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Chapter 12

Crystalline Solids and Modern Materials

Educators

LE
Gl
+ 7 more educators

Problem 1

What is graphene? Why is graphene unique?

Matthew H.
Numerade Educator

Problem 2

Explain the basic principles involved in X-ray crystallography. Include Bragg's law in your explanation.

Wilson M.
The University of Alabama

Problem 3

What is a crystalline lattice? How is the lattice represented with the unit cell?

Matthew H.
Numerade Educator

Problem 4

Make a drawing of each unit cell: simple cubic, body-centered cubic, and face-centered cubic.

LE
Leon E.
Numerade Educator

Problem 5

For each of the cubic cells in the previous problem, give the coordination number, edge length in terms of r, and number of atoms per unit cell.

Matthew H.
Numerade Educator

Problem 6

What is the difference between hexagonal closest packing and cubic closest packing? What are the unit cells for each of these structures?

Wilson M.
The University of Alabama

Problem 7

What are the three basic types of solids and the composite units of each? What types of forces hold each type of solid together?

Matthew H.
Numerade Educator

Problem 8

What are the three categories of atomic solids?

LE
Leon E.
Numerade Educator

Problem 9

What kinds of forces hold each of the three basic categories of atomic solids together?

Matthew H.
Numerade Educator

Problem 10

What is a polymorph?

LE
Leon E.
Numerade Educator

Problem 11

In an ionic compound, how are the relative sizes of the cation and anion related to the coordination number of the crystal structure?

Matthew H.
Numerade Educator

Problem 12

Show how the cesium chloride, sodium chloride, and zinc blende unit cells each contain a cation-to-anion ratio of 1:1.

LE
Leon E.
Numerade Educator

Problem 13

Show how the fluorite structure accommodates a cation-to-anion ratio of 1:2.

Matthew H.
Numerade Educator

Problem 14

Name and describe the different allotropes of carbon.

LE
Leon E.
Numerade Educator

Problem 15

What are silicates? What is quartz?

Matthew H.
Numerade Educator

Problem 16

What is the definition of a ceramic? What are the three categories of ceramics?

LE
Leon E.
Numerade Educator

Problem 17

List the major and minor components of Portland cement. What is the difference between the hardening process of Portland cement and the hardening process of clays?

Matthew H.
Numerade Educator

Problem 18

How is concrete made from Portland cement? What advantage does concrete have for building compared to the construction methods that predated the development of concrete?

Aadit S.
Numerade Educator

Problem 19

Describe what happens on the molecular level when silica is heated and then cooled to make glass.

Matthew H.
Numerade Educator

Problem 20

Describe the difference between vitreous silica and soda-lime glass. What are some advantages and disadvantages of each of these types of glass?

Wilson M.
The University of Alabama

Problem 21

In band theory of bonding for solids, what is a band? What is the difference between the valence band and the conduction band?

Matthew H.
Numerade Educator

Problem 22

In band theory of bonding for solids, what is a band gap? Howdoes the band gap differ in metals, semiconductors, and insulators?

Wilson M.
The University of Alabama

Problem 23

Explain how doping can increase the conductivity of a semiconductor. What is the difference between an n-type semiconductor and a p-type semiconductor?

Matthew H.
Numerade Educator

Problem 24

What is the trend in the size of the band gap as you move down the column of the group 4A elements?

Wilson M.
The University of Alabama

Problem 25

What is a polymer? What is the difference between a polymer and a copolymer?

Matthew H.
Numerade Educator

Problem 26

How do an addition polymer and a condensation polymer differ from each other?

Wilson M.
The University of Alabama

Problem 27

An X-ray beam with l = 154 pm incident on the surface of a crystal produced a maximum reflection at an angle of u = 28.3 . Assuming n = 1, calculate the separation between layers of atoms in the crystal.

Matthew H.
Numerade Educator

Problem 28

An X-ray beam of unknown wavelength is diffracted from a NaCl surface. If the interplanar distance in the crystal is 286 pm and the angle of maximum reflection is found to be 7.23 , what is the wavelength of the X-ray beam? (Assume n = 1.)

Wilson M.
The University of Alabama

Problem 29

Determine the number of atoms per unit cell for each metal.
a. Polonium
b. Tungsten
c. Nickel

Matthew H.
Numerade Educator

Problem 30

Determine the coordination number for each structure.
a. Gold
b. Ruthenium
c. Chromium

LE
Leon E.
Numerade Educator

Problem 31

Calculate the packing efficiency of the body-centered cubic unit cell. Show your work.

Matthew H.
Numerade Educator

Problem 32

Calculate the packing efficiency of the face-centered cubic unit cell. Show your work.

Wilson M.
The University of Alabama

Problem 33

Platinum crystallizes with the face-centered cubic unit cell. Theradius of a platinum atom is 139 pm. Calculate the edge length of the unit cell and the density of platinum in g/cm3.

Matthew H.
Numerade Educator

Problem 34

Molybdenum crystallizes with the body-centered unit cell. Theradius of a molybdenum atom is 136 pm. Calculate the edge length of the unit cell and the density of molybdenum.

Wilson M.
The University of Alabama

Problem 35

Rhodium has a density of 12.41 g>cm3 and crystallizes with the face-centered cubic unit cell. Calculate the radius of a rhodium atom.

Matthew H.
Numerade Educator

Problem 36

Barium has a density of 3.59 g>cm3 and crystallizes with the body-centered cubic unit cell. Calculate the radius of a barium atom.

Wilson M.
The University of Alabama

Problem 37

Polonium crystallizes with a simple cubic structure. It has a density of 9.3 g/cm3, a radius of 167 pm, and a molar mass of 209 g/mol. Use these data to calculate Avogadro's number (the number of atoms in one mole).

Matthew H.
Numerade Educator

Problem 38

Palladium crystallizes with a face-centered cubic structure. It has a density of 12.0 g/cm3, a radius of 138 pm, and a molar mass of 106.42 g/mol. Use these data to calculate Avogadro's number.

Wilson M.
The University of Alabama

Problem 39

Identify each solid as molecular, ionic, or atomic.
a. Ar(s)
b. H2O(s)
c. K2O(s)
d. Fe(s)

Matthew H.
Numerade Educator

Problem 40

Identify each solid as molecular, ionic, or atomic.
a. CaCl2(s)
b. CO2(s)
c. Ni(s)
d. I2(s)

MD
Madeline D.
Numerade Educator

Problem 41

Which solid has the highest melting point? Why?
Ar(s), CCl4(s), LiCl(s), CH3OH(s)

David C.
Numerade Educator

Problem 42

Which solid has the highest melting point? Why?
C(s, diamond), Kr(s), NaCl(s), H2O(s)

Wilson M.
The University of Alabama

Problem 43

Which solid in each pair has the higher melting point and why?
a. TiO2(s) or HOOH(s)
b. CCl4(s) or SiCl4(s)
c. Kr(s) or Xe(s)
d. NaCl(s) or CaO(s)

Matthew H.
Numerade Educator

Problem 44

Which solid in each pair has the higher melting point and why?
a. Fe(s) or CCl4(s)
b. KCl(s) or HCl(s)
c. Ti(s) or Ne(s)
d. H2O(s) or H2S(s)

Aadit S.
Numerade Educator

Problem 45

An oxide of titanium crystallizes with the unit cell shown here (titanium = gray; oxygen = red). What is the formula of the oxide?

Matthew H.
Numerade Educator

Problem 46

An oxide of rhenium crystallizes with the unit cell shown here (rhenium = gray; oxygen = red). What is the formula of the oxide?

Wilson M.
The University of Alabama

Problem 47

The unit cells for cesium chloride and barium(II) chloride are shown here. Show that the ratio of cations to anions in each unit cell corresponds to the ratio of cations to anions in the formula of each compound.

Matthew H.
Numerade Educator

Problem 48

The unit cells for lithium oxide and silver iodide are shown at the top of the next column. Show that the ratio of cations to anions in each unit cell corresponds to the ratio of cations to anions in the formula of each compound.

Wilson M.
The University of Alabama

Problem 49

Identify the structure of each of the two unit cells shown in Problem 47 as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.

Matthew H.
Numerade Educator

Problem 50

Identify the structure of each of the two unit cells shown in Problem 48 as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.

Wilson M.
The University of Alabama

Problem 51

Consider the rock salt structure in Figure 12.13. What type of structure would result if all the anions were somehow removed, leaving only one type of atom?

Matthew H.
Numerade Educator

Problem 52

Consider the zinc blende structure in Figure 12.14. What type of structure would result if the remaining tetrahedral sites in the unit cell were also filled with cations?

Wilson M.
The University of Alabama

Problem 53

Classify each of the following as a component of a silicate ceramic, an oxide ceramic, or a nonoxide ceramic.
a. B4C
b. Mg2SiO4
c. MoSi2

Matthew H.
Numerade Educator

Problem 54

Classify each of the following as a component of a silicate ceramic, an oxide ceramic, or a nonoxide ceramic.
a. TiB2
b. ZrO2
c. NaAlSi3O8

Wilson M.
The University of Alabama

Problem 55

What are the name and formula of the compound commonly used in the manufacture of glass to reduce its tendency to crack or shatter under thermal shock?

Matthew H.
Numerade Educator

Problem 56

What are the name and formula of the compound commonly used in the manufacture of glass to increase the index of refraction?

Wilson M.
The University of Alabama

Problem 57

One of the key components in the manufacture of Portland cement is Ca3SiO5, a compound that is obtained by firing the reactants in a kiln at 1400-1500 C. Assign an oxidation state to each element in this compound.

Matthew H.
Numerade Educator

Problem 58

Replacement of aluminum ions in kaolinite with magnesium ions yields a compound with the formula Mg3Si2O5(OH)4. Assign an oxidation state to each element in this compound.

Wilson M.
The University of Alabama

Problem 59

Which solid would you expect to have little or no band gap?
a. Zn(s)
b. Si(s)
c. As(s)

Matthew H.
Numerade Educator

Problem 60

Which solid would you expect to have the largest band gap?
a. As(s)
b. Sb(s)
c. Bi(s)

Wilson M.
The University of Alabama

Problem 61

How many molecular orbitals are present in the conduction band of a lithium crystal with a mass of 11.2 g?

Matthew H.
Numerade Educator

Problem 62

How many molecular orbitals are present in the valence band of a sodium crystal with a mass of 5.45 g?

Wilson M.
The University of Alabama

Problem 63

A substance has a band gap of 6.9 eV at 273 K. Is this substance best classified as an insulator, a semiconductor, or a metal?

Matthew H.
Numerade Educator

Problem 64

A substance has a band gap of 0.85 eV at 273 K. Is this substance best classified as an insulator, a semiconductor, or a metal?

Wilson M.
The University of Alabama

Problem 65

Indicate if each solid forms an n-type or a p-type semiconductor.
a. germanium doped with gallium
b. silicon doped with arsenic

Matthew H.
Numerade Educator

Problem 66

Indicate if each solid forms an n-type or a p-type semiconductor.
a. silicon doped with gallium
b. germanium doped with antimony

Wilson M.
The University of Alabama

Problem 67

Does a photon of red light with a frequency of 4.29 * 1014 Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?

Matthew H.
Numerade Educator

Problem 68

Which wavelength of light (in nm) is emitted if an electron moves from the conduction band to the valence band in a sample of diamond (diamond has a band gap of 5.5 eV)?

Wilson M.
The University of Alabama

Problem 69

Teflon is an addition polymer formed from the monomer shown here. Draw the structure of the polymer.

Matthew H.
Numerade Educator

Problem 70

Saran, the polymer used to make saran wrap, is an addition polymer formed from two monomers-vinylidene chloride and vinyl chloride. Draw the structure of the polymer. (Hint: The monomers alternate.)

Wilson M.
The University of Alabama

Problem 71

One kind of polyester is a condensation copolymer formed from terephthalic acid and ethylene glycol. Draw the structure of the dimer. [Hint: Water (circled) is eliminated when the bond between the monomers forms.]

Matthew H.
Numerade Educator

Problem 72

Nomex, a condensation copolymer used by firefighters because of its flame-resistant properties, forms from isophthalic acid and m-aminoaniline. Draw the structure of the dimer. (Hint:Water is eliminated when the bond between the monomers forms.)

Wilson M.
The University of Alabama

Problem 73

Polyacetylene is an addition polymer with the structure shown here. Draw the structure of the monomer.

Matthew H.
Numerade Educator

Problem 74

Polyacrylonitrile (PAN) is an addition polymer with the structure shown here. Draw the structure of the monomer.

Wilson M.
The University of Alabama

Problem 75

The polycarbonate Lexan is a condensation polymer and has the structure shown here:

Assuming this polymer was formed from the monomer shown here plus another monomer, provide a structure of the other monomer that would be required to form Lexan.

Matthew H.
Numerade Educator

Problem 76

Consider the following condensation polymer with the structure shown here:

Assuming this polymer was formed from the monomer shown here plus another monomer, provide a structure of the other monomer that would be required to form this polymer.

Wilson M.
The University of Alabama

Problem 77

Silver iodide crystallizes in the zinc blende structure. The separation between nearest-neighbor cations and anions is approximately 325 pm, and the melting point is 558 C. Cesium chloride, by contrast, crystallizes in the structure shown in Figure 12.12. Even though the separation between nearestneighbor cations and anions is greater (348 pm), the melting point of cesium chloride is higher (645 C). Explain.

Matthew H.
Numerade Educator

Problem 78

Copper iodide crystallizes in the zinc blende structure. The separation between nearest-neighbor cations and anions is approximately 311 pm, and the melting point is 606 C. Potassium chloride, by contrast, crystallizes in the rock salt structure. Even though the separation between nearest-neighbor cations and anions is greater (319 pm), the melting point of potassium chloride is higher (776 C). Explain.

Aadit S.
Numerade Educator

Problem 79

Consider the face-centered cubic structure shown here:
a. What is the length of the line (labeled c) that runs diagonally across one of the faces of the cube in terms of r (the atomic radius)?
b. Use the answer to part a and the Pythagorean theorem to derive the expression for the edge length (l) in terms of r.

Matthew H.
Numerade Educator

Problem 80

Consider the body-centered cubic structure shown here:
a. What is the length of the line (labeled c) that runs from one corner of the cube diagonally through the center of the cube to the other corner in terms of r (the atomic radius)?
b. Use the Pythagorean theorem to derive an expression for the length of the line (labeled b) that runs diagonally across one of the faces of the cube in terms of the edge length (l).
c. Use the answer to parts a and b along with the Pythagorean theorem to derive the expression for the edge length (l) in terms of r.

Wilson M.
The University of Alabama

Problem 81

The volume of a unit cell of diamond is 0.0454 nm3, and the density of diamond is 3.52 g/cm3. Find the number of carbon atoms in a unit cell of diamond.

Matthew H.
Numerade Educator

Problem 82

The density of an unknown metal is 12.3 g>cm3, and its atomic radius is 0.134 nm. It has a face-centered cubic lattice. Find the atomic mass of this metal.

Wilson M.
The University of Alabama

Problem 83

An unknown metal is found to have a density of 7.8748 g/cm3 and to crystallize in a body-centered cubic lattice. The edge of the unit cell is 0.28664 nm. Calculate the atomic mass of the metal.

Matthew H.
Numerade Educator

Problem 84

When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68.0% of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube, in terms of r.

Wilson M.
The University of Alabama

Problem 85

Potassium chloride crystallizes in the rock salt structure. Estimate the density of potassium chloride using the ionic radii provided in Chapter 3.

Matthew H.
Numerade Educator

Problem 86

Calculate the fraction of empty space in cubic closest packing to five significant figures.

Wilson M.
The University of Alabama

Problem 87

A tetrahedral site in a closest-packed lattice is formed by four spheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a closest-packed arrangement, the spheres are in contact, and if the spheres have a radius r, the diagonal of the face of the cube is 2r. The tetrahedral hole is inside the middle of the cube. Find first the length of the body diagonal of this cube and then the radius of the tetrahedral hole.

Matthew H.
Numerade Educator

Problem 88

X-ray diffractometers often use metals that have had their core electrons excited as a source of X-rays. Consider the 2p 1s transition for copper, which is called the Ka transition. Calculate the wavelength of X-rays (in A) given off by the Ka transition if the energy given off by a mole of copper atoms is 7.77 X 105 kJ.

Wilson M.
The University of Alabama

Problem 89

Why is it necessary to use the Ka transition (2p 1s) in copper (see Problem 88) to generate X-rays? Why not use, for example, the 4s 3p transition?

Matthew H.
Numerade Educator

Problem 90

In certain cases where X-ray diffraction is unsuitable for determining the structure of a crystal, neutron diffraction can be used. Instead of X-rays, a beam of neutrons is used to analyze the sample. Calculate the velocity of a beam of neutrons with a wavelength of 2.00 A.

Wilson M.
The University of Alabama

Problem 91

The structure of the addition polymer polypropylene is shown in Table 12.2.
a. Draw the structure of the monomer.
b. Show how an alternate version of the polypropylene polymer (with a different arrangement) could be formed from the monomer you found in part a.

Matthew H.
Numerade Educator

Problem 92

Perovskite is a compound with a cubic unit cell and has a strontium atom at the center of the cell, titanium atoms at the corners of the unit cell, and oxygen atoms at the centers of each edge of the unit cell.
a. What is the formula of perovskite?
b. What is the coordination number of strontium in the perovskite structure?
c. If the edge length of the unit cell is 3.905 A, calculate the density of perovskite in g/cm3.

Wilson M.
The University of Alabama

Problem 93

A compound with the formula Rb3C60 has been shown to demonstrate superconductivity below 30.0 K. Given that the C60 molecules have a face-centered cubic arrangement, which of the tetrahedral and octahedral sites are occupied by Rb atoms?

Matthew H.
Numerade Educator

Problem 94

Despite Dalton's laws, it is now known that many ionic compounds do not always contain atoms in small integer ratios. For example, a sample of iron(II) oxide may, in fact, contain a significant amount of Fe3+ in addition to Fe2+. This is an example of a nonstoichiometric compound. A sample of iron(II) oxide is
found to be 75.65% iron by mass. Determine the percentage of Fe3+ ions in the sample.

Jennifer H.
Numerade Educator

Problem 95

During the glass manufacturing process, the liquid must be cooled relatively quickly to form the glass. Why?

Matthew H.
Numerade Educator

Problem 96

Why are X-rays used for crystallography? Why not use some other, more accessible type of electromagnetic radiation such as ultraviolet light?

Wilson M.
The University of Alabama

Problem 97

Compare the crystal structure of diamond (C) and zinc blende (ZnS). What are the key similarities and differences between the two structures?

Matthew H.
Numerade Educator

Problem 98

In X-ray crystallography, a small amount of oil is often used to mount the crystal sample on a glass fiber. Explain why neither the oil nor the glass fiber interferes with the diffraction pattern of the crystal.

Wilson M.
The University of Alabama

Problem 99

Which is not likely to lead to an increase in electrical conductivity?
a. increasing the temperature of a semiconductor
b. choosing a semiconductor with a smaller band gap
c. doping the semiconductor
d. All of the above would likely lead to an increase in electrical conductivity.

Matthew H.
Numerade Educator

Problem 100

Have each group member select one of the cubic crystalline lattices. Learn everything you can about your lattice, and present it to the group.

Wilson M.
The University of Alabama

Problem 101

Using group members to play the role of atoms or molecules, demonstrate the main structural features of the following categories of crystalline solids: molecular solid, ionic solid, nonbonded solid, metallic solid, and network covalent solid. Clearly identify what each individual represents and how you are representing various interactions between particles (e.g., covalent bond, ionic bond, etc.).

Matthew H.
Numerade Educator

Problem 102

List the questions you would need to ask in order to classify a solid into one of the categories of crystalline solids (molecular solid, ionic solid, nonbonded solid, metallic solid, and network covalent solid). In what sequence is it best to ask them? (Hint: You may need a branching decision tree.) Once you have agreed on a good set of questions, have each group member choose a substance from the chapter, and have the other group members ask the questions from the list in turn until the correct classification is reached. Group members may agree to edit the list if they discover ways to improve it while using it.

Jennifer H.
Numerade Educator

Problem 103

Have each group member select and study a material from Section 12.7 on ceramics, cement, and glass. Take turns describing your material to the group, and see if group members can identify the type of material based on your description (without consulting the text).

Matthew H.
Numerade Educator

Problem 104

Describe how a common object or toy (e.g., a train, building blocks, or beads on a string) could represent the structure of a polymer. Describe how you can represent the following terms using your model: monomer, dimer, addition polymer, condensation polymer, branching.

Jennifer H.
Numerade Educator

Problem 105

An alloy is a metallic mixture composed of two or more elements. As is the case in all mixtures, the relative amounts of the elements in an alloy can vary. In some cases, the components of an alloy can have different crystal structures. For example, a nickel-chromium alloy consists of nickel, which has a face-centered cubic structure, and chromium, which has a body-centered cubic structure. Which structure does the alloy adopt? It depends on the relative compositions. The phase diagrams for alloys such as these reveal the structure as a function of the alloy composition. For example, the nickel and chromium phase diagram from 700 degree C to 1900 degree C is shown here:

Notice that the diagram has two different solid phases: face-centered cubic and body-centered cubic. From pure nickel (0 mol % chromium) to about 40-50 mol % chromium, the structure is face-centered cubic. In this structure, Cr atoms substitute for Ni atoms in the face-centered cubic structure of nickel. However, when an amount of chromium beyond a certain percentage (which depends on temperature) is added, that structure is no longer stable. At the other end of the diagram, from pure chromium to about 75% chromium (depending on temperature), the structure is body-centered cubic, with nickel substituting into the body-centered cubic structure of the chromium. The region in between the two phases is called the two-phase region. At these compositions, the two phases (nickel-rich face-centered cubic and chromium-rich body-centered cubic) exist together (the solution is not homogeneous in this region). Use the phase diagram to answer the following questions.
a. What is the relative composition of the mixture at point A? At what temperature does a solid mixture having this composition melt?
b. Is it possible to have a homogeneous solid mixture that is 50% Ni and 50% Cr? If so, what crystalline structure would it have?
c. What is the relative composition at point B? What is the crystalline structure at point B?
d. At what temperature does the solid present at point B begin to melt?

Matthew H.
Numerade Educator