Solution: Ionic and Molecular Solids (Sections)The

(a) What kind of packing arrangement is seen in the accompanying photo?

(b) What is the coordination number of each cannonball in the interior of the stack?

(c) What are the coordination numbers for the numbered cannonballs on the visible side of the stack? [Section 12.3]

Which arrangement of cations (yellow) and anions (blue) in a lattice is the more stable? Explain your reasoning. [Section 12.5] (a) (b)

Which of these molecular fragments would you expect to be more likely to give rise to electrical conductivity? Explain your reasoning. [Sections 12.6, 12.8] (a) (b)

The electronic structure of a doped semiconductor is shown here. (a) Which band, A or B, is the valence band? (b) Which band is the conduction band? (c) Which band consists of bonding molecular orbitals? (d) Is this an example of an ntype or p-type semiconductor? (e) If the semiconductor is germanium, which of the following elements could be the dopant: Ga, Si, or P? [Section 12.7] Energy Band B Band A Empty MOs Filled MOs

Shown here are cartoons of two different polymers. Which of these polymers would you expect to be more crystalline? Which one would have the higher melting point? [Section 12.8] (a) (b)

The accompanying image shows photoluminescence from four different samples of CdTe nanocrystals, each embedded in a polymer matrix. The photoluminescence occurs because the samples are being irradiated by a UV light source. The nanocrystals in each vial have different average sizes. The sizes are 4.0, 3.5, 3.2, and 2.8 nm. (a) Which vial contains the 4.0-nm nanocrystals? (b) Which vial contains the 2.8-nm nanocrystals? (c) Crystals of CdTe that have sizes that are larger than approximately 100 nm have a band gap of 1.5 eV. What would be the wavelength and frequency of light emitted from these crystals? What type of light is this? [Sections 12.7 and 12.9]

Covalent bonding occurs in both molecular and covalentnetwork solids. Which of the following statements best explains why these two kinds of solids differ so greatly in their hardness and melting points? (a) The molecules in molecular solids have stronger covalent bonding than covalent-network solids do. (b) The molecules in molecular solids are held together by weak intermolecular interactions. (c) The atoms in covalent-network solids are more polarizable than those in molecular solids. (d) Molecular solids are denser than covalent-network solids.

Silicon is the fundamental component of integrated circuits. Si has the same structure as diamond. (a) Is Si a molecular, metallic, ionic, or covalent-network solid? (b) Silicon readily reacts to form silicon dioxide, SiO2, which is quite hard and is insoluble in water. Is SiO2 most likely a molecular, metallic, ionic, or covalent-network solid?

What kinds of attractive forces exist between particles (atoms, molecules, or ions) in (a) molecular crystals, (b) covalentnetwork crystals, (c) ionic crystals, (d) and metallic crystals?

Which type (or types) of crystalline solid is characterized by each of the following? (a) High mobility of electrons throughout the solid; (b) softness, relatively low melting point; (c) high melting point and poor electrical conductivity; (d) network of covalent bonds.

Indicate the type of solid (molecular, metallic, ionic, or covalent-network) for each compound: (a) CaCO3, (b) Pt, (c) ZrO2 (melting point, 2677 C), (d) table sugar 1C12H22O112, (e) benzene 1C6H62, (f) I2.

Indicate the type of solid (molecular, metallic, ionic, or covalent-network) for each compound: (a) InAs, (b) MgO, (c) HgS, (d) In, (e) HBr

A white substance melts with some decomposition at 730 C. As a solid, it does not conduct electricity, but it dissolves in water to form a conducting solution. Which type of solid (molecular, metallic, covalent-network, or ionic) might the substance be?

You are given a white substance that sublimes at 3000 C; the solid is a nonconductor of electricity and is insoluble in water. Which type of solid (molecular, metallic, covalent-network, or ionic) might this substance be?

(a) Draw a picture that represents a crystalline solid at the atomic level.

(b) Now draw a picture that represents an amorphous solid at the atomic level.

Amorphous silica, SiO2, has a density of about 2.2 g>cm3 , whereas the density of crystalline quartz, another form of SiO2, is 2.65 g>cm3 . Which of the following statements is the best explanation for the difference in density? (a) Amorphous silica is a network-covalent solid, but quartz is metallic. (b) Amorphous silica crystallizes in a primitive cubic lattice. (c) Quartz is harder than amorphous silica. (d) Quartz must have a larger unit cell than amorphous silica. (e) The atoms in amorphous silica do not pack as efficiently in three dimensions as compared to the atoms in quartz.

Two patterns of packing for two different spheres are shown here. For each structure (a) draw the two- dimensional unit cell; (b) determine the angle between the lattice vectors, g, and determine whether the lattice vectors are of the same length or of different lengths; and (c) determine the type of two- dimensional lattice (from Figure 12.4). A B A B (i) (ii)

Two patterns of packing two different spheres are shown here. For each structure (a) draw the two- dimensional unit cell; (b) determine the angle between the lattice vectors, g, and determine whether the lattice vectors are of the same length or of different lengths; (c) determine the type of twodimensional lattice (from Figure 12.4). (i) (ii)

Imagine the primitive cubic lattice. Now imagine grabbing the top of it and stretching it straight up. All angles remain 90. What kind of primitive lattice have you made?

Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. All angles remain 90. What kind of primitive lattice have you made

Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is 90? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

Besides the cubic unit cell, which other unit cell(s) has edge lengths that are all equal to each other? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5.

What is the minimum number of atoms that could be contained in the unit cell of an element with a face-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5

The unit cell of nickel arsenide is shown here. (a) What type of lattice does this crystal possess? (b) What is the empirical formula? Ni As 120 3.57 side view top view 5.10 3.57

The unit cell of a compound containing strontium, iron, and oxygen is shown here. (a) What type of lattice does this crystal possess (all three lattice vectors are mutually perpendicular)? (b) What is the empirical formula? O Sr Fe 3.47 3.98 3.98

The densities of the elements K, Ca, Sc, and Ti are 0.86, 1.5, 3.2, and 4.5 g>cm3 , respectively. One of these elements crystallizes in a body-centered cubic structure; the other three crystallize in a face- centered cubic structure. Which one crystallizes in the body-centered cubic structure? Justify your answer.

For each of these solids, state whether you would expect it to possess metallic properties: (a) TiCl4, (b) NiCo alloy, (c) W, (d) Ge, (e) ScN.

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms? (b) Which structure(s) corresponds to the least dense packing of atoms? Structure type A Structure type B Structure type C

Sodium metal (atomic weight 22.99 g>mol) adopts a bodycentered cubic structure with a density of 0.97 g>cm3 . (a) Use this information and Avogadros number 1NA = 6.022 * 1023 /mol2 to estimate the atomic radius of sodium. (b) If sodium didnt react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close-packed metal. Would it still float on water?

Iridium crystallizes in a face-centered cubic unit cell that has an edge length of 3.833 . (a) Calculate the atomic radius of an iridium atom. (b) Calculate the density of iridium metal.

Calcium crystallizes in a body-centered cubic structure. (a) How many Ca atoms are contained in each unit cell? (b) How many nearest neighbors does each Ca atom possess? (c) Estimate the length of the unit cell edge, a, from the atomic radius of calcium (1.97 ). (d) Estimate the density of Ca metal.

Aluminum metal crystallizes in a face-centered cubic unit cell. (a) How many aluminum atoms are in a unit cell? (b) What is the coordination number of each aluminum atom? (c) Estimate the length of the unit cell edge, a, from the atomic radius of aluminum (1.43 ). (d) Calculate the density of aluminum metal

An element crystallizes in a body-centered cubic lattice. The edge of the unit cell is 2.86 , and the density of the crystal is 7.92 g>cm3 . Calculate the atomic weight of the element.

Which of these statements about alloys and intermetallic compounds is false? (a) Bronze is an example of an alloy. (b) Alloy is just another word for a chemical compound of fixed composition that is made of two or more metals. (c) Intermetallics are compounds of two or more metals that have a definite composition and are not considered alloys. (d) If you mix two metals together and, at the atomic level, they separate into two or more different compositional phases, you have created a heterogeneous alloy. (e) Alloys can be formed even if the atoms that comprise them are rather different in size

Determine if each statement is true or false: (a) Substitutional alloys are solid solutions, but interstitial alloys are heterogenous alloys. (b) Substitutional alloys have solute atoms that replace solvent atoms in a lattice, but interstitial alloys have solute atoms that are in between the solvent atoms in a lattice. (c) The atomic radii of the atoms in a substitutional alloy are similar to each other, but in an interstitial alloy, the interstitial atoms are a lot smaller than the host lattice atoms.

For each of the following alloy compositions, indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound: (a) Fe0.97Si0.03, (b) Fe0.60Ni0.40, (c) SmCo5.

For each of the following alloy compositions, indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound: (a) Cu0.66Zn0.34, (b) Ag3Sn, (c) Ti0.99O0.01.

Indicate whether each statement is true or false: (a) Substitutional alloys tend to be more ductile than interstitial alloys. (b) Interstitial alloys tend to form between elements with similar ionic radii. (c) Nonmetallic elements are never found in alloys.

Indicate whether each statement is true or false: (a) Intermetallic compounds have a fixed composition. (b) Copper is the majority component in both brass and bronze. (c) In stainless steel, the chromium atoms occupy interstitial positions.

Which element or elements are alloyed with gold to make the following types of colored gold used in the jewelry industry? For each type, also indicate what type of alloy is formed: (a) white gold, (b) rose gold, (c) green gold.

Look up the chemical composition of purple gold. Is the composition variable? Why dont jewelers use purple gold to make rings or necklaces?

State whether each sentence is true or false: (a) Metals have high electrical conductivities because the electrons in the metal are delocalized. (b) Metals have high electrical conductivities because they are denser than other solids. (c) Metals have large thermal conductivities because they expand when heated. (d) Metals have small thermal conductivities because the delocalized electrons cannot easily transfer the kinetic energy imparted to the metal from heat.

Imagine that you have a metal bar sitting half in the Sun and half in the dark. On a sunny day, the part of the metal that has been sitting in the Sun feels hot. If you touch the part of the metal bar that has been sitting in the dark, will it feel hot or cold? Justify your answer in terms of thermal conductivity

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (a) How many molecular orbitals are there in the diagram? (b) How many nodes are in the lowestenergy molecular orbital? (c) How many nodes are in the highest-energy molecular orbital? (d) How many nodes are in the highest-energy occupied molecular orbital (HOMO)? (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)? (f) How does the HOMOLUMO energy gap for this case compare to that of the four-atom case?

Repeat Exercise 12.47 for a linear chain of eight lithium atoms.

Which would you expect to be the more ductile element, (a) Ag or Mo, (b) Zn or Si? In each case explain your reasoning.

Which of the following statements does not follow from the fact that the alkali metals have relatively weak metalmetal bonding? (a) The alkali metals are less dense than other metals. (b) The alkali metals are soft enough to be cut with a knife. (c) The alkali metals are more reactive than other metals. (d) The alkali metals have higher melting points than other metals. (e) The alkali metals have low ionization energies.

Explain this trend in melting points: Y 1522 C, Zr 1852 C, Nb 2468 C, Mo 2617 C.

For each of the following groups, which metal would you expect to have the highest melting point: (a) gold, rhenium, or cesium; (b) rubidium, molybdenum, or indium; (c) ruthenium, strontium, or cadmium?

Tausonite, a mineral composed of \(\mathrm{Sr}, \mathrm{O}\), and \(\mathrm{Ti}\), has the cubic unit cell shown in the drawing. (a) What is the empirical formula of this mineral? (b) It is easy to see that \(\mathrm{Ti}\) is coordinated by six oxygen atoms because the \(\mathrm{Ti}\) atom is located at the center of the unit cell. To see the full coordination environment of the other ions, we have to consider neighboring unit cells. How many oxygens are coordinated to strontium? Equation Transcription: Text Transcription: Sr, O Ti

Rutile is a mineral composed of Ti and O. Its unit cell, shown in the drawing, contains Ti atoms at each corner and a Ti atom at the center of the cell. Four O atoms are on the opposite faces of the cell, and two are entirely within the cell. (a) What is the chemical formula of this mineral? (b) What is the coordination number of each atom? Oxygen Titanium

NaF has the same structure as NaCl. (a) Use ionic radii from Chapter 7 to estimate the length of the unit cell edge for NaF. (b) Use the unit cell size calculated in part (a) to estimate the density of NaF.

Clausthalite is a mineral composed of lead selenide (PbSe). The mineral adopts the rock salt structure. The density of PbSe at 25 C is 8.27 g>cm3 . Calculate the length of an edge of the PbSe unit cell

A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 . (a) Calculate the density of HgS in this form. (b) The mineral tiemmanite (HgSe) also forms a solid phase with the zinc blende structure. The length of the unit cell edge in this mineral is 6.085 . What accounts for the larger unit cell length in tiemmanite? (c) Which of the two substances has the higher density? How do you account for the difference in densities?

At room temperature and pressure RbI crystallizes with the NaCl-type structure. (a) Use ionic radii to predict the length of the cubic unit cell edge. (b) Use this value to estimate the density. (c) At high pressure the structure transforms to one with a CsCl-type structure. (c) Use ionic radii to predict the length of the cubic unit cell edge for the highpressure form of RbI. (d) Use this value to estimate the density. How does this density compare with the density you calculated in part (b)?

CuI, CsI, and NaI each adopt a different type of structure. The three different structures are those shown in Figure 12.26. (a) Use ionic radii, Cs + 1r = 1.81 A 2, Na + 1r = 1.16 A 2, Cu+ 1r = 0.74 A 2, and, I - 1r = 2.06 A 2, to predict which compound will crystallize with which structure. (b) What is the coordination number of iodide in each of these structures?

The rutile and fluorite structures, shown here (anions are colored green), are two of the most common structure types of ionic compounds where the cation to anion ratio is 1:2. (a) For CaF2 and ZnF2 use ionic radii, Ca 2+ 1r = 1.14 A 2, Zn2+ 1r = 0.88 A 2, and F- 1r = 1.19 A 2, to predict which compound is more likely to crystallize with the fluorite structure and which with the rutile structure. (b) What are the coordination numbers of the cations and anions in each of these structures? Rutile Fluorite

The coordination number for Mg2 + ion is usually six. Assuming this assumption holds, determine the anion coordination number in the following compounds: (a) MgS, (b) MgF2, (c) MgO.

The coordination number for the Al 3+ ion is typically between four and six. Use the anion coordination number to determine the Al 3 + coordination number in the following compounds: (a) AlF3 where the fluoride ions are two coordinate, (b) Al2O3 where the oxygen ions are six coordinate, (c) AlN where the nitride ions are four coordinate.

Classify each of the following statements as true or false: (a) Although both molecular solids and covalent-network solids have covalent bonds, the melting points of molecular solids are much lower because their covalent bonds are much weaker. (b) Other factors being equal, highly symmetric molecules tend to form solids with higher melting points than asymmetrically shaped molecules

Classify each of the following statements as true or false: (a) For molecular solids, the melting point generally increases as the strengths of the covalent bonds increase. (b) For molecular solids, the melting point generally increases as the strengths of the intermolecular forces increase.

Both covalent-network solids and ionic solids can have melting points well in excess of room temperature, and both can be poor conductors of electricity in their pure form. However, in other ways their properties are quite different. (a) Which type of solid is more likely to dissolve in water? (b) Which type of solid can become an electrical conductor via chemical substitution?

Which of the following properties are typical characteristics of a covalent-network solid, a metallic solid, or both: (a) ductility, (b) hardness, (c) high melting point

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) CdS or CdTe, (b) GaN or InP, (c) GaAs or InAs?

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) InP or InAs, (b) Ge or AlP, (c) AgI or CdTe?

If you want to dope GaAs to make an n-type semiconductor with an element to replace Ga, which element(s) would you pick?

If you want to dope GaAs to make a p-type semiconductor with an element to replace As, which element(s) would you pick?

Silicon has a band gap of 1.1 eV at room temperature. (a) What wavelength of light would a photon of this energy correspond to? (b) Draw a vertical line at this wavelength in the figure shown, which shows the light output of the Sun as a function of wavelength. Does silicon absorb all, none, or a portion of the visible light that comes from the Sun? (c) You can estimate the portion of the overall solar spectrum that silicon absorbs by considering the area under the curve. If you call the area under the entire curve 100%, what approximate percentage of the area under the curve is absorbed by silicon? x 200 600 1000 Wavelength (nm) 1400 1800 2200 2600 3000 Visible Infrared Ultraviolet Solar spectrum at sea level Solar spectrum outside atmospher

Cadmium telluride is an important material for solar cells. (a) What is the band gap of CdTe? (b) What wavelength of light would a photon of this energy correspond to? (c) Draw a vertical line at this wavelength in the figure shown in Exercise 12.71, which shows the light output of the sun as a function of wavelength. (d) With respect to silicon, does CdTe absorb a larger or smaller portion of the solar spectrum?

The semiconductor GaP has a band gap of 2.26 eV. What wavelength of light would be emitted from an LED made from GaP? What color is this?

The first LEDs were made from GaAs, which has a band gap of 1.43 eV. What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: ultraviolet, visible, or infrared?

GaAs and GaP make solid solutions that have the same crystal structure as the parent materials, with As and P randomly distributed throughout the crystal. GaPxAs1 - x exists for any value of x. If we assume that the band gap varies linearly with composition between x = 0 and x = 1, estimate the band gap for GaP0.5As0.5. (See the previous two exercises for GaAs and GaP band gaps.) What wavelength of light does this correspond to?

Red light-emitting diodes are made from GaAs and GaP solid solutions, GaPxAs1 - x (see Exercise 12.75). The original red LEDs emitted light with a wavelength of 660 nm. If we assume that the band gap varies linearly with composition between x = 0 and x = 1, estimate the composition (the value of x) that is used in these LEDs.

(a) What is a monomer?

(b) Which of these molecules can be used as a monomer: benzene, ethene (also called ethylene), methane?

The molecular formula of n-decane is CH31CH228CH3. Decane is not considered a polymer, whereas polyethylene is. What is the distinction?

State whether each of these numbers is a reasonable value for a polymers molecular weight: 100 amu, 10,000 amu, 100,000 amu, 1,000,000 amu?

Indicate whether the following statement is true or false: For an addition polymerization, there are no by-products of the reaction (assuming 100% yield).

An ester is a compound formed by a condensation reaction between a carboxylic acid and an alcohol that eliminates a water molecule. Read the discussion of esters in Section 24.4 and then give an example of a reaction forming an ester. How might this kind of reaction be extended to form a polymer (a polyester)?

Write a balanced chemical equation for the formation of a polymer via a condensation reaction from the monomers succinic acid 1HOOCCH2CH2COOH2 and ethylenediamine 1H2NCH2CH2NH22.

Draw the structure of the monomer(s) that are used to make each of the polymers shown in Table 12.5: (a) polyvinyl chloride, (b) nylon 6,6, (c) polyethylene terephthalate.

Write the chemical equation that represents the formation of (a) polychloroprene from chloroprene (polychloroprene is used in highway-pavement seals, expansion joints, conveyor belts, and wire and cable jackets) CH2 CH CH2 Cl C Chloroprene (b) polyacrylonitrile from acrylonitrile (polyacrylonitrile is used in home furnishings, craft yarns, clothing, and many other items). CH2 CH CN Acrylonitrile

The nylon Nomex, a condensation polymer, has the following structure: C O NH NH n C O Draw the structures of the two monomers that yield Nomex.

Proteins are naturally occurring polymers formed by condensation reactions of amino acids, which have the general structure H N C H R O C O H H In this structure, R represents H, CH3, or another group of atoms; there are 20 different natural amino acids, and each has one of 20 different R groups. (a) Draw the general structure of a protein formed by condensation polymerization of the generic amino acid shown here. (b) When only a few amino acids react to make a chain, the product is called a peptide rather than a protein; only when there are 50 amino acids or more in the chain would the molecule be called a protein. For three amino acids (distinguished by having three different R groups, R1, R2, and R3), draw the peptide that results from their condensation reactions. (c) The order in which the R groups exist in a peptide or protein has a huge influence on its biological activity. To distinguish different peptides and proteins, chemists call the first amino acid the one at the N terminus and the last one the one at the C terminus. From your drawing in part (b) you should be able to figure out what N terminus and C terminus mean. How many different peptides can be made from your three different amino acids?

(a) What molecular features make a polymer flexible?

(b) If you cross-link a polymer, is it more flexible or less flexible than it was before?

What molecular structural features cause high-density polyethylene to be denser than low-density polyethylene?

If you want to make a polymer for plastic wrap, should you strive to make a polymer that has a high or low degree of crystallinity?

Indicate whether each statement is true or false: (a) Elastomers are rubbery solids. (b) Thermosets cannot be reshaped. (c) Thermoplastic polymers can be recycled.

Explain why bands may not be the most accurate description of bonding in a solid when the solid has nanoscale dimensions

CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (a) What color is the emitted light? (b) Would appropriately sized CdS quantum dots be able to emit blue light? (c) What about red light?

Indicate whether each statement is true or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the 110-nm range. (b) The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.

Indicate whether this statement is true or false: If you want a semiconductor that emits blue light, you could either use a material that has a band gap corresponding to the energy of a blue photon or you could use a material that has a smaller band gap but make an appropriately sized nanoparticle of the same material

Gold adopts a face-centered cubic structure with a unit cell edge of 4.08 (Figure 12.11). How many gold atoms are there in a sphere that is 20 nm in diameter? Recall that the volume of a sphere is 4 3pr 3 .

Cadmium telluride, CdTe, adopts the zinc blende structure with a unit cell edge length of 6.49 . There are four cadmium atoms and four tellurium atoms per unit cell. How many of each type of atom are there in a cubic crystal with an edge length of 5.00 nm?

Which statement correctly describes a difference between graphene and graphite? (a) Graphene is a molecule but graphite is not. (b) Graphene is a single sheet of carbon atoms and graphite contains many, and larger, sheets of carbon atoms. (c) Graphene is an insulator but graphite is a metal. (d) Graphite is pure carbon but graphene is not. (e) The carbons are sp2 hybridized in graphene but sp3 hybridized in graphite

What evidence supports the notion that buckyballs are actual molecules and not extended materials? (a) Buckyballs are made of carbon. (b) Buckyballs have a well-defined atomic structure and molecular weight. (c) Buckyballs have a well-defined melting point. (d) Buckyballs are semiconductors. (e) More than one of the previous choices.

A face-centered tetragonal lattice is not one of the 14 threedimensional lattices. Show that a face- centered tetragonal unit cell can be redefined as a body-centered tetragonal lattice with a smaller unit cell.

Pure iron crystallizes in a body-centered cubic structure, but small amounts of impurities can stabilize a face-centered cubic structure. Which form of iron has a higher density?

Introduction of carbon into a metallic lattice generally results in a harder, less ductile substance with lower electrical and thermal conductivities. Explain why this might be so.

Ni3Al is used in the turbines of aircraft engines because of its strength and low density. Nickel metal has a cubic closepacked structure with a face-centered cubic unit cell, while Ni3Al has the ordered cubic structure shown in Figure 12.17. The length of the cubic unit cell edge is 3.53 for nickel and 3.56 for Ni3Al. Use these data to calculate and compare the densities of these two materials.

For each of the intermetallic compounds shown in Figure 12.17 determine the number of each type of atom in the unit cell. Do your answers correspond to the ratios expected from the empirical formulas: Ni3Al, Nb3Sn, and SmCo5?

What type of latticeprimitive cubic, body-centered cubic, or face-centered cubicdoes each of the following structure types possess: (a) CsCl, (b) Au, (c) NaCl, (d) Po, (e) ZnS?

Tin exists in two allotropic forms: Gray tin has the diamond structure, and white tin has a close- packed structure. One of these allotropic forms is a semiconductor with a small band gap, while the other is a metal. (a) Which one is which? (b) Which form would you expect to have the longer SnSn bond distance?

The electrical conductivity of aluminum is approximately 109 times greater than that of its neighbor in the periodic table, silicon. Aluminum has a face-centered cubic structure, and silicon has the diamond structure. A classmate of yours tells you that density is the reason aluminum is a metal but silicon is not; therefore, if you were to put silicon under high pressure, it too would act like a metal. Discuss this idea with your classmates, looking up data about Al and Si as needed

Silicon carbide, SiC, has the three-dimensional structure shown in the figure. (a) Name another compound that has the same structure. (b) Would you expect the bonding in SiC to be predominantly ionic, metallic, or covalent? (c) How do the bonding and structure of SiC lead to its high thermal stability (to 2700 C) and exceptional hardness?

Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.

Rhenium oxide crystallizes with a structure that has a primitive cubic lattice, as shown here. In the image on the left, the sizes of the ions have been reduced to show the entire unit cell. (a) How many atoms of each type are there per unit cell? (b) Use the ionic radii of rhenium (0.70 ) and oxygen (1.26 ) to estimate the length of the edge of the unit cell. (c) Use your answers to parts (a) and (b) to estimate the density of this compound. Re O

Teflon is a polymer formed by the polymerization of F2CCF2. (a) Draw the structure of a section of this polymer. (b) What type of polymerization reaction is required to form Teflon?

Hydrogen bonding between polyamide chains plays an important role in determining the properties of a nylon such as nylon 6,6 (Table 12.5). Draw the structural formulas for two adjacent chains of nylon 6,6 and show where hydrogenbonding interactions could occur between them.

Explain why X rays can be used to measure atomic distances in crystals but visible light cannot be used for this purpose.

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 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).

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 the previous problem but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle u?

(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?

(b) X-ray diffraction studies of buckminsterfullerene show that it has a face-centered cubic lattice of C60 molecules. The length of an edge of the unit cell is 14.2 . Calculate the density of buckminsterfullerene.

When you shine light of band gap energy or higher on a semiconductor and promote electrons from the valence band to the conduction band, do you expect the conductivity of the semiconductor to (a) remain unchanged, (b) increase, or (c) decrease?

The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is 50 mol% silver and 50 mol% gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy. (b) If an alloy is formed that is 50 mol% copper and 50 mol% gold, what is the karat number of the alloy? What is the color of this alloy?

Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g>cm3 . The unit cell is cubic with an edge length of 8.09 . How many atoms of each type are in the unit cell?

(a) What are the CCC 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?

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).

Although polyethylene can twist and turn in random ways, the most stable form is a linear one with the carbon backbone oriented as shown in the following figure: H H H H H H H H H H H H H H H H H H H H H H H H The solid wedges in the figure indicate bonds from carbon that come out of the plane of the page; the dashed wedges indicate bonds that lie behind the plane of the page. (a) What is the hybridization of orbitals at each carbon atom? What angles do you expect between the bonds? (b) Now imagine that the polymer is polypropylene rather than polyethylene. Draw structures for polypropylene in which (i) the CH3 groups all lie on the same side of the plane of the paper (this form is called isotactic polypropylene), (ii) the CH3 groups lie on alternating sides of the plane (syndiotactic polypropylene), or (iii) the CH3 groups are randomly distributed on either side (atactic polypropylene). Which of these forms would you expect to have the highest crystallinity and melting point, and which the lowest? Explain in terms of intermolecular interactions and molecular shapes. (c) Polypropylene fibers have been employed in athletic wear. The product is said to be superior to cotton or polyester clothing in wicking moisture away from the body through the fabric to the outside. Explain the difference between polypropylene and polyester or cotton (which has many OH groups along the molecular chain) in terms of intermolecular interactions with water.

(a) In polyvinyl chloride shown in Table 12.5, which bonds have the lowest average bond enthalpy?

(b) When subjected to high pressure and heated, polyvinyl chloride converts to diamond. During this transformation which bonds are most likely to break first?

(c) Employing the values of average bond enthalpy in Table 8.4, estimate the overall enthalpy change for converting PVC to diamond.

Silicon has the diamond structure with a unit cell edge length of 5.43 and eight atoms per unit cell. (a) How many silicon atoms are there in 1 cm3 of material? (b) Suppose you dope that 1 cm3 sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

KCl has the same structure as NaCl. The length of the unit cell is 6.28 . The density of KCl is 1.984 g>cm3 , and its formula mass is 74.55 amu. Using this information, calculate Avogadros number.

Look up the diameter of a silicon atom, in . The latest semiconductor chips have fabricated lines as small as 22 nm. How many silicon atoms does this correspond to?

Problem 1DE Polymers were commercially made by the DuPont™ Company starting in the late 1920s. At that time, some chemists still could not believe that polymers were molecules: they thought covalent bonding would not last’ for millions of atoms, and that polymers were really clumps of molecules held together by weak intermolecular forces. Design an experiment to demonstrate that polymers really are large molecules and not little clumps of small molecules that are held together by weak intermolecular forces.

Visualizing Concepts Two solids are shown below. One is a semiconductor and one is an insulator. Which one is which? Explain your reasoning. [Sections 12.1, 12.7]

Visualizing Concepts For each of the two-dimensional structures shown here (a) draw the unit cell, (b) determine the type of two-dimensional lattice (from Figure 12.4), and (c) determine how many of each type of circle (white or black) there are per unit cell. [Section 12.2]

Visualizing Concepts (a) What kind of packing arrangement is seen in the accompanying photo? (b) What is the coordination number of each cannonball in the interior of the stack? (c) What are the coordination numbers for the numbered cannonballs on the visible side of the stack? [Section 12.3]

Visualizing Concepts Which arrangement of cations (yellow) and anions (blue) in a lattice is the more stable? Explain your reasoning. [Section 12.5]

Problem 5E Visualizing Concepts Which of these molecular fragments would you expect to be more likely to give rise to electrical conductivity? Explain your reasoning. [Sections 12.6, 12.8]

Visualizing Concepts Shown here are cartoons of two different polymers. Which of these polymers would you expect to be more crystalline? Which one would have the higher melting point? [Section 12.8]

Visualizing Concepts The electronic structure of a doped semiconductor is shown here. (a) Which band, A or B, is the valence band? (b) Which band is the conduction band? (c) Which band consists of bonding molecular orbitals? (d) Is this an example of an ntype or p-type semiconductor? (e) If the semiconductor is germanium, which of the following elements could be the dopant: Ga, Si, or P? [Section 12.7]

Visualizing Concepts The accompanying image shows photoluminescence from four different samples of CdTe nanocrystals, each embedded in a polymer matrix. The photoluminescence occurs because the samples are being irradiated by a UV light source. The nanocrystals in each vial have different average sizes. The sizes are 4.0, 3.5, 3.2, and 2.8 nm. (a) Which vial contains the 4.0-nm nanocrystals? (b) Which vial contains the 2.8-nm nanocrystals? (c) Crystals of CdTe that have sizes that are larger than approximately 100 nm have a band gap of 1.5 eV. What would be the wavelength and frequency of light emitted from these crystals? What type of light is this? [Sections 12.7 and 12.9]

Problem 9E Classification of Solids (Section) Covalent bonding occurs in both molecular and covalent-network solids. Which of the following statements best explains why these two kinds of solids differ so greatly in their hardness and melting points? (a) The molecules in molecular solids have stronger covalent bonding than covalent-network solids do. (b) The molecules in molecular solids are held together by weak intermolecular interactions, (c) The atoms in covalent-network solids are more polarizable than those in molecular solids, (d) Molecular solids are denser than covalent-network solids.

Problem 10E Classification of Solids (Section) Silicon is the fundamental component of integrated circuits. Si has the same structure as diamond (a) Is Si a molecular, metallic, ionic, or covalent-network solid? (b) Silicon readily reacts to form silicon dioxide. Si02, which is quite hard and is insoluble in water. Is Si02 most likely a molecular, metallic, ionic, or covalent-network solid?

Problem 11E Classification of Solids (Section) What kinds of attractive forces exist between particles (atoms, molecules, or ions) in (a) molecular crystals, (b) covalent network crystals, (c) ionic crystals, (d) and metallic crystals?

Problem 12E Classification of Solids (Section) Which type (or types) of crystalline solid is characterized by each of the following? (a) High mobility of electrons throughout the solid: (b) softness, relatively low melting point; (c) high melting point and poor electrical conductivity; (d) network of covalent bonds.

Problem 13E Classification of Solids (Section) Indicate the type of solid (molecular, metallic, ionic, or covalent- network) for each compound: (a) CaC03, (b) Pt, (c) Zr02 (melting point. 2677 °C), (d) table sugar (C12H22011), (e) benzene (C6H6), (f) I2.

Problem 14E Classification of Solids (Section) Indicate the type of solid (molecular, metallic, ionic, or covalent- network) for each compound (a) InAs, (b) MgO, (c) HgS, (d) In, (e) HBr.

Problem 15E Classification of Solids (Section) A white substance melts with some decomposition at 730 °C. As a solid, it does not conduct electricity, but it dissolves in water to form a conducting solution. Which type of solid ( molecular, metallic, covalent-network, or ionic) might the substance be?

Problem 16E You are given a white substance that sublimes at 3000 °C; the solid is a nonconductor of electricity and is insoluble in water. Which type of solid (molecular, metallic, covalent-network, or ionic) might this substance be?

Problem 17E Structures of Solids (Section) (a) Draw a picture that represents a crystalline solid at the atomic level (b) Now draw a picture that represents an amorphous solid at the atomic level.

Structures of Solids Two patterns of packing two different spheres are shown here. For each structure (a) draw the two-dimensional unit cell; (b) determine the angle between the lattice vectors, \(\gamma\), and determine whether the lattice vectors are of the same length or of different lengths; (c) determine the type of two-dimensional lattice (from Figure 12.4). Equation Transcription: Text Transcription: gamma

Structures of Solids Two patterns of packing for two different spheres are shown here. For each structure (a) draw the two-dimensional unit cell; (b) determine the angle between the lattice vectors, \(\gamma\), and determine whether the lattice vectors are of the same length or of different lengths; and (c) determine the type of two-dimensional lattice (from Figure 12.4). Equation Transcription: Text Transcription: gamma

Problem 18E Structures of Solids (Section) Amorphous silica. Si02, has a density of about 2.2 g/cm3, whereas the density of crystalline quartz, another form of Si02, is 2.65 g/cm3. Which of the following statements is the best explanation for the difference in density? (a) Amorphous silica is a network-covalent solid, but quartz is metallic, (b) Amorphous silica crystallizes in a primitive cubic lattice, (c) Quartz is harder than amorphous silica, (d) Quartz must have a larger unit cell than amorphous silica, (e) The atoms in amorphous silica do not pack as efficiently in three dimensions as compared to the atoms in quartz.

Structures of Solids Imagine the primitive cubic lattice. Now imagine grabbing the top of it and stretching it straight up. All angles remain \(90^{\circ}\). What kind of primitive lattice have you made? Equation Transcription: Text Transcription: 90^o

Structures of Solids Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. All angles remain \(90^{\circ}\). What kind of primitive lattice have you made? Equation Transcription: Text Transcription: 90^o

Problem 23E Structures of Solids (Section) Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is 90°? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral. (d) triclinic, (e) both rhombohedral and triclinic.

Problem 24E Structures of Solids (Section) Besides the cubic unit cell, which other unit cell(s) has edge lengths that are all equal to each other? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral. (d) triclinic, (e) both rhombohedral and triclinic.

Problem 25E Structures of Solids (Section) What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4. (e) 5.

Problem 26E Structures of Solids (Section) What is the minimum number of atoms that could be contained in the unit cell of an element with a face-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5.

Structures of Solids The unit cell of nickel arsenide is shown here. (a) What type of lattice does this crystal possess? (b) What is the empirical formula? Equation Transcription: Å Å Å Text Transcription: 5.10 AA 3.57 AA 3.57 AA 120^o

Structures of Solids The unit cell of a compound containing strontium, iron, and oxygen is shown here. (a) What type of lattice does this crystal possess (all three lattice vectors are mutually perpendicular)? (b) What is the empirical formula? Equation Transcription: Å Å Å Text Transcription: 3.47 AA 3.98 AA 3.98 AA Sr Fe

Problem 29E Metallic Solids (Section) The densities of the elements K. Ca. Sc, and Ti are 0.86. 1.5, 3.2, and 4.5 g/cm3, respectively. One of these elements crystallizes in a body-centered cubic structure; the other three crystallize in a face-centered cubic structure. Which one crystallizes in the body-centered cubic structure? Justify your answer.

Problem 30E Metallic Solids (Section) For each of these solids, state whether you would expect it to possess metallic properties: (a) T1CI4. (b) NiCo alloy, (c) W, (d) Ge, (e) ScN.

Metallic Solids Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms? (b) Which structure(s) corresponds to the least dense packing of atoms?

Problem 33E Metallic Solids (Section) Iridium crystallizes in a face-centered cubic unit cell that has an edge length of 3.833 A (a) Calculate the atomic radius of an iridium atom, (b) Calculate the density of iridium metal.

Problem 32E Metallic Solids (Section) Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3 (a) Use this information and Avogadro's number (A/A = 6.022 x 1023/mol) to estimate the atomic radius of sodium, (b) If sodium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close-packed metal. Would it still float on water?

Problem 34E Metallic Solids (Section) Calcium crystallizes in a body-centered cubic structure, (a) How many Ca atoms are contained in each unit cell? (b) How many nearest neighbors does each Ca atom possess? (c) Estimate the length of the unit cell edge. a. from the atomic radius of calcium (1.97 A) (d) Estimate the density of Ca metal.

Problem 35E Metallic Solids (Section) Aluminum metal crystallizes in a face-centered cubic unit cell, (a) How many aluminum atoms are in a unit cell? (b) What is the coordination number of each aluminum atom? (c) Estimate the length of the unit cell edge. a. from the atomic radius of aluminum (1.43 A), (d) Calculate the density of aluminum metal.

Problem 36E Metallic Solids (Section) An element crystallizes in a body-centered cubic lattice. The edge of the unit cell is 2.86 A. and the density of the crystal is 7.92 g/cm3. Calculate the atomic weight of the element.

Problem 37E Metallic Solids (Section) Which of these statements about alloys and intermetallic compounds is false? (a) Bronze is an example of an alloy, (b) “Alloy’’ is just another word for “a chemical compound of fixed composition that is made of two or more metals”, (c) Intermetallics are compounds of two or more metals that have a definite composition and are not considered alloys, (d) If you mix two metals together and. at the atomic level, they separate into two or more different compositional phases, you have created a heterogeneous alloy, (e) Alloys can be formed even if the atoms that comprise them are rather different in size.

Problem 38E Metallic Solids (Section) Determine if each statement is true or false: (a) Substitutional alloys are solid solutions, but interstitial alloys are heterogeneous alloys, (b) Substitutional alloys have "solute’ atoms that replace "solvent’ atoms in a lattice, but interstitial alloys have "solute’ atoms that are in between the "solvent’ atoms in a lattice, (c) The atomic radii of the atoms in a substitutional alloy are similar to each other, but in an interstitial alloy, the interstitial atoms are a lot smaller than the host lattice atoms.

Problem 40E Metallic Solids (Section) For each of the following alloy compositions, indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound: (a) Cu0.66Zn0.34, (b) Ag3Sn. (c) Ti0.9900.01.

Problem 39E Metallic Solids (Section) For each of the following alloy compositions, indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound: (a) Fe0.97Si0.03, (b) Fe0.60Ni0.40, (c) SmCo5.

Problem 41E Metallic Solids (Section) Indicate whether each statement is true or false: (a) Substitutional alloys tend to be more ductile than interstitial alloys, (b) Interstitial alloys tend to form between elements with similar ionic radii, (c) Nonmetallic elements are never found in alloys.

Problem 42E Metallic Solids (Section) Indicate whether each statement is true or false: (a) Intermetallic compounds have a fixed composition, (b) Copper is the majority component in both brass and bronze, (c) In stainless steel, the chromium atoms occupy interstitial positions.

Problem 43E Metallic Solids (Section) Which element or elements are alloyed with gold to make the following types of “colored gold" used in the jewelry industry? For each type, also indicate what type of alloy is formed: (a) white gold, (b) rose gold, (c) green gold.

Problem 44E Metallic Solids (Section) Look up the chemical composition of purple gold. Is the composition variable? Why don't jewelers use purple gold to make rings or necklaces?

Problem 45E Metallic Bonding (Section) State whether each sentence is true or false: (a) Metals have high electrical conductivities because the electrons in the metal are delocalized, (b) Metals have high electrical conductivities because they are denser than other solids, (c) Metals have large thermal conductivities because they expand when heated, (d) Metals have small thermal conductivities because the delocalized electrons cannot easily transfer the kinetic energy imparted to the metal from heat.

Problem 46E Metallic Bonding (Section) Imagine that you have a metal bar sitting half in the Sun and half in the dark. On a sunny day, the part of the metal that has been sitting in the Sun feels hot. If you touch the part of the metal bar that has been sitting in the dark, will it feel hot or cold? Justify your answer in terms of thermal conductivity.

Metallic Bonding The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: Discrete energy levels in individual molecules become continuous energy bands in a solid. Occupied orbitals are shaded blue, and empty orbitals pink. (a) How many molecular orbitals are there in the diagram? (b) How many nodes are in the lowest-energy molecular orbital? (c) How many nodes are in the highest-energy molecular orbital? (d) How many nodes are in the highest-energy occupied molecular orbital (HOMO)? (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)? (f) How does the HOMO–LUMO energy gap for this case compare to that of the four- atom case? Equation Transcription: Text Transcription: Li Li_2 Li_4 Li_{infinity}

Problem 49E Metallic Bonding (Section) Which would you expect to be the more ductile element (a) Ag or Mo, (b) Zn or Si? In each case explain your reasoning.

Problem 48E Metallic Bonding (Section) Repeat Exercise 12.47 for a linear chain of eight lithium atoms.

Problem 50E Metallic Bonding (Section) Which of the following statements does not follow from the fact that the alkali metals have relatively weak metal-metal bonding? (a) The alkali metals are less dense than other metals, (b) The alkali metals are soft enough to be cut with a knife, (c) The alkali metals are more reactive than other metals, (d) The alkali metals have higher melting points than other metals, (e) The alkali metals have low ionization energies.

Problem 51E Metallic Bonding (Section) Explain this trend in melting points: Y 1522 °C, Zr

Problem 52E Metallic Bonding (Section) For each of the following groups, which metal would you expect to have the highest melting point: (a) gold, rhenium, or cesium: (b) rubidium, molybdenum, or indium; (c) ruthenium, strontium, or cadmium?

Ionic and Molecular Solids Tausonite, a mineral composed of Sr, O, and Ti, has the cubic unit cell shown in the drawing. (a) What is the empirical formula of this mineral? (b) How many oxygens are coordinated to titanium? (c) To see the full coordination environment of the other ions, we have to consider neighboring unit cells. How many oxygens are coordinated to strontium?

Ionic and Molecular Solids Rutile is a mineral composed of Ti and O. Its unit cell, shown in the drawing, contains Ti atoms at each corner and a Ti atom at the center of the cell. Four O atoms are on the opposite faces of the cell, and two are entirely within the cell. (a) What is the chemical formula of this mineral? (b) What is the coordination number of each atom?

Problem 55E Ionic and Molecular Solids (Sections) NaF has the same structure as NaCl (a) Use ionic radii from Chapter to estimate the length of the unit cell edge for NaF, (b) Use the unit cell size calculated in part (a) to estimate the density of NaF

Problem 56E Clausthalite is a mineral composed of lead selenide (PbSe). The mineral adopts the rock salt structure. The density of PbSe at 25 °C is 8.27 g/cm3. Calculate the length of an edge of the PbSe unit cell.

Problem 57E Ionic and Molecular Solids (Sections) A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 A (a) Calculate the density of HgS in this form, (b) The mineral tiemmanite (HgSe) also forms a solid phase with the zinc blende structure. The length of the unit cell edge in this mineral is 6.085 A. What accounts for the larger unit cell length in tiemmanite? (c) Which of the two substances has the higher density? How do you account for the difference in densities?

Problem 58E Ionic and Molecular Solids (Sections) At room temperature and pressure Rbl crystallizes with the NaCI-type structure (a) Use ionic radii to predict the length of the cubic unit cell edge, (b) Use this value to estimate the density, (c) At high pressure the structure transforms to one with a CsCI-type structure, (c) Use ionic radii to predict the length of the cubic unit cell edge for the high pressure form of Rbl. (d) Use this value to estimate the density. How does this density compare with the density you calculated in part (b)?

Ionic and Molecular Solids CuI, CsI, and NaI each adopt a different type of structure. The three different structures are those shown in Figure 12.26. (a) Use ionic radii, \(\mathrm{Cs}^{+}(r=1.81\ \AA)\), \(\mathrm{Na}^{+}(r=1.16\ \AA)\), \(\mathrm {Cu}^{+}(r=0.74\ \AA)\), and, \(\mathrm {I}^{-}(r=2.06\ \AA)\), to predict which compound will crystallize with which structure. (b) What is the coordination number of iodide in each of these structures? Equation Transcription: Å) Å) Å) Å) Text Transcription: Cs^{+}(r=1.81{AA}) Na^{+}(r=1.16{AA}) Cu^{+}(r=0.74{AA}) I^{-}(r=2.06{AA})

The rutile and fluorite structures, shown here (anions are colored green), are two of the most common structure types of ionic compounds where the cation to anion ratio is 1:2. (a) For \(\mathrm{CaF}_{2}\) and \(\mathrm{ZnF}_{2}\) use ionic radii, \(\mathrm{Ca}^{2+}(r=1.14\ \AA)\), \(\mathrm{Zn}^{2+}(r=0.88\ \AA \text { ) }\), and \(\mathrm{F}^{-}(r=1.19\ \AA)\), to predict which compound is more likely to crystallize with the fluorite structure and which with the rutile structure. (b) What are the coordination numbers of the cations and anions in each of these structures? Equation Transcription: Å) Å) Å) Text Transcription: CaF_2 ZnF_2 Ca^{2+}(r=1.14{AA}) Zn^{2+}(r=0.88{AA}) F^{-}(r=1.19{AA})

Problem 61E Ionic and Molecular Solids (Sections) The coordination number for Mg2+ ion is usually six. Assuming this assumption holds, determine the anion coordination number in the following compounds: (a) MgS, (b) MgF2, (c) MgO.

Problem 62E Ionic and Molecular Solids (Sections) The coordination number for the Al3+ ion is typically between four and six. Use the anion coordination number to determine the Al3+ coordination number in the following compounds: (a) AlF3 where the fluoride ions are two coordinate,, (b) Al2O3 where the oxygen ions are six coordinate,, (c) AlN where the nitride ions are four coordinate.

Problem 63E Ionic and Molecular Solids (Sections) Classify each of the following statements as true or false: (a) Although both molecular solids and covalent-network solids have covalent bonds, the melting points of molecular solids are much lower because their covalent bonds are much weaker. (b) Other factors being equal, highly symmetric molecules tend to form solids with higher melting points than asymmetrically shaped molecules.

Problem 64E Ionic and Molecular Solids (Sections) Classify each of the following statements as true or false: (a) For molecular solids, the melting point generally increases as the strengths of the covalent bonds increase. (b) For molecular solids, the melting point generally increases as the strengths of the intermolecular forces increase.

Problem 66E Which of the following properties are typical characteristics of a covalent-network solid, a metallic solid, or both: (a) ductility,, (b) hardness, (c) high melting point?

Problem 67E Covalent-Network Solids (Section) For each of the following pairs of semiconductors, which one will have the larger band gap: (a) CdS or CdTe, (b) GaN or InP, (c) GaAs or InAs?

Problem 68E Covalent-Network Solids (Section) For each of the following pairs of semiconductors, which one will have the larger band gap: (a) InP or InAs, (b) Ge or AlP, (c) AgI or CdTe?

Problem 69E Covalent-Network Solids (Section) If you want to dope GaAs to make an n-type semiconductor with an element to replace Ga, which element(s) would you pick?

Problem 70E Covalent-Network Solids (Section) If you want to dope GaAs to make a p-type semiconductor with an element to replace As, which element(s) would you pick?

Covalent-Network Solids Silicon has a band gap of 1.1 eV at room temperature. (a) What wavelength of light would a photon of this energy correspond to? (b) Draw a vertical line at this wavelength in the figure shown, which shows the light output of the Sun as a function of wavelength. Does silicon absorb all, none, or a portion of the visible light that comes from the Sun? (c) You can estimate the portion of the overall solar spectrum that silicon absorbs by considering the area under the curve. If you call the area under the entire curve “100%,” what approximate percentage of the area under the curve is absorbed by silicon?

Problem 72E Covalent-Network Solids (Section) Cadmium telluride is an important material for solar cells (a) What is the band gap of CdTe? (b) What wavelength of light would a photon of this energy correspond to? (c) Draw a vertical line at this wavelength in the figure shown in Exercise 12.71, which shows the light output of the sun as a function of wavelength, (d) With respect to silicon, does CdTe absorb a larger or smaller portion of the solar spectrum?

Problem 73E Covalent-Network Solids (Section) The semiconductor GaP has a band gap of 2.26 eV. What wavelength of light would be emitted from an LED made from GaP? What color is this?

Problem 74E Covalent-Network Solids (Section) The first LEDs were made from GaAs, which has a band gap of 1.43 eV. What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: ultraviolet, visible, or infrared?

Problem 75E Covalent-Network Solids (Section) GaAs and GaP make solid solutions that have the same crystal structure as the parent materials, with As and P randomly distributed throughout the crystal. GaPxAs1- x exists for any value of x. If we assume that the band gap varies linearly with composition between x = 0 and x = 1, estimate the band gap for GaP0.5As0.5. (See the previous two exercises for GaAs and GaP band gaps.) What wavelength of light does this correspond to?

Problem 65E Covalent-Network Solids (Section) Both covalent-network solids and ionic solids can have melting points well in excess of room temperature, and both can be poor conductors of electricity in their pure form. However, in other ways their properties are quite different. (a) Which type of solid is more likely to dissolve in water? (b) Which type of solid can become an electrical conductor via chemical substitution?

Problem 76E Covalent-Network Solids (Section) Red light-emitting diodes are made from GaAs and GaP solid solutions, GaPxAs1-x (see Exercise 12.75). The original red LEDs emitted light with a wavelength of 660 nm. If we assume that the band gap varies linearly with composition between x = 0 and x = 1, estimate the composition (the value of x) that is used in these LEDs.

Problem 77E Polymers (Section) (a) What is a monomer? (b) Which of these molecules can be used as a monomer: benzene, ethene (also called ethylene), methane?

Problem 78E Polymers (Section) The molecular formula of n-decane is CH3(CH2)8CH3. Decane is not considered a polymer, whereas polyethylene is. What is the distinction?

Problem 79E Polymers (Section) State whether each of these numbers is a reasonable value for a polymer's molecular weight: 100 amu. 10,000 amu. 100,000 amu, 1,000,000 amu?

Problem 80E Polymers (Section) Indicate whether the following statement is true or false: For an addition polymerization, there are no by-products of the reaction (assuming 100% yield).

Problem 81E Polymers (Section) An ester is a compound formed by a condensation reaction between a carboxylic acid and an alcohol that eliminates a water molecule. Read the discussion of esters in Section and then give an example of a reaction forming an ester. How might this kind of reaction be extended to form a polymer (a polyester)?

Problem 82E Polymers (Section) Write a balanced chemical equation for the formation of a polymer via a condensation reaction from the monomers succinic acid (HOOCCH2CH2COOH) and ethylenediamine (H2NCH2CH2NH2).

Polymers Write the chemical equation that represents the formation of (a) polychloroprene from chloroprene (polychloroprene is used in highway-pavement seals, expansion joints, conveyor belts, and wire and cable jackets) (b) polyacrylonitrile from acrylonitrile (polyacrylonitrile is used in home furnishings, craft yarns, clothing, and many other items). Equation Transcription: Text Transcription: CH2=CH-C=CH2 Cl CH2=CH CN

Polymers The nylon Nomex, a condensation polymer, has the following structure: Draw the structures of the two monomers that yield Nomex. Equation Transcription: Text Transcription: NH NH

Polymers Draw the structure of the monomer(s) that are used to make each of the polymers shown in Table 12.5: (a) polyvinyl chloride, (b) nylon 6,6, (c) polyethylene terephthalate. Equation Transcription: Text Transcription: (-CH_{2}-CH_{2}-)_n -CH_{2}-CH CH_{3} -CH_{2}-CH- -CH_{2}-CH- Cl -NH-R-NH-C-(CH_{2})_{4}C- CH_{3} CH_{3} O-C

Proteins are naturally occurring polymers formed by condensation reactions of amino acids, which have the general structure In this structure, ? R represents ? H, \(-\mathrm{CH}_{3}\), or another group of atoms; there are 20 different natural amino acids, and each has one of 20 different R groups. (a) Draw the general structure of a protein formed by condensation polymerization of the generic amino acid shown here. (b) When only a few amino acids react to make a chain, the product is called a “peptide” rather than a protein; only when there are 50 amino acids or more in the chain would the molecule be called a protein. For three amino acids (distinguished by having three different R groups, R1, R2, and R3), draw the peptide that results from their condensation reactions. (c) The order in which the R groups exist in a peptide or protein has a huge influence on its biological activity. To distin- guish different peptides and proteins, chemists call the first amino acid the one at the “N terminus” and the last one the one at the “C terminus.” From your drawing in part (b) you should be able to figure out what “N terminus” and “C terminus” mean. How many different peptides can be made from your three different amino acids? Equation Transcription: Text Transcription: H-N-C-C-O-H -R -H -CH_3

Problem 87E Polymers (Section) (a) What molecular features make a polymer flexible-7 (b) If you cross-link a polymer, is it more flexible or less flexible than it was before?

Problem 89E Polymers (Section) If you want to make a polymer for plastic wrap, should you strive to make a polymer that has a high or low degree of crystallinity?

Problem 88E Polymers (Section) What molecular structural features cause high-density polyethylene to be denser than low-density polyethylene?

Problem 90E Polymers (Section) Indicate whether each statement is true or false: (a) Elastomers are rubbery solids, (b) Thermosets cannot be reshaped, (c) Thermoplastic polymers can be recycled.

Problem 91E Nanomaterials (Section) Explain why ‘bands" may not be the most accurate description of bonding in a solid when the solid has nanoscale dimensions.

Problem 92E Nanomaterials (Section) CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy (a) What color is the emitted light? (b) Would appropriately sized CdS quantum dots be able to emit blue light? (c) What about red light?

Problem 93E Nanomaterials (Section) Indicate whether each statement is true or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the 1-10-nm range, (b) The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.

Problem 94E Nanomaterials (Section) Indicate whether this statement is true or false: If you want a semiconductor that emits blue light, you could either use a material that has a band gap corresponding to the energy of a blue photon or you could use a material that has a smaller band gap but make an appropriately sized nanoparticle of the same material.

Problem 95E Nanomaterials (Section) Gold adopts a face-centered cubic structure with a unit cell edge of 4.08 Å (Figure). How many gold atoms are there in a sphere that is 20 nm in diameter? Recall that the volume of a sphere is 4/3 ?r3. Figure The structures of (a) primitive cubic (b) body-centered cubic, and (c) face-centered cubic metals. Each structure can be generated by the combination of a single-atom motif and the appropriate lattice (d) Corner atoms (one shown in red) are shared among eight neighboring cubic unit cells.

Problem 96E Nanomaterials (Section) Cadmium telluride, CdTe, adopts the zinc blende structure with a unit cell edge length of 6.49 Å. There are four cadmium atoms and four tellurium atoms per unit cell. How many of each type of atom are there in a cubic crystal with an edge length of 5.00 nm?

Problem 97E Nanomaterials (Section) Which statement correctly describes a difference between grapheme and graphite? (a) Graphene is a molecule but graphite is not. (b) Graphene is a single sheet of carbon atoms and graphite contains many, and larger, sheets of carbon atoms, (c) Graphene is an insulator but graphite is a metal, (d) Graphite is pure carbon but graphene is not. (e) The carbons are sp2 hybridized in grapheme but sp3 hybridized in graphite.

Problem 98E Nanomaterials (Section) What evidence supports the notion that buckyballs are actual molecules and not extended materials? (a) Buckyballs are made of carbon. (b) Buckyballs have a well-defined atomic structure and molecular weight. (c) Buckyballs have a well-defined melting point. (d) Buckyballs are semiconductors. (e) More than one of the previous choices.

Problem 99AE A face-centered tetragonal lattice is not one of the 14 three dimensional lattices. Show that a face-centered tetragonal unit cell can be redefined as a body-centered tetragonal lattice with a smaller unit cell.

Problem 100AE Pure iron crystallizes in a body-centered cubic structure, but small amounts of impurities can stabilize a face-centered cubic structure. Which form of iron has a higher density?

Problem 101AE Introduction of carbon into a metallic lattice generally results in a harder less ductile substance with lower electrical and thermal conductivities. Explain why this might be so.

\(\mathrm{Ni}_{3} \mathrm{Al}\) is used in the turbines of aircraft engines because of its strength and low density. Nickel metal has a cubic close-packed structure with a face-centered cubic unit cell, while \(\(\mathrm{Ni}_{3} \mathrm{Al}\)\) has the ordered cubic structure shown in Figure 12.17. The length of the cubic unit cell edge is \(3.53 \AA\) for nickel and \(3.56 \AA\) for \(\(\mathrm{Ni}_{3} \mathrm{Al}\)\). Use these data to calculate and compare the densities of these two materials. Equation Transcription: Å Å Text Transcription: Ni_{3}Al Ni_{3}Al 3.53{AA} 3.56{AA} Ni_{3}Al

Problem 103AE For each of the intermetallic compounds shown in Figure determine the number of each type of atom in the unit cell. Do your answers correspond to the ratios expected from the empirical formulas: Ni3Al, Nb3Sn, and SmCo5? Figure Three examples of intermetallic compounds.

Problem 104AE What type of lattice—primitive cubic, body-centered cubic, or face-centered cubic—does each of the following structure types possess: (a) CsCl, (b) Au, (c) NaCl, (d) Po, (e) ZnS?

Problem 105AE Tin exists in two allotropic forms: Gray tin has the diamond structure, and white tin has a close-packed structure. One of these allotropic forms is a semiconductor with a small band gap. while the other is a metal (a) Which one is which? (b) Which form would you expect to have the longer Sn—Sn bond distance?

Problem 106AE The electrical conductivity of aluminum is approximately 109 times greater than that of its neighbor in the periodic table, silicon. Aluminum has a face-centered cubic structure, and silicon has the diamond structure. A classmate of yours tells you that density is the reason aluminum is a metal but silicon is not: therefore, if you were to put silicon under high pressure, it too would act like a metal. Discuss this idea with your classmates, looking up data about Al and Si as needed.

Silicon carbide, SiC, has the three-dimensional structure shown in the figure. (a) Name another compound that has the same structure. (b) Would you expect the bonding in SiC to be predominantly ionic, metallic, or covalent? (c) How do the bonding and structure of SiC lead to its high thermal stability (to \(\mathrm {2700\ ^\circ C}\)) and exceptional hardness? Equation Transcription: Text Transcription: 2700 ^oC

Rhenium oxide crystallizes with a structure that has a primitive cubic lattice, as shown here. In the image on the left, the sizes of the ions have been reduced to show the entire unit cell. (a) How many atoms of each type are there per unit cell? (b) Use the ionic radii of rhenium \((0.70\ \AA)\) and oxygen \((1.26\ \AA)\) to estimate the length of the edge of the unit cell. (c)Use your answers to parts (a) and (b) to estimate the density of this compound. Equation Transcription: Å) Å) Text Transcription: (0.70{AA}) (1.26{AA})

Problem 108AE Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.

Problem 110AE Teflon is a polymer formed by the polymerization of F2C?CF2 (a) Draw the structure of a section of this polymer. (b) What type of polymerization reaction is required to form Teflon?

Teflon is a polymer formed by the polymerization of \(\mathrm{F}_{2} \mathrm{C}=\mathrm{CF}_{2}\). (a) Draw the structure of a section of this polymer. (b) What type of polymerization reaction is required to form Teflon? Equation Transcription: Text Transcription: F_{2}C=CF_{2}

Problem 112AE Explain why X rays can be used to measure atomic distances in crystals but visible light cannot be used for this purpose.

Problem 113AE In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation (?), the angle at which the radiation is diffracted (?), 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).

Problem 115AE (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? (b) X-ray diffraction studies of buckminsterfullerene show that it has a face-centered cubic lattice of C60 molecules. The length of an edge of the unit cell is 14.2 Å. Calculate the density of buckminsterfullerene.

Problem 114AE 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 the previous problem but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle 0?

Problem 116AE When you shine light of band gap energy or higher on a semiconductor and promote electrons from the valence band to the conduction band, do you expect the conductivity of the semiconductor to (a) remain unchanged (b) increase, or (c) decrease7

Problem 118IE Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g/cm3. The unit cell is cubic with an edge length of 8.09 Å. How many atoms of each type are in the unit cell?

The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is 50 mol% silver and 50 mol% gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy. (b) If an alloy is formed that is 50 mol% copper and 50 mol% gold, what is the karat number of the alloy? What is the color of this alloy?

Problem 119IE (a) What are the C?C?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?

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).

Although polyethylene can twist and turn in random ways, the most stable form is a linear one with the carbon backbone oriented as shown in the following figure: The solid wedges in the figure indicate bonds from carbon that come out of the plane of the page; the dashed wedges indicate bonds that lie behind the plane of the page. (a) What is the hybridization of orbitals at each carbon atom? What angles do you expect between the bonds? (b) Now imagine that the polymer is polypropylene rather than polyethylene. Draw structures for polypropylene in which (i) the \(\mathrm {CH_3}\) groups all lie on the same side of the plane of the paper (this form is called isotactic polypropylene), (ii) the \(\mathrm {CH_3}\) groups lie on alternating sides of the plane (syndiotactic polypropylene), or (iii) the \(\mathrm {CH_3}\) groups are randomly distributed on either side (atactic polypropylene). Which of these forms would you expect to have the highest crystallinity and melting point, and which the lowest? Explain in terms of intermolecular interactions and molecular shapes. (c) Polypropylene fibers have been employed in athletic wear. The product is said to be superior to cotton or polyester clothing in wicking moisture away from the body through the fabric to the outside. Explain the difference between polypropylene and polyester or cotton (which has many \(\mathrm {-OH}\) groups along the molecular chain) in terms of intermolecular interactions with water. Equation Transcription: Text Transcription: CH_{3} CH_{3} CH_{3} -OH

Problem 123IE Silicon has the diamond structure with a unit cell edge length of 5.43 Å and eight atoms per unit cell. (a) How many silicon atoms are there in 1 cm3 of material? (b) Suppose you dope that 1 cm3sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

(a) In polyvinyl chloride shown in Table 12.5, which bonds have the lowest average bond enthalpy? (b) When subjected to high pressure and heated, polyvinyl chloride converts to diamond. During this transformation which bonds are most likely to break first? (c) Employing the values of average bond enthalpy in Table 8.4, estimate the overall enthalpy change for converting PVC to diamond.

Problem 124IE KCl has the same structure as NaCl. The length of the unit cell is 6.28 Å. The density of KCl is 1.984 g/cm3, and its formula mass is 74.55 amu. Using this information, calculate Avogadro’s number.

Problem 125IE Look up the diameter of a silicon atom, in Å. The latest semiconductor chips have fabricated lines as small as 22 nm. How many silicon atoms does this correspond to?