Ch.12 - Solids and Modern Materials

Problem 122a

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Chapter 12, Problem 122a

(a) What are the C¬C¬C bond angles in diamond?

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Identify the structure of diamond, which is a three-dimensional network of carbon atoms.

Recognize that each carbon atom in diamond is sp3 hybridized, forming four single covalent bonds with other carbon atoms.

Understand that in an sp3 hybridized carbon, the bond angles are determined by the tetrahedral geometry.

Recall that the ideal bond angle in a tetrahedral geometry is 109.5 degrees.

Conclude that the C-C-C bond angles in diamond are approximately 109.5 degrees.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Tetrahedral Geometry

In diamond, each carbon atom is bonded to four other carbon atoms in a tetrahedral arrangement. This geometry arises from the sp3 hybridization of carbon, where the bond angles between the carbon-carbon bonds are approximately 109.5 degrees. This spatial arrangement contributes to the strength and rigidity of the diamond structure.

Bond Angles

Bond angles are the angles formed between two bonds that share a common atom. In the case of diamond, the bond angles between the carbon-carbon bonds are crucial for understanding its three-dimensional structure. The tetrahedral bond angles of 109.5 degrees ensure that the carbon atoms are optimally spaced, minimizing electron pair repulsion according to VSEPR theory.

Crystal Lattice Structure

Diamond has a crystal lattice structure, which is a repeating pattern of atoms in three-dimensional space. This arrangement not only defines the bond angles but also contributes to diamond's exceptional hardness and thermal conductivity. The regularity of the lattice allows for uniform bond angles and distances, reinforcing the stability of the material.

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Lattice Energy

Related Practice

In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation 1l2, the angle at which the radiation is diffracted 1u2, and the distance between planes of atoms in the crystal that cause the diffraction (d) is given by nl = 2d sin u. X rays from a copper X-ray tube that have a wavelength of 1.54 Å are diffracted at an angle of 14.22 degrees by crystalline silicon. Using the Bragg equation, calculate the distance between the planes of atoms responsible for diffraction in this crystal, assuming n = 1 (first-order diffraction).

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Textbook Question

Germanium has the same structure as silicon, but the unit cell size is different because Ge and Si atoms are not the same size. If you were to repeat the experiment described in Additional Exercise 12.117, but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle 𝜃?

Textbook Question

(a) The density of diamond is 3.5 g>cm3, and that of graphite is 2.3 g>cm3. Based on the structure of buckminsterfullerene, what would you expect its density to be relative to these other forms of carbon?

Employing the bond enthalpy values listed in Table 8.4, estimate the molar enthalpy change occurring upon (a) polymerization of ethylene. (b) formation of nylon 6,6. (c) formation of polyethylene terephthalate (PET).

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Textbook Question

Employing the bond enthalpy values listed in Table 8.3 estimate the molar enthalpy change occurring upon c. formation of polyethylene terephthalate (PET).