12: Solids
 Page ID
 205366
Prelude
Crystal Lattices and Unit Cells
Exercise \(\PageIndex{2a}\)
Crystalline solids differ from amorphous solids by _____.
 Substantial intermolecular attractive forces
 A longrange repeating pattern of atoms, molecules, or ions
 Atoms, molecule, or ions that are close together
 Much larger atoms, molecules, or ions
 No orderly structure
 Answer

b. A longrange repeating pattern of atoms, molecules, or ions
Exercise \(\PageIndex{2b}\)
______ is a unit cell with all sides the same length and all angles equal to 90° that has lattice points only at the corners.
 Bodycentered cubic
 Facecentered cubic
 Monoclinic
 Primitive cubic
 Spherical cubic
 Answer

d. Primitive cubic
Exercise \(\PageIndex{2c}\)
What is the fraction that each corner atom takes up in a facecentered cubic unit cell?
 1
 1/2
 1/4
 1/8
 1/16
 Answer

d. 1/8
Exercise \(\PageIndex{2d}\)
A facecentered cubic unit cell contains how many atoms?
 Answer

Four
Exercise \(\PageIndex{2e}\)
Based on sodium chloride structure, which of the following cannot form a solid lattice?
 NaBr
 LiF
 RbI
 CuO
 CuCl_{2}
 Answer

e. CuCl_{2}
Exercise \(\PageIndex{2f}\)
What type of solid is held together by dispersion, dipoledipole or hydrogen bonds?
 Ionic
 metallic
 molecular
 covalent network
 Answer

c. molecular
Exercise \(\PageIndex{2g}\)
What type of compounds are held together by covalent bonds? (there can be more than one correct answer)
 ionic
 metallic
 molecular
 covalent network
 Answer

d. covalent network and molecular
Exercise \(\PageIndex{2h}\)
Solid Iodine is a ____type of substance:
 ionic lattice
 metallic
 molecular
 covalent network
 Answer

c. molecular
Exercise \(\PageIndex{2i}\)
Diamond lattices are a ___ type of substance
 ionic crystal
 metallic
 molecular
 network covalent
 Answer

d. network covalent
Exercise \(\PageIndex{2j}\)
How many basic crystal systems are there?
 3
 4
 6
 7
 Answer

d. 7
Exercise \(\PageIndex{2k}\)
Which is not a type of cubic unit cell?
 tetragonal
 bodycentered
 face centered
 primitive
 Answer

a. tetragonal
Exercise \(\PageIndex{2l}\)
Which type of cubic unit cell is the least efficient in packing?
 primitive
 bodycentered
 facecentered
 none of the above
 Answer

a. primitive
Exercise \(\PageIndex{2m}\)
Which type of cubic unit cell is most efficient in packing?
 primitive
 bodycentered
 facecentered
 none of the above
 Answer

c. facecentered
Exercise \(\PageIndex{2n}\)
Primitive, FaceCentered & BodyCentered Cubic Cells have respective coordination numbers of
 1,2,4
 2,4,6
 6,8,12
 6,12,8
 Answer

d. 6,12,8
Exercise \(\PageIndex{2o}\)
In a facecentered cubic cell, what portion of the volume of each atom or ion on the face of a unit is within the unit cell?
 Answer

1/2 of the atom is within the unit cell
Exercise \(\PageIndex{2p}\)
Gallium crystallizes in a primitive cubic unit cell. What is the radius of the Ga atom in Angstroms if the length of the unit cell edge is 3.70Å?
 Answer

\[l=2r\]
\[r=\frac{l}{2}=\frac{3.70\AA }{2}=1.85 \AA\]
Exercise \(\PageIndex{2q}\)
Potassium metal crystallizes in a bodycentered cubic unit cell. What is the radius of the K atom in Angstroms if the length of the unit cell edge is 5.31 Å?
 Answer

\[b^{2}=a^{2}+a^{2}\]
\[b=\sqrt{2a^{2}}=\sqrt{2*(5.31)^{2}}=7.51\AA\]
\[c^{2}=a^{2}+b^{2}\
\[c=\sqrt{a^{2}+b^{2}}=\sqrt{(5.31)^{2}+(7.51)^{2}}=9.20\AA\]
\[c=4r\]
\[r=\frac{c}{4}=\frac{9.20\AA }{4}=2.30\AA\]
Exercise \(\PageIndex{2r}\)
What is the radius of a copper atom in Angstroms if the length of the unit cell edge is 5.34Å? Copper has a facecentered cubic structure.
 Answer

\[c^{2}=a^{2}+a^{2}\]
\[c=\sqrt{2a^{2}}=\sqrt{2*\left ( 5.34\AA \right )^{2}}=7.55 \AA \]
\[r=\frac{c}{4}=\frac{7.55\AA }{4}=1.89 \AA \]
Exercise \(\PageIndex{2s}\)
Silver has a density of 10.5g/cm^{3} and forms an FCC structure. What is the atomic radius of silver in Angstroms? Assume that nearestneighbor atoms contact each other.
 Answer

 Calculate volume of unit cell
\[\left ( \frac{4\,atoms}{unit\,cell} \right )\left ( \frac{1\,mol}{6.022*10^{23}\,atoms} \right )\left ( \frac{107.87\,g}{1\,mol} \right )\left ( \frac{1\,cm^{3}}{10.5\,g} \right )=6.82*10^{23}\,cm^{3}\]
 Calculate length of unit cell
\[V=l^{3}\]
\[l=\sqrt[3]{V}\]
\[l=\sqrt[3]{V}=\sqrt[3]{6.82*10^{23}cm^{3}}=4.09*10^{8}cm*\left ( \frac{10^{10}\AA }{100cm} \right )=4.09\AA\]
 Calculate radius of unit cell
\[c^{2}=a^{2}+a^{2}\]
\[c=\sqrt{2a^{2}}=\sqrt{2*\left ( 4.09\AA \right )^{2}}=5.78\AA\]
\[r=\frac{c}{4}=\frac{5.78\AA }{4}=1.44\AA\]
Exercise \(\PageIndex{2t}\)
An unknown element has a density of 11.07g/mL and forms a Simple Cubic Cell. What is the atomic radius of the unknown element in Angstroms? (unknown element has molar mass of 207.2g/mol)
 Answer

 Calculate volume of unit cell
\[\left ( \frac{1 atom}{unit cell} \right )\left ( \frac{1 mol}{6.022*10^{23}atoms} \right )\left ( \frac{207.2g}{1mol} \right )\left ( \frac{1mL}{11.07g} \right )=3.11*10^{23}cm^{3}\]
 Calculate length of unit cell
\[V=l^{3}\]
\[l=\sqrt[3]{V}\]
\[l=\sqrt[3]{V}=\sqrt[3]{3.11*10^{23}cm^{3}}=3.14*10^{8}cm*\left ( \frac{10^{10}\AA }{100cm} \right )=3.14\AA\]
 Calculate radius of unit cell
\[l=2r\]
\[r=\frac{l}{2}=\frac{3.14\AA }{2}=1.57\AA\]
Exercise \(\PageIndex{2u}\)
Tungsten has a density of 19.25g/cm3 and forms a BCC structure. What is the atomic radius of tungsten in Angstroms?
 Answer

 Calculate volume of unit cell
\[\left ( \frac{2\,atoms}{unit\,cell} \right )\left ( \frac{mol}{6.022*10^{23}\,atoms} \right )\left ( \frac{183.94\,g}{mol} \right )\left ( \frac{1\,cm^{3}}{19.25\,g} \right )=3.17*10^{23}\,cm^{3}\]

Calculate length of unit cell
\[V=l^{3}\]
\[l=\sqrt[3]{V}\]
\[l=\sqrt[3]{V}=\sqrt[3]{3.17*10^{23}cm^{3}}=3.17*10^{8}cm*\left ( \frac{10^{10}\AA }{100cm} \right )=3.17\AA=a\]
 Calculate radius of unit cell
\[b^{2}=a^{2}+a^{2}\]
\[b=\sqrt{2a^{2}}=\sqrt{2*(3.17)^{2}}=4.48\AA\]
\[c^{2}=a^{2}+b^{2}\]
\[c=\sqrt{a^{2}+b^{2}}=\sqrt{(3.17)^{2}+(4.48)^{2}}=5.49\AA\]
\[c=4r\]
\[r=\frac{c}{4}=\frac{5.49\AA }{4}=1.37\AA\]
Ionic Solids
Bonding in Metals and Semiconductors
Network and Amorphous Solids
Phase Diagrams
Exercise \(\PageIndex{6a}\)
A substance under normal conditions would rather sublime than melt if _____.
 Its critical point occurs at a pressure above atmospheric pressure
 Its critical point occurs at a temperature above room temperature
 Its critical temperature is above its normal boiling point
 Its triple point occurs at a pressure above atmospheric pressure
 Its triple point occurs at a pressure below atmospheric pressure
 Answer

d. Its triple point occurs at a pressure above atmospheric pressure
Exercise \(\PageIndex{6b}\)
If a phase diagram has a solidliquid phase boundary line that has a negative slope (leans to left) the substance,
 Can go from solid to liquid, within a small temperature range, via the application of pressure
 Cannot be liquefied above its triple point
 Cannot go from solid to liquid by application of pressure at any temperature
 Melts rather than sublimes under ordinary conditions
 Sublimes rather than melts under ordinary conditions
 Answer

a. Can go from solid to liquid, within a small temperature range, via the application of pressure
Exercise \(\PageIndex{6c}\)
The critical temperature, on a phase diagram, is _____.
 The temperature above which a gas cannot be liquefied
 The temperature at which all these states are in equilibrium
 The temperature below which a gas cannot be liquefied
 The temperature required to cause sublimation of a solid
 The temperature required to melt a solid
 Answer

a. The temperature above which a gas cannot be liquefied
Exercise \(\PageIndex{6d}\)
The point X represents
 the critical point, where a solid, liquid and vapor can coexist
 The critical point where the two fluid phases cannot be distinguished
 The triple point, where a solid, liquid and vapor can coexist
 The triple point, where the fluid phases cannot be separated
 Answer

c. The triple point, where a solid, liquid and vapor can coexist
Exercise \(\PageIndex{6e}\)
The point Y in the figure represents
 the critical point, where a solid, liquid and vapor can coexist
 The critical point where the two fluid phases cannot be distinguished
 The triple point, where a solid, liquid and vapor can coexist
 The triple point, where the fluid phases cannot be separated
 Answer

b. The critical point where the two fluid phases cannot be distinguished
Exercise \(\PageIndex{6f}\)
Region A of the figure represents
 solid
 liquid
 vapor
 none of the above
 Answer

a. solid
Exercise \(\PageIndex{6g}\)
Region B of the figure represents
 solid
 liquid
 vapor
 none of the above
 Answer

b. liquid
Exercise \(\PageIndex{6.8}\)
Region C of the figure represents
 solid
 liquid
 vapor
 none of the above
 Answer

c. vapor
Exercise \(\PageIndex{6h}\)
The negative slope between regions A and B of figure 12.7.1 indicates:
 the solid is denser than the liquid
 the liquid is denser than the solid
 the vapor is denser than the liquid
 the vapor is denser than the solid
 Answer

b. the liquid is denser than the solid
Exercise \(\PageIndex{6i}\)
Figure 12.7.1 is consistent with a phase diagram for which compound
 carbon dioxide
 sodium
 water
 carbon dioxide and water
 Answer

c. water
Exercise \(\PageIndex{6j}\)
The compound in figure 12.7.1 sublimes at pressures:
 greater than deg O°C
 Pressures greater than 1.0 atm
 pressures between 0.0060 and 1.00 atm
 pressures less than 0.0060 atm
 Answer

d. pressures less than 0.0060 atm
Exercise \(\PageIndex{6k}\)
Consider a 1 atm isobar for the compound in figure 12.7.1. Moving left to right in region A represents
 freezing
 melting
 heating supercooled ice
 none of the above
 Answer

c. heating supercooled ice
Exercise \(\PageIndex{6l}\)
Consider a 1 atm isobar for the compound in figure 12.7.1. Adding heat to a substance in region A causes it to warm, what happens when you reach the line between region A & B?
 it boils
 it melts
 it freezes
 it continues to warm up
 Answer

b. it melts
Exercise \(\PageIndex{6m}\)
Consider a 1 atm isobar for the compound in figure 12.7.1. Moving left to right in region B represents
 melting
 boiling
 heating liquid water
 cooling liquid water
 Answer

c. heating liquid water
Exercise \(\PageIndex{6n}\)
Consider a 1 atm isobar for the compound in figure 12.7.1. Adding heat to a substance in region B causes it to warm, what happens when you reach the line between region B & C?
 it continues to warm
 it condenses
 it boils
 all of the above
 Answer

c. it boils
Exercise \(\PageIndex{6o}\)
Consider a 1 atm isobar for the compound in figure 12.7.1. Moving left to right in region C represents
 cooling water
 heating liquid water
 heating ice
 heating steam
 Answer

d. heating steam
Exercise \(\PageIndex{6p}\)
At what pressure can liquid, solid and gaseous water coexist?
 218 atm
 1.00 atm
 0.0060 atm
 none of the above
 Answer

c. 0.0060 atm
Exercise \(\PageIndex{6q}\)
Consider a 50°C isotherm for the compound in Figure 12.7.2. Moving from region A to C represents
 Condensation then Freezing
 Freezing then Condensation
 Melting then Vaporizing
 Vaporizing then Melting
 Answer

c. Melting then Vaporizing
Exercise \(\PageIndex{6r}\)
Consider a 5 atm isobar for the compound in Figure 12.7.2. Moving from region C to A represents
 Condensation
 Deposition
 Sublimation
 Vaporization
 Answer

b. Deposition
Exercise \(\PageIndex{6s}\)
What phase would this compound be in if the pressure and temperature were at room conditions?
 Answer

This substance would be a gas
Exercise \(\PageIndex{6t}\)
The positive slope between regions A and B of figure 12.7.2 indicates:
 the solid is denser than the liquid
 the liquid is denser than the solid
 the vapor is denser than the liquid
 the vapor is denser than the solid
 Answer

a. the solid is denser than the liquid
Exercise \(\PageIndex{6u}\)
Figure 12.7.2 is consistent with a phase diagram for which compound
 Carbon dioxide
 Carbon dioxide and water
 Sodium
 Water
 Answer

a. Carbon dioxide