamond are approximately 109.471°.

Step 3: 3: Understanding the structure of graphite

Graphite is composed of layers of carbon atoms bonded together in hexagonal structures. These layers are weakly connected with each other by van der Waals forces, making graphite a good lubricant and conductor of electricity. Each carbon atom in the hexagonal structure is bonded to three other carbon atoms, forming a planar structure.

Step 4: 4: Finding bond angles in graphite

Since the carbon atoms in graphite's hexagonal structure form planar arrangements, the bond angles can be found based on the hexagonal geometry (angles in a regular hexagon). In this case, the C-C-C bond angle can be found using the following formula: \(angle = \frac{360 °}{\text{number of sides in hexagon}}\) angle = \( \frac{360 °}{6} \) angle = 120 ° So, the C-C-C bond angles in graphite are equal to 120°.

Key Concepts

Diamond Structure

In a diamond structure, carbon atoms are arranged in a highly symmetric manner. This structure is known for its incredible strength and unique properties. Each carbon atom in a diamond is covalently bonded to four other carbon atoms.
This bonding pattern forms a three-dimensional lattice which is called a tetrahedral lattice.
Due to the strong covalent bonds between the carbon atoms, diamond becomes one of the hardest known materials.

• The tetrahedral arrangement allows for equal spacing between all bonding pairs.
• This uniform distribution leads to a specific bond angle.

The C-C-C bond angles in this tetrahedral geometry are approximately 109.471°, which can be calculated using the formula:
\( \text{angle} = \cos^{-1}(-\frac{1}{3}) \).
This particular angle is a hallmark of the diamond's crystalline structure, providing it with immense strength and stability.

Graphite Structure

Graphite stands in contrast to diamond in terms of structure and properties. While both are forms of carbon, graphite consists of layers of carbon atoms arranged in a two-dimensional hexagonal lattice.
These layers slide over each other easily, which is why graphite can be used as a lubricant or in pencils as lead.

• Each carbon atom in graphite is bonded to three other carbon atoms.
• This forms a planar arrangement, which is robust in the plane but weak between the planes.

The bond angles within each hexagonal layer of graphite are 120°, which are characteristic of hexagonal geometry. This angle can be calculated as:
\( \text{angle} = \frac{360°}{6} \), illustrating that each carbon atom forms bonds at these angles to maintain the planar structure.
The weak van der Waals forces between layers allow them to slide easily past one another, making graphite soft and flexible.

Tetrahedral Geometry

Tetrahedral geometry is a fundamental concept in chemistry, especially in the analysis of molecular and crystal structures. This geometry occurs when four atoms are symmetrically spaced around a central atom.
The perfect symmetry of a tetrahedral shape leads to equal bond angles.

• Each of the four bonding pairs extends from the central atom at the same angle.
• This angle is approximately 109.471°, which is derived from the geometry's specific spatial arrangement.

The importance of tetrahedral geometry is evident in structures like methane (CH₄) and diamond. It helps to explain why bonds are equally spaced and why the properties of these compounds are so distinctive.
This arrangement minimizes repulsion between the bond electron pairs, resulting in a stable and energetically favorable configuration.