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Chemistry LibreTexts

12: Solids

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    12.1: Crystal Lattices and Unit Cells

    Exercise \(\PageIndex{1.1}\)

    Crystalline solids differ from amorphous solids by _____.

    1. Substantial intermolecular attractive forces
    2. A long-range repeating pattern of atoms, molecules, or ions
    3. Atoms, molecule, or ions that are close together
    4. Much larger atoms, molecules, or ions
    5. No orderly structure
    Answer

    b. A long-range repeating pattern of atoms, molecules, or ions 

    Exercise \(\PageIndex{1.2}\)

    ______ is a unit cell with all sides the same length and all angles equal to 90° that has lattice points only at the corners.

    1. Body-centered cubic
    2. Face-centered cubic
    3. Monoclinic
    4. Primitive cubic
    5. Spherical cubic
    Answer

    d. Primitive cubic

    Exercise \(\PageIndex{1.3}\)

    What is the fraction that each corner atom takes up in a face-centered cubic unit cell?

    1. 1
    2. 1/2
    3. 1/4
    4. 1/8
    5. 1/16
    Answer

    d. 1/8

    Exercise \(\PageIndex{1.4}\)

    A face-centered cubic unit cell contains how many atoms?

    Answer

    Add texts here. Do not delete this text first.

    Exercise \(\PageIndex{1.5}\)

    Based on sodium chloride structure, which of the following cannot form a solid lattice?

    1. NaBr
    2. LiF
    3. RbI
    4. CuO
    5. CuCl2
    Answer

    e. CuCl2

    Exercise \(\PageIndex{1.6}\)

     What type of solid is held together by dispersion, dipole-dipole or hydrogen bonds?

    1. Ionic
    2. metallic
    3. molecular
    4. covalent network
    Answer

    c. molecular

    Exercise \(\PageIndex{1.7}\)

    What type of compounds are held together by covalent bonds?

    1. ionic
    2. metallic
    3. molecular
    4. covalent network
    Answer

    d. covalent network

    Exercise \(\PageIndex{1.8}\)

    Solid Iodine is a ____type of substance:

    1. ionic lattice
    2. metallic
    3. molecular
    4. covalent network
    Answer

    c. molecular

    Exercise \(\PageIndex{1.9}\)

    Diamond lattices are a ___ type of substance

    1. ionic crystal
    2. metallic
    3. molecular
    4. network covalent
    Answer

    d. network covalent

    Exercise \(\PageIndex{1.10}\)

    How many basic crystal systems are there?

    1. 3
    2. 4
    3. 6
    4. 7
    Answer

    d. 7

    Exercise \(\PageIndex{1.11}\)

    Which is not a type of cubic unit cell?

    1. tetragonal
    2. body-centered
    3. face centered
    4. primitive
    Answer

    a. tetragonal

    Exercise \(\PageIndex{1.12}\)

    Which type of unit cell is the least efficient in packing?

    1. primitive
    2. body-centered
    3. face-centered
    4. none of the above
    Answer

    a. primitive

    Exercise \(\PageIndex{1.13}\)

    Which type of unit cell is most efficient in packing?

    1. primitive
    2. body-centered
    3. face-centered
    4. none of the above
    Answer

    c. face-centered

    Exercise \(\PageIndex{1.14}\)

    Primitive, Face-Centered & Body-Centered Cubic Cells have respective coordination numbers of

    1. 1,2,4
    2. 2,4,6
    3. 6,8,12
    4. 6,12,8
    Answer

    d. 6,12,8

    Exercise \(\PageIndex{1.15}\)

    What is the unit cell of CsCl, when it crystallizes in a unit cell that contains a Cs+ ion at the center of a cube and a Cl- ion at each corner?

    1. Amorphous
    2. Body-centered cubic
    3. Close packed
    4. Face-centered cubic
    5. Primitive cubic
    Answer

    e. Primitive cubic

    Exercise \(\PageIndex{1.16}\)

    In a face-centered cubic cell, what portion of the volume of each atom or ion on the face of a unit is within the unit cell? The atoms or ions in corners?

    Answer

    faces 1/2 atom is within the unit cell

    corners 1/8 atom is within the unit cell

    Exercise \(\PageIndex{1.17}\)

    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 \(\PageIndex{1.18}\)

    Potassium metal crystallizes in a body-centered 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 \(\PageIndex{1.19}\)

    What is the radius of a copper atom in Angstroms if the length of the unit cell edge is 5.34Å? Copper has a face-centered 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 \(\PageIndex{1.20}\)

    Silver has a density of 10.5g/cm3 and forms an FCC structure. What is the atomic radius of silver in Angstroms? Assume that nearest-neighbor atoms contact each other.

    Answer
    1. Calculate volume of unit cell

    \[\left ( \frac{4\,atoms}{unit\,cell} \right )\left ( \frac{1\,mol}{6.022*10^{23}\,atoms} \right )\left ( \frac{107.87\,g}{1\,mol} \right )\left ( \frac{1\,cm^{3}}{10.5\,g} \right )=6.82*10^{-23}\,cm^{3}\]

    1. Calculate length of unit cell

    \[V=l^{3}\]

    \[l=\sqrt[3]{V}\]

    \[l=\sqrt[3]{V}=\sqrt[3]{6.82*10^{-23}cm^{3}}=4.09*10^{-8}cm*\left ( \frac{10^{10}\AA }{100cm} \right )=4.09\AA\]

    1. 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 \(\PageIndex{1.21}\)

    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
    1. Calculate volume of unit cell

    \[\left ( \frac{1 atom}{unit cell} \right )\left ( \frac{1 mol}{6.022*10^{23}atoms} \right )\left ( \frac{207.2g}{1mol} \right )\left ( \frac{1mL}{11.07g} \right )=3.11*10^{-23}cm^{3}\]

    1. Calculate length of unit cell

    \[V=l^{3}\]

    \[l=\sqrt[3]{V}\]

    \[l=\sqrt[3]{V}=\sqrt[3]{3.11*10^{-23}cm^{3}}=3.14*10^{-8}cm*\left ( \frac{10^{10}\AA }{100cm} \right )=3.14\AA\]

    1. Calculate radius of unit cell

    \[l=2r\]

    \[r=\frac{l}{2}=\frac{3.14\AA }{2}=1.57\AA\] 

    Exercise \(\PageIndex{1.22}\)

    Tungsten has a density of 19.25g/cm3 and forms a BCC structure. What is the atomic radius of tungsten in Angstroms?

    Answer
    1. Calculate volume of unit cell

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

    1. Calculate length of unit cell

    \[V=l^{3}\]

    \[l=\sqrt[3]{V}\]

    \[l=\sqrt[3]{V}=\sqrt[3]{3.17*10^{-23}cm^{3}}=3.17*10^{-8}cm*\left ( \frac{10^{10}\AA }{100cm} \right )=3.17\AA=a\]

    1. 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}\

    \[c=\sqrt{a^{2}+b^{2}}=\sqrt{(3.17)^{2}+(4.48)^{2}}=5.49\AA\]

    \[c=4r\]

    \[r=\frac{c}{4}=\frac{5.49\AA }{4}=1.37\AA\]

    12.7: Phase Diagrams

    Exercise \(\PageIndex{7.1}\)

    A substance under normal conditions would rather sublime than melt if _____.

    1. Its critical point occurs at a pressure above atmospheric pressure
    2. Its critical point occurs at a temperature above room temperature
    3. Its critical temperature is above its normal boiling point
    4. Its triple point occurs at a pressure above atmospheric pressure
    5. Its triple point occurs at a pressure below atmospheric pressure
    Answer

    d. Its triple point occurs at a pressure above atmospheric pressure 

    Exercise \(\PageIndex{7.2}\)

    If a phase diagram has a solid-liquid phase boundary line that has a negative slope (leans to left) the substance,

    1. Can go from solid to liquid, within a small temperature range, via the application of pressure
    2. Cannot be liquefied above its triple point
    3. Cannot go from solid to liquid by application of pressure at any temperature
    4. Melts rather than sublimes under ordinary conditions
    5. 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 \(\PageIndex{7.3}\)

    The critical temperature, on a phase diagram, is _____.

    1. The temperature above which a gas cannot be liquefied
    2. The temperature at which all these states are in equilibrium
    3. The temperature below which a gas cannot be liquefied
    4. The temperature required to cause sublimation of a solid
    5. The temperature required to melt a solid
    Answer

    a. The temperature above which a gas cannot be liquefied

    clipboard_ebb47ef99197c192f4b8666e4b1173979.png


    Figure 12.7.1: Use this figure to answer the following questions.

    Exercise \(\PageIndex{7.4}\)

    The point X represents

    1. the critical point, where a solid, liquid and vapor can coexist
    2. The critical point where the two fluid phases cannot be distinguished
    3. The triple point, where a solid, liquid and vapor can coexist
    4. The triple point, where the fluid phases cannot be separated
    Answer

    c. The triple point, where a solid, liquid and vapor can coexist

    Exercise \(\PageIndex{7.5}\)

    The point Y in the figure represents

    1. the critical point, where a solid, liquid and vapor can coexist
    2. The critical point where the two fluid phases cannot be distinguished
    3. The triple point, where a solid, liquid and vapor can coexist
    4. The triple point, where the fluid phases cannot be separated
    Answer

    b. The critical point where the two fluid phases cannot be distinguished

    Exercise \(\PageIndex{7.6}\)

    Region A of the figure represents

    1. solid
    2. liquid
    3. vapor
    4. none of the above
    Answer

    a. solid

    Exercise \(\PageIndex{7.7}\)

    Region B of the figure represents

    1. solid
    2. liquid
    3. vapor
    4. none of the above
    Answer

    b. liquid

    Exercise \(\PageIndex{7.8}\)

    Region C of the figure represents

    1. solid
    2. liquid
    3. vapor
    4. none of the above
    Answer

    c. vapor

    Exercise \(\PageIndex{7.9}\)

    The negative slope between regions A and B of figure 12.7.1 indicates:

    1. the solid is denser than the liquid
    2. the liquid is denser than the solid
    3. the vapor is denser than the liquid
    4. the vapor is denser than the solid
    Answer

    b. the liquid is denser than the solid

    Exercise \(\PageIndex{7.10}\)

    Figure 12.7.1 is consistent with a phase diagram for which compound

    1. carbon dioxide
    2. sodium
    3. water
    4. carbon dioxide and water
    Answer

    c. water

    Exercise \(\PageIndex{7.11}\)

    The compound in figure 12.7.1 sublimes at pressures:

    1. greater than deg O°C
    2. Pressures greater than 1.0 atm
    3. pressures between 0.0060 and 1.00 atm
    4. pressures less than 0.0060 atm
    Answer

    d. pressures less than 0.0060 atm

    Exercise \(\PageIndex{7.12}\)

    Consider a 1 atm isobar for the compound in figure 12.7.1. Moving left to right in region A represents

    1. freezing
    2. melting
    3. heating supercooled ice
    4. none of the above
    Answer

    c. heating supercooled ice

    Exercise \(\PageIndex{7.13}\)

    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?

    1. it boils
    2. it melts
    3. it freezes
    4. it continues to warm up
    Answer

    b. it melts

    Exercise \(\PageIndex{7.14}\)

    Consider a 1 atm isobar for the compound in figure 12.7.1. Moving left to right in region B represents

    1. melting
    2. boiling
    3. heating liquid water
    4. cooling liquid water
    Answer

    c. heating liquid water

    Exercise \(\PageIndex{7.15}\)

    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?

    1. it continues to warm
    2. it condenses
    3. it boils
    4. one of the above
    Answer

    c. it boils

    Exercise \(\PageIndex{7.16}\)

    Consider a 1 atm isobar for the compound in figure 12.7.1. Moving left to right in region C represents

    1. cooling water
    2. heating liquid water
    3. heating ice
    4. heating steam
    Answer

    d. heating steam

    Exercise \(\PageIndex{7.17}\)

    At what pressure can liquid, solid and gaseous water coexist?

    1. 218 atm
    2. 1.00 atm
    3. 0.0060 atm
    4. none of the above
    Answer

    c. 0.0060 atm

    clipboard_e82b8879ed5cfc25159ff55e759dc0c24.png
    Figure 12.7.2: Use this phase diagram to answer the following questions.

    Exercise \(\PageIndex{7.18}\)

    Consider a -50°C isotherm for the compound in Figure 12.7.2. Moving from region A to C represents

    1. Condensation then Freezing
    2. Freezing then Condensation
    3. Melting then Vaporizing
    4. Vaporizing then Melting
    Answer

    c. Melting then Vaporizing

    Exercise \(\PageIndex{7.19}\)

    Consider a 5 atm isobar for the compound in Figure 12.7.2. Moving from region C to A represents

    1. Condensation
    2. Deposition
    3. Sublimation
    4. Vaporization
    Answer

    c. Sublimation

    Exercise \(\PageIndex{7.20}\)

    What phase would this compound be in if the pressure and temperature were at room conditions?

    Answer

    This substance would be a gas

    Exercise \(\PageIndex{7.21}\)

    The positive slope between regions A and B of figure 12.7.2 indicates:

    1. the solid is denser than the liquid
    2. the liquid is denser than the solid
    3. the vapor is denser than the liquid
    4. the vapor is denser than the solid
    Answer

    a. the solid is denser than the liquid

    Exercise \(\PageIndex{7.22}\)

    Figure 12.7.2 is consistent with a phase diagram for which compound

    1. Carbon dioxide
    2. Carbon dioxide and water
    3. Sodium
    4. Water
    Answer

    a. Carbon dioxide