Chemistry

John E. Mcmurry, Robert C. Fay, Jordan Fantini

Chapter 10

Liquids, Solids, and Phase Changes - all with Video Answers

Educators

Chapter Questions

Problem 1

The dipole moment of $\mathrm{HF}$ is $\mu=1.83 \mathrm{D},$ and the bond length is 92 $\mathrm{pm} .$ Calculate the percent ionic character of the $\mathrm{H}-\mathrm{F}$ bond. Is $\mathrm{HF}$ more ionic or less ionic than $\mathrm{HCl}(\text { Worked Example } 10.1) ?$

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Problem 2

Tell which of the following compounds is likely to have a dipole moment, and show the direction of each.
$\begin{array}{llll}{\text { (a) } \mathrm{SF}_{6}} & {\text { (b) } \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}} & {\text { (c) } \mathrm{CHCl}_{3}} & {\text { (d) } \mathrm{CH}_{2} \mathrm{Cl}_{2}}\end{array}$

April Berlyoung

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Problem 3

The dipole moment of methanol is $\mu=1.70 \mathrm{D}$ . Use arrows to indicate the direction in which electrons are displaced.

April Berlyoung

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Problem 4

Methylamine, $\mathrm{CH}_{3} \mathrm{NH}_{2},$ is responsible for the odor of rotting fish. Look at the following electrostatic potential map of methylamine, and explain
the observed polarity.

April Berlyoung

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Problem 5

Of the substances Ar $\mathrm{Cl}_{2} \mathrm{CCl}_{4}$ and $\mathrm{HNO}_{3},$ which has:
(a) The largest dipole-dipole forces?
(b) The largest hydrogen-bond forces?
(c) The smallest dispersion forces?

April Berlyoung

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Problem 6

Consider the kinds of intermolecular forces present in the following
compounds, and rank the substances in likely order of increasing boiling point: $\mathrm{H}_{2} \mathrm{S}$ $(34 \mathrm{amu}), \mathrm{CH}_{3} \mathrm{OH}(32 \mathrm{amu}), \mathrm{C}_{2} \mathrm{H}_{6}(30 \mathrm{amu}), \mathrm{Ar}(40 \mathrm{amu})$

April Berlyoung

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Problem 7

Which of the following processes would you expect to have a positive value of $\Delta S,$ and which a negative value?
(a) Sublimation of dry ice
(b) Formation of dew on a cold morning
(c) Mixing of cigarette smoke with air in a closed room

April Berlyoung

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Problem 8

Chloroform $\left(\mathrm{CHCl}_{3}\right)$ has $\Delta H_{\mathrm{vap}}=29.2 \mathrm{kJ} / \mathrm{mol}$ and $\Delta S_{\mathrm{vap}}=$ 87.5 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol}) .$ What is the boiling point of chloroform in kelvin?

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Problem 9

The normal boiling point of benzene is $80.1^{\circ} \mathrm{C},$ and the heat of
vaporization is $\Delta H_{\mathrm{vap}}=30.7 \mathrm{kJ} / \mathrm{mol}$ . What is the boiling point of benzene in $^{\circ} \mathrm{C}$ on top of Mt. Everest, where $P=260 \mathrm{mm} \mathrm{Hg}$ ?

April Berlyoung

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Problem 10

Bromine has $P_{\text { vap }}=400 \mathrm{mm}$ Hg at $41.0^{\circ} \mathrm{C}$ and a normal boiling point of 331.9 $\mathrm{K}$ . What is the heat of vaporization, $\Delta H_{\mathrm{vap}},$ of bromine in $\mathrm{kJ} / \mathrm{mol} ?$

April Berlyoung

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Problem 11

How many atoms are in the following:
(a) One body-centered cubic unit cell of a metal
(b) One face-centered cubic unit cell of a metal

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Problem 12

Polonium metal crystallizes in a simple cubic arrangement, with the edge of a unit cell having a length $d=334 \mathrm{pm}$ . What is the radius in picometers of a polonium atom?

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Problem 13

What is the density of polonium (Problem 10.12$)$ in $\mathrm{g} / \mathrm{cm}^{3} ?$

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Problem 14

Imagine a tiled floor in the following pattern. Identify the smallest repeating unit, analogous to a two-dimensional unit cell.

Ahmed Ali

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Problem 15

Count the numbers of $+$ and $-$ charges in the CuCl and $\mathrm{BaCl}_{2}$ unit cells (Figure 10.25$)$ , and show that both cells are electrically neutral.

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Problem 16

Rhenium oxide crystallizes in the following cubic unit cell:
(a) How many rhenium atoms and how many oxygen atoms are in each unit cell?
(b) What is the formula of rhenium oxide?
(c) What is the oxidation state of rhenium?
(d) What is the geometry around each oxygen atom?
(e) What is the geometry around each rhenium atom?

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Problem 17

Look at the phase diagram of $\mathrm{CO}_{2}$ in Figure $10.29,$ and tell the minimum pressure in atmospheres at which liquid $\mathrm{CO}_{2}$ can exist.

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Problem 18

Look at the phase diagram of $\mathrm{CO}_{2}$ in Figure $10.29,$ and describe what happens to a CO_ sample when the following changes are made:
$\quad$ (a) The temperature is increased from $-100^{\circ} \mathrm{C}$ to $0^{\circ} \mathrm{C}$ at a constant pressure of 2 $\mathrm{atm} .$
(b) The pressure is reduced from 72 atm to 5.0 atm at a constant temperature of $30^{\circ} \mathrm{C}$ .
(c) The pressure is first increased from 3.5 $\mathrm{atm}$ to 76 $\mathrm{atm}$ at $-10^{\circ} \mathrm{C},$ and the temperature is then increased from $-10^{\circ} \mathrm{C}$ to $45^{\circ} \mathrm{C} .$

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Problem 19

Gallium metal has the following phase diagram (the pressure axis is not to scale). In the region shown, gallium has two different solid phases.
(a) Where on the diagram are the solid, liquid, and vapor regions?
(b) How many triple points does gallium have? Circle each on the diagram.
(c) At 1 atm pressure, which phase is more dense, solid or liquid? Explain.

Ahmed Ali

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Problem 20

How does an ionic liquid differ from a typical molecular liquid, such as water?

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Problem 21

What structural features do ionic liquids have that prevent them from forming solids easily?

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Problem 22

Ethyl acetate, $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3},$ is commonly used as a solvent and nail-polish remover. Look at the following electrostatic potential map of ethyl acetate, and explain the observed polarity.

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Problem 23

Identify each of the following kinds of packing:

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Problem 24

Zinc sulfide, or sphalerite, crystallizes in the following cubic unit cell:
(a) What kind of packing do the sulfide ions adopt?
(b) How many $\mathrm{S}^{2-}$ ions and how many $\mathrm{Zn}^{2+}$ ions are in the unit cell?

Ahmed Ali

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Problem 25

Perovskite, a mineral containing calcium, oxygen, and titanium, crystallizes in the following cubic unit cell:
(a) What is the formula of perovskite?
(b) What is the oxidation number of the titanium atom in perovskite?

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Problem 26

The phase diagram of a substance is shown below.
(a) Approximately what is the normal boiling point and what is the normal melting point of the substance?
(b) What is the physical state of the substance under the following conditions?
(i) $T=150 \mathrm{K}, P=0.5 \mathrm{atm}$
(ii) $T=325 \mathrm{K}, P=0.9 \mathrm{atm}$
(iii) $T=450 \mathrm{K}, P=265 \mathrm{atm}$

Ahmed Ali

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Problem 27

Boron nitride, BN, is a covalent network solid with a structure similar to that of graphite. Sketch a small portion of the boron nitride structure.

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Problem 28

Imagine a tiled floor made of square and octagonal tiles in the following pattern. Identify the smallest repeating unit, analogous to a unit cell.

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Problem 29

The following phase diagram of elemental carbon has three different solid phases in the region shown.
(a) Show where the solid, liquid, and vapor regions are on the diagram.
(b) How many triple points does carbon have? Circle each on the diagram.
(c) Graphite is the most stable solid phase under normal conditions. Identify the graphite phase on the diagram.
(d) On heating graphite to 2500 K at a pressure of 100,000 atm, it can be converted into diamond. Identify the diamond phase on the graph.
(e) Which phase is more dense, graphite or diamond? Explain.

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Problem 30

Acetic acid, the principal nonaqueous constituent of vinegar, exists as a dimer in the liquid phase, with two acetic acid molecules joined together by two hydrogen bonds. Sketch the structure you would expect this dimer to have.

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Problem 31

Assume that you have a liquid in a cylinder equipped with a movable piston. There is no air in the cylinder, the volume of space above the liquid is 200 mL, and the equilibrium vapor pressure above the liquid is 28.0 mm Hg. What is the equilibrium pressure above the liquid when the volume of space is decreased from 200 mL to 100 mL at constant temperature?

Ahmed Ali

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Problem 32

Why don’t all molecules with polar covalent bonds have dipole moments?

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Problem 33

What is the difference between London dispersion forces and dipole–dipole forces?

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Problem 34

What are the most important kinds of intermolecular forces present in each of the following substances?
$\begin{array}{ll}{\text { (a) Chloroform, } \mathrm{CHCl}_{3}} & {\text { (b) Oxygen, } \mathrm{O}_{2}} \\ {\text { (c) Polyethylene, } \mathrm{C}_{n} \mathrm{H}_{2 n+2}} & {\text { (d) Methanol, CH_{3} \mathrm { OH } }}\end{array}$

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Problem 35

Of the substances $X \mathrm{e}, \mathrm{CH}_{3} \mathrm{Cl}, \mathrm{HE}$ , which has:
(a) The smallest dipole-dipole forces?
(b) The largest hydrogen bond forces?
(c) The largest dispersion forces?

Ahmed Ali

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Problem 36

Methanol $\left(\mathrm{CH}_{3} \mathrm{OH} ; \mathrm{bp}=65^{\circ} \mathrm{C}\right)$ boils nearly $230^{\circ} \mathrm{C}$ higher than methane $\left(\mathrm{CH}_{4} ; \quad \mathrm{bp}=-164^{\circ} \mathrm{C}\right),$ but 1 -decanol $\left(\mathrm{C}_{10} \mathrm{H}_{21} \mathrm{OH} ; \mathrm{bp}=231^{\circ} \mathrm{C}\right)$ boils only $57^{\circ} \mathrm{C}$ higher than decane $\left(\mathrm{C}_{10} \mathrm{H}_{22} ; \mathrm{bp}=174^{\circ} \mathrm{C}\right) .$ Explain.

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Problem 37

Which substance in each of the following pairs would you expect to have larger dispersion forces?
(a) Ethane, $\mathrm{C}_{2} \mathrm{H}_{6},$ or octane, $\mathrm{C}_{8} \mathrm{H}_{18}$
(b) HCl or HI
(c) $\mathrm{H}_{2} \mathrm{O}$ or $\mathrm{H}_{2} \mathrm{Se}$

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Problem 38

Which of the following substances would you expect to have a nonzero dipole moment? Explain, and show the direction of each.
$\begin{array}{ll}{\text { (a) } \mathrm{Cl}_{2} \mathrm{O}} & {\text { (b) } \mathrm{XeF}_{4}} \\ {\text { (c) Chloroethane, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}} & {\text { (d) } \mathrm{BF}_{3}}\end{array}$

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Problem 39

Which of the following substances would you expect to have a nonzero dipole moment? Explain, and show the direction of each.
$\begin{array}{llll}{\text { (a) } \mathrm{NF}_{3}} & {\text { (b) } \mathrm{CH}_{3} \mathrm{NH}_{2}} & {\text { (c) } \mathrm{XeF}_{2}} & {\text { (d) } \mathrm{PCl}_{5}}\end{array}$

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Problem 40

The dipole moment of $\mathrm{BrCl}$ is 0.518 $\mathrm{D}$ and the distance between atoms is 213.9 $\mathrm{pm} .$ What is the percent ionic character of the BrCl bond?

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Problem 41

The dipole moment of ClF is 0.887 $\mathrm{D}$ and the distance between atoms is 162.8 $\mathrm{pm} .$ What is the percent ionic character of the ClF bond?

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Problem 42

Why is the dipole moment of $\mathrm{SO}_{2} 1.63 \mathrm{D},$ but that of $\mathrm{CO}_{2}$ is
zero?

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Problem 44

The class of ions $\mathrm{Pt} \mathrm{X}_{4}^{2-},$ where $\mathrm{X}$ is a halogen, has a square
planar geometry.
(a) Draw a structure for a $\mathrm{PtBr}_{2} \mathrm{Cl}_{2}^{2-}$ ion that has no dipole moment.
(b) Draw a structure for a $\mathrm{PtBr}_{2} \mathrm{Cl}_{2}^{2-}$ ion that has a dipole moment.

Ahmed Ali

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Problem 45

Of the two compounds $\mathrm{SiF}_{4}$ and $\mathrm{SF}_{4},$ which is polar and which is nonpolar?

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Problem 46

Draw three-dimensional structures of $\mathrm{PCl}_{3}$ and $\mathrm{PCl}_{5},$ and
then explain why one of the molecules has a dipole moment and one does not.

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Problem 46

Draw a picture showing how hydrogen bonding takes place between two ammonia molecules.

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Problem 47

$1,3$ -Propanediol can form intramolecular as well as intermolecular hydrogen bonds. Draw a structure of $1,3-$ propanediol showing an intramolecular hydrogen bond.

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Problem 48

A magnetized needle gently placed on the surface of a glass of water acts like a makeshift compass. Is it water's viscosity or its surface tension that keeps the needle on top?

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Problem 49

Water flows quickly through the narrow neck of a bottle, but maple syrup flows sluggishly. Is this different behavior due to a difference in viscosity or in surface tension for the liquids?

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Problem 50

Why is $\Delta H_{\text { vap }}$ usually larger than $\Delta H_{\text { fusion }} ?$

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Problem 51

Why is the heat of sublimation, $\Delta H_{\text { subl }}$ equal to the sum of $\Delta H_{\text { vap }}$ and $\Delta H_{\text { fusion }}$ at the same temperature?

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Problem 52

Iodine has $\mathrm{mp}=113.7^{\circ} \mathrm{C}$ and $\mathrm{bp}=184.4^{\circ} \mathrm{C} .$ What, if any, phase changes take place under the following conditions at 1.0 atm pressure?
(a) The temperature of a solid sample is held at $113.7^{\circ} \mathrm{C}$ while heat is added.
(b) The temperature of a sample is lowered from 452 $\mathrm{Kto}$ 389 $\mathrm{K}$

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Problem 52

Mercury has $m p=-38.8^{\circ} \mathrm{C}$ and $b p=356.6^{\circ} \mathrm{C} .$ What, if any, phase changes take place under the following conditions at 1.0 atm pressure?
(a) The temperature of a sample is raised from $-30^{\circ} \mathrm{C}$ to $365^{\circ} \mathrm{C} .$
(b) The temperature of a sample is lowered from 291 $\mathrm{K}$ to 238 $\mathrm{K}$ .
(c) The temperature of a sample is lowered from 638 $\mathrm{K}$ to 231 $\mathrm{K} .$

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Problem 54

Water at room temperature is placed in a flask connected by rubber tubing to a vacuum pump, and the pump is turned on. After several minutes, the volume of the water has decreased and what remains has turned to ice. Explain.

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Problem 55

Ether at room temperature is placed in a flask connected by a rubber tube to a vacuum pump, the pump is turned on, and the ether begins boiling. Explain.

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Problem 56

How much energy in kilojoules is needed to heat 5.00 $\mathrm{g}$ of ice from $-10.0^{\circ} \mathrm{C}$ to $30.0^{\circ} \mathrm{C} ?$ The heat of fusion of water is $6.01 \mathrm{kJ} / \mathrm{mol},$ and the molar heat capacity is 36.6 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$
for ice and 75.3 $\mathrm{J} /(\mathrm{K} \cdot \text { mol) for liquid water. }$

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Problem 57

How much energy in kilojoules is released when 15.3 $\mathrm{g}$ of steam at $115.0^{\circ} \mathrm{C}$ is condensed to give liquid water at $75.0^{\circ} \mathrm{C}$ ? The heat of vaporization of liquid water is 40.67 $\mathrm{kJ} / \mathrm{mol}$ , and the molar heat capacity is 75.3 $\mathrm{J} /(\mathrm{K} \cdot \text { mol) for the liquid }$ and 33.6 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ for the vapor.

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Problem 58

How much energy in kilojoules is released when 7.55 $\mathrm{g}$ of water at $33.5^{\circ} \mathrm{C}$ is cooled to $-10.0^{\circ} \mathrm{C} ?$ (See Problem 10.56 for the necessary data.)

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Problem 59

How much energy in kilojoules is released when 25.0 $\mathrm{g}$ of ethanol vapor at $93.0^{\circ} \mathrm{C}$ is cooled to $-10.0^{\circ} \mathrm{C} ?$ Ethanol has $\mathrm{mp}=-114.1^{\circ} \mathrm{C}, \quad \mathrm{bp}=78.3^{\circ} \mathrm{C}, \quad \Delta H_{\mathrm{vap}}=38.56 \mathrm{kJ} / \mathrm{mol}$ and $\Delta H_{\text { fusion }}=4.93 \mathrm{k} J / \mathrm{mol}$ . The molar heat capacity is 112.3 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ for the liquid and 65.6 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ for the vapor.

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Problem 60

Draw a molar heating curve for ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},$ similar to that shown for water in Figure 10.10 on page $360 .$ Begin with solid ethanol at its melting point, and raise the temperature to $100^{\circ} \mathrm{C}$ . The necessary data are given in Problem 10.59 .

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Problem 61

Draw a molar heating curve for sodium similar to that shown for water in Figure 10.10 . Begin with solid sodium at its melting point, and raise the temperature to $1000^{\circ} \mathrm{C}$ . The necessary data are $\mathrm{mp}=97.8^{\circ} \mathrm{C}, \quad \mathrm{bp}=883^{\circ} \mathrm{C}$ $\Delta H_{\mathrm{vap}}=89.6 \mathrm{kJ} / \mathrm{mol},$ and $\Delta H_{\mathrm{fusion}}=2.64 \mathrm{kJ} / \mathrm{mol}$ . Assume that the molar heat capacity is 20.8 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ for both liquid and vapor phases and does not change with temperature.

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Problem 62

Naphthalene, better known as "mothballs," has bp $=218^{\circ} \mathrm{C}$ and $\Delta H_{\text { vap }}=43.3 \mathrm{kJ} / \mathrm{mol}$ . What is the entropy of vaporization, $\Delta S_{\text { vap }}$ in $\mathrm{J} /(\mathrm{K} \cdot \text { mol) for naphthalene? }$

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Problem 63

What is the entropy of fusion, $\Delta S_{\text { fusion in }} \mathrm{J} /(\mathrm{K} \cdot \text { mol) for }$ sodium? The necessary data are given in Problem 10.61

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Problem 64

Carbon disulfide, $\mathrm{CS}_{2},$ has $P_{\text { vap }}=100 \mathrm{mm}$ Hg at $-5.1^{\circ} \mathrm{C}$ and a normal boiling point of $46.5^{\circ} \mathrm{C}$ . What is $\Delta H_{\text { vap }}$ for carbon disulfide in $\mathrm{kJ} / \mathrm{mol}$ ?

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Problem 65

The vapor pressure of $\mathrm{SiCl}_{4}$ is 100 $\mathrm{mm}$ $\mathrm{Hg}$ at $5.4^{\circ} \mathrm{C},$ and the normal boiling point is $57.7^{\circ} \mathrm{C} .$ What is $\Delta H_{\mathrm{vap}}$ for $\mathrm{SiCl}_{4}$ in $\mathrm{kJ} / \mathrm{mol} ?$

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Problem 66

What is the vapor pressure of $\mathrm{CS}_{2}$ in $\mathrm{mm}$ Hg at $20.0^{\circ} \mathrm{C}$ ?
(See Problem 10.64 )

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Problem 67

What is the vapor pressure of $\mathrm{SiCl}_{4}$ in mm Hg at 30.0 "C? (See Problem $10.65 . )$

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Problem 68

Dichloromethane, $\mathrm{CH}_{2} \mathrm{Cl}_{2},$ is an organic solvent used for removing caffeine from coffee beans. The following table gives the vapor pressure of dichloromethane at various
temperatures. Fill in the rest of the table, and use the data to plot curves of $P_{\text { vap }}$ versus $T$ and $\ln P_{\text { vap }}$ versus 1$/ T$

Ahmed Ali

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Problem 69

The following table gives the vapor pressure of mercury at various temperatures. Fill in the rest of the table, and use the data to plot curves of $P_{\text { vap }}$ versus $T$ and $\ln P_{\text { vap }}$ versus 1$/ T$

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Problem 70

Use the plot you made in Problem 10.68 to find a value in $\mathrm{kJ} / \mathrm{mol}$ for $\Delta H_{\mathrm{vap}}$ for dichloromethane.

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Problem 71

Use the plot you made in Problem 10.69 to find a value in $\mathrm{kJ} / \mathrm{mol}$ for $\Delta H_{\mathrm{vap}}$ for mercury. The normal boiling point of mercury is 630 $\mathrm{K}$

Ahmed Ali

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Problem 72

Choose any two temperatures and corresponding vapor pressures in the table given in Problem $10.68,$ and use those values to calculate $\Delta H_{\text { vap }}$ for dichloromethane in $\mathrm{kJ} / \mathrm{mol}$ . How does the value you calculated compare to the value you read from your plot in Problem 10.70$?$

Ahmed Ali

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Problem 73

Choose any two temperatures and corresponding vapor pressures in the table given in Problem $10.69,$ and use those values to calculate $\Delta H_{\text { vap }}$ for mercury in $\mathrm{kJ} /$ mol. How does he value you calculated compare to the value you read rom your plot in Problem 10.71$?$

Ahmed Ali

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Problem 74

List the four main classes of crystalline solids, and give a specific example of each.

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Problem 75

What kinds of particles are present in each of the four main classes of crystalline solids?

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Problem 76

Which of the substances $\mathrm{Na}_{3} \mathrm{PO}_{4}, \mathrm{CBr}_{4},$ rubber, Au, and
quartz best fits each of the following descriptions?
$\begin{array}{ll}{\text { (a) amorphous solid }} & {\text { (b) ionic solid }} \\ {\text { (c) molecular solid }} & {\text { (d) covalent network solid }} \\ {\text { (e) metallic solid }}\end{array}$

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Problem 77

Which of the substances diamond, Hg, Cl, glass, and KCl best fits each of the following descriptions?
$\begin{array}{ll}{\text { (a) amorphous solid }} & {\text { (b) ionic solid }} \\ {\text { (c) molecular solid }} & {\text { (d) covalent network solid }} \\ {\text { (e) metallic solid }}\end{array}$

Ahmed Ali

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Problem 78

Silicon carbide is very hard, has no known melting point, and diffracts $\mathrm{X}$ rays. What type of solid is it: amorphous, ionic, molecular, covalent network, or metallic?

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Problem 79

Arsenic tribromide melts at $31.1^{\circ} \mathrm{C},$ diffracts $X$ rays, and does not conduct electricity in either the solid or liquid phase. What type of solid is it: amorphous, ionic, molecular, covalent network, or metallic?

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Problem 80

Diffraction of $X$ rays with $\lambda=154.2 \mathrm{pm}$ occurred at an angle $\theta=22.5^{\circ}$ from a metal surface. What is the spacing (in pm) between the layers of atoms that diffracted the $X$ rays?

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Problem 81

Diffraction of $X$ rays with $\lambda=154.2 \mathrm{pm}$ occurred at an angle $\theta=76.84^{\circ}$ from a metal surface. What is the spacing $(\text { in pm) between layers of atoms that diffracted the } X \text { rays? }$

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Problem 82

What is a unit cell?

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Problem 83

Which of the four kinds of packing used by metals makes the most efficient use of space, and which makes the least efficient use?

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Problem 84

Copper crystallizes in a face-centered cubic unit cell with an edge length of 362 $\mathrm{pm}$ . What is the radius of a copper atom in picometers? What is the density of copper in $\mathrm{g} / \mathrm{cm}^{3} ?$

Ahmed Ali

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Problem 85

Lead crystallizes in a face-centered cubic unit cell with an edge length of 495 $\mathrm{pm}$ . What is the radius of a lead atom in picometers? What is the density of lead in $\mathrm{g} / \mathrm{cm}^{3} ?$

Ahmed Ali

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Problem 86

Aluminum has a density of 2.699 $\mathrm{g} / \mathrm{cm}^{3}$ and crystallizes with a face-centered cubic unit cell. What is the edge length of a unit cell in picometers?

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Problem 87

Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 317 $\mathrm{pm}$ . What is the length in picometers of a unit-cell diagonal that passes through the center atom?

Ronald Prasad

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Problem 88

In light of your answer to Problem $10.87,$ what is the radius in picometers of a tungsten atom?

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Problem 89

Sodium has a density of 0.971 $\mathrm{g} / \mathrm{cm}^{3}$ and crystallizes with a body-centered cubic unit cell. What is the radius of a sodium atom, and what is the edge length of the cell in
picometers?

Ahmed Ali

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Problem 90

Titanium metal has a density of 4.506 $\mathrm{g} / \mathrm{cm}^{3}$ and an atomic radius of 144.8 $\mathrm{pm} .$ In what cubic unit cell does titanium crystallize?

Ahmed Ali

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Problem 91

Calcium metal has a density of 1.55 $\mathrm{g} / \mathrm{cm}^{3}$ and crystallizes in a cubic unit cell with an edge length of 558.2 $\mathrm{pm} .$
(a) How many Ca atoms are in one unit cell?
(b) In which of the three cubic unit cells does calcium crystallize?

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Problem 92

Sodium hydride, NaH, crystallizes in a face-centered cubic unit cell similar to that of NaCl (Figure $10.24 ;$ page 376$)$ How many $Na^{+}$ ions touch each $\mathrm{H}^{-}$ ion, and how many $\mathrm{H}^{-}$ ions touch each $Na^{+}$ ion?

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Problem 93

Cesium chloride crystallizes in a cubic unit cell with $\mathrm{Cl}^{-}$ ions at the corners and a $\mathrm{Cs}^{+}$ ion in the center. Count the numbers of $+$ and $-$ charges, and show that the unit cell is electrically neutral.

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Problem 94

If the edge length of an NaH unit cell is $488 \mathrm{pm},$ what is the length in picometers of an Na - H bond? (See Problem 10.92 )

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Problem 95

The edge length of a CsCl unit cell (Problem 10.93 ) is 412.3 $\mathrm{pm}$ . What is the length in picometers of the Cs - Cl bond? If the ionic radius of a Cl- ion is $181 \mathrm{pm},$ what is the
ionic radius in picometers of a Cs $^{+}$ ion?

Ahmed Ali

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Problem 96

Look at the phase diagram of $\mathrm{CO}_{2}$ in Figure $10.29,$ and tell what phases are present under the following conditions:
(a) $T=-60^{\circ} \mathrm{C}, P=0.75 \mathrm{atm}$
(b) $T=-35^{\circ} \mathrm{C}, P=18.6 \mathrm{atm}$
(c) $T=-80^{\circ} \mathrm{C}, P=5.42 \mathrm{atm}$

Ahmed Ali

Numerade Educator

Problem 97

Look at the phase diagram of $\mathrm{H}_{2} \mathrm{O}$ in Figure 10.28 , and tell what happens to an $\mathrm{H}_{2} \mathrm{O}$ sample when the following changes are made:
(a) The temperature is reduced from $48^{\circ} \mathrm{C}$ to $-4.4^{\circ} \mathrm{C}$ at a constant pressure of 6.5 $\mathrm{atm}$ .
(b) The pressure is increased from 85 atm to 226 atm at a constant temperature of $380^{\circ} \mathrm{C}$

Ahmed Ali

Numerade Educator

Problem 98

Bromine has $T_{\mathrm{t}}=-7.3^{\circ} \mathrm{C}, P_{\mathrm{t}}=44 \mathrm{mm}$ Hg, $T_{\mathrm{c}}=315^{\circ} \mathrm{C}$ and $P_{\mathrm{c}}=102 \mathrm{atm} .$ The density of the liquid is 3.1 $\mathrm{g} / \mathrm{cm}^{3}$ , and the density of the solid is 3.4 $\mathrm{g} / \mathrm{cm}^{3} .$ Sketch a phase diagram for bromine, and label all points of interest.

Ahmed Ali

Numerade Educator

Problem 99

Oxygen has $T_{\mathrm{t}}=54.3 \mathrm{K}, P_{\mathrm{t}}=1.14 \mathrm{mm} \mathrm{Hg}, T_{\mathrm{c}}=154.6 \mathrm{K}$ and $P_{\mathrm{c}}=49.77 \mathrm{atm} .$ The density of the liquid is $1.14 \mathrm{g} / \mathrm{cm}^{3},$ and the density of the solid is 1.33 $\mathrm{g} / \mathrm{cm}^{3} .$ Sketch a phase diagram for oxygen, and label all points of interest.

Ahmed Ali

Numerade Educator

Problem 100

Refer to the bromine phase diagram you sketched in Problem $10.98,$ and tell what phases are present under the following conditions:
(a) $T=-10^{\circ} \mathrm{C}, P=0.0075$ atm
(b) $T=25^{\circ} \mathrm{C}, P=16$ atm

Ahmed Ali

Numerade Educator

Problem 101

Refer to the oxygen phase diagram you sketched in Problem $10.99,$ and tell what phases are present under the following conditions:
(a) $T=-210^{\circ} \mathrm{C}, P=1.5 \mathrm{atm}$
(b) $T=-100^{\circ} \mathrm{C}, P=66 \mathrm{atm}$

Ahmed Ali

Numerade Educator

Problem 102

Does solid oxygen (Problem 10.99$)$ melt when pressure is applied, as water does? Explain.

Ahmed Ali

Numerade Educator

Problem 103

Assume that you have samples of the following three gases at $25^{\circ} \mathrm{C} .$ Which of the three can be liquefied by applying pressure, and which cannot? Explain.
Ammonia: $T_{\mathrm{c}}=132.5^{\circ} \mathrm{C}$ and $P_{\mathrm{c}}=112.5 \mathrm{atm}$
Methane: $T_{\mathrm{c}}=-82.1^{\circ} \mathrm{C}$ and $P_{\mathrm{c}}=45.8 \mathrm{atm}$
Sulfur dioxide: $T_{\mathrm{c}}=157.8^{\circ} \mathrm{C}$ and $P_{\mathrm{c}}=77.7 \mathrm{atm}$

Ahmed Ali

Numerade Educator

Problem 104

Benzene has a melting point of $5.53^{\circ} \mathrm{C}$ and a boiling point of $80.09^{\circ} \mathrm{C}$ at atmospheric pressure. Its density is 0.8787 $\mathrm{g} / \mathrm{cm}^{3}$ when liquid and 0.899 $\mathrm{g} / \mathrm{cm}^{3}$ when solid; it has $T_{\mathrm{c}}=289.01^{\circ} \mathrm{C}, P_{\mathrm{c}}=48.34 \mathrm{atm}, T_{\mathrm{t}}=5.52^{\circ} \mathrm{C},$ and $P_{\mathrm{t}}=0.0473 \mathrm{atm} .$ Starting from a point at 200 $\mathrm{K}$ and $66.5 \mathrm{atm},$ trace the following path on a phase diagram:
(1) First, increase $T$ to 585 $\mathrm{K}$ while keeping $P$ constant.
(2) Next, decrease $P$ to 38.5 atm while keeping $T$ constant.
(3) Then, decrease $T$ to 278.66 $\mathrm{K}$ while keeping $P$ constant.
(4) Finally, decrease $P$ to 0.0025 atm while keeping $T$ constant.
What is your starting phase, and what is your final phase?

Lottie Adams

Numerade Educator

Problem 105

Refer to the oxygen phase diagram you drew in Problem 10.99 , and trace the following path starting from a point at 0.0011 atm and $-225^{\circ} \mathrm{C} :$
(1) First, increase $P$ to 35 atm while keeping $T$ constant.
(2) Next, increase $T$ to $-150^{\circ} \mathrm{C}$ while keeping $P$ constant.
(3) Then, decrease $P$ to 1.0 atm while keeping $T$ constant.
(4) Finally, decrease $T$ to $-215^{\circ} \mathrm{C}$ while keeping $P$ constant.
What is your starting phase, and what is your final phase?

Ahmed Ali

Numerade Educator

Problem 106

How many phase transitions did you pass through in Problem $10.104,$ and what are they?

Ahmed Ali

Numerade Educator

Problem 107

What phase transitions did you pass through in Problem 10.105$?$

Ahmed Ali

Numerade Educator

Problem 108

Fluorine is more electronegative than chlorine (Figure 7.4$)$ yet fluoromethane $\left(\mathrm{CH}_{3} \mathrm{F} ; \mu=1.86 \mathrm{D}\right)$ has a smaller dipole moment than chloromethane $\left(\mathrm{CH}_{3} \mathrm{Cl} ; \mu=1.90 \mathrm{D}\right) .$ Explain.

Ahmed Ali

Numerade Educator

Problem 109

What is the atomic radius in picometers of an argon atom if solid argon has a density of 1.623 $\mathrm{g} / \mathrm{cm}^{3}$ and crystallizes at low temperature in a face-centered cubic unit cell?

Ahmed Ali

Numerade Educator

Problem 110

Mercury has $m p=-38.8^{\circ} \mathrm{C},$ a molar heat capacity of 27.9 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ for the liquid and 28.2 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ for the
solid, and $\Delta H_{\mathrm{fusion}}=2.33 \mathrm{kJ} / \mathrm{mol}$ . Assuming that the heat
capacities don't change with temperature, how much energy in kilojoules is needed to heat 7.50 $\mathrm{g}$ of Hg from a temperature of $-50.0^{\circ} \mathrm{C}$ to $+50.0^{\circ} \mathrm{C} ?$

Ahmed Ali

Numerade Educator

Problem 111

Silicon carbide, $\mathrm{SiC},$ is a covalent network solid with a structure similar to that of diamond. Sketch a small portion of the SiC structure.

Ahmed Ali

Numerade Educator

Problem 112

In Denver, the Mile-High City, water boils at $95^{\circ} \mathrm{C}$ . What is atmospheric pressure in atmospheres in Denver? $\Delta H_{\text { vap }}$ for $\mathrm{H}_{2} \mathrm{O}$ is 40.67 $\mathrm{kJ} / \mathrm{mol} .$

Ahmed Ali

Numerade Educator

Problem 113

There are three compounds with the formula $\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Br}_{2} .$ Two
of the three have dipole moments, and one does not. Draw the structures of all three compounds, and tell which has no dipole moment.

Ahmed Ali

Numerade Educator

Problem 114

If a protein can be induced to crystallize, its molecular structure can be determined by X-ray crystallography. Protein crystals, though solid, contain a large amount of water molecules along with the protein. The protein chicken egg-white lysozyme, for instance, crystallizes with a unit cell having angles of $90^{\circ}$ and with edge lengths of $7.9 \times 10^{3} \mathrm{pm}, 7.9 \times 10^{3} \mathrm{pm},$ and $3.8 \times 10^{3} \mathrm{pm} .$ There are eight molecules in the unit cell. If the lysozyme molecule has a molecular mass of $1.44 \times 10^{4}$ amu and a density of $1.35 \mathrm{g} / \mathrm{cm}^{3},$ what percent of the unit cell is occupied by the protein?

Ahmed Ali

Numerade Educator

Problem 115

The molecular structure of a scorpion toxin, a small protein, was determined by X-ray crystallography. The unit cell has angles of $90^{\circ},$ contains 16 molecules, and has a volume of $1.019 \times 10^{2} \mathrm{nm}^{3} .$ If the molecular mass of the toxin is 3336 amu and the density is about $1.35 \mathrm{g} / \mathrm{cm}^{3},$ what percent of the unit cell is occupied by protein?

Ahmed Ali

Numerade Educator

Problem 116

Magnesium metal has $\Delta H_{\text { fusion }}=9.037 \mathrm{kJ} / \mathrm{mol}$ and
$\Delta S_{\text { fusion }}=9.79 \mathrm{J} /\left(\mathrm{K} \cdot \text { mol). What is the melting point in }^{\circ} \mathrm{C}\right.$ of magnesium?

Ahmed Ali

Numerade Educator

Problem 117

Titanium tetrachloride, $\mathrm{TiCl}_{4}$ , has a melting point of $-23.2^{\circ} \mathrm{C}$ and has $\Delta H_{\mathrm{fusion}}=9.37 \mathrm{kJ} / \mathrm{mol.}$ What is the entropy of fusion, $\Delta S_{\text { fusion }}$ in $\mathrm{J} /(\mathrm{K} \cdot \text { mol), for TiCl_? }$

Ahmed Ali

Numerade Educator

Problem 118

Dichlorodifluoromethane, $\mathrm{CCl}_{2} \mathrm{F}_{2},$ one of the chlorofluorocarbon refrigerants responsible for destroying part of the Earth's ozone layer, has $P_{\mathrm{vap}}=40.0 \mathrm{mm} \mathrm{Hg}$ at $-81.6^{\circ} \mathrm{C}$ and $P_{\mathrm{vap}}=400 \mathrm{mm} \mathrm{Hg}$ at $-43.9^{\circ} \mathrm{C} .$ What is the normal boiling point of $\mathrm{CCl}_{2} \mathrm{F}_{2}$ in $^{\circ} \mathrm{C} ?$

Ahmed Ali

Numerade Educator

Problem 119

The chlorofluorocarbon refrigerant trichlorofluoromethane, $\mathrm{CCl}_{3} \mathrm{F},$ has $P_{\mathrm{vap}}=100.0 \mathrm{mm} \mathrm{Hg}$ at $-23^{\circ} \mathrm{C}$ and $\Delta H_{\mathrm{vap}}=$ 24.77 $\mathrm{kJ} / \mathrm{mol} .$
(a) What is the normal boiling point of trichlorofluoromethane in $^{\circ} \mathrm{C}$ ?
(b) What is $\Delta S_{\text { vap }}$ for trichlorofluoromethane?

Ahmed Ali

Numerade Educator

Problem 120

Nitrous oxide, $\mathrm{N}_{2} \mathrm{O},$ occasionally used as an anesthetic by dentists under the name "laughing gas," has $P_{\text { vap }}=$ 100 $\mathrm{mm}$ Hg at $-110.3^{\circ} \mathrm{C}$ and a normal boiling point of $-88.5^{\circ} \mathrm{C} .$ What is the heat of vaporization of nitrous oxide in $\mathrm{kJ} / \mathrm{mol} ?$

Ahmed Ali

Numerade Educator

Problem 121

Acetone, a common laboratory solvent, has $\Delta H_{\mathrm{vap}}=29.1 \mathrm{kJ} / \mathrm{mol}$ and a normal boiling point of $56.1^{\circ} \mathrm{C}$ . At what temperature
in ' $\mathrm{C}$ does acetone have $P_{\mathrm{vap}}=$ 105 $\mathrm{mm} \mathrm{Hg}$ ?

Ahmed Ali

Numerade Educator

Problem 122

Use the following data to sketch a phase diagram for krypton: $T_{t}=-169^{\circ} \mathrm{C}, P_{t}=133 \mathrm{mm}$ Hg, $T_{\mathrm{c}}=-63^{\circ} \mathrm{C}$ $P_{\mathrm{c}}=54 \mathrm{atm}, \mathrm{mp}=-156.6^{\circ} \mathrm{C}, \mathrm{bp}=-152.3^{\circ} \mathrm{C} .$ The density of solid krypton is $2.8 \mathrm{g} / \mathrm{cm}^{3},$ and the density of the liquid is 2.4 $\mathrm{g} / \mathrm{cm}^{3} .$ Can a sample of gaseous krypton at room temperature be liquefied by raising the pressure?

Ahmed Ali

Numerade Educator

Problem 123

What is the physical phase of krypton (Problem 10.122$)$ under the following conditions:
(a) $P=5.3 \mathrm{atm}, T=-153^{\circ} \mathrm{C}$
(b) $P=65 \mathrm{atm}, T=250 \mathrm{K}$

Ahmed Ali

Numerade Educator

Problem 124

Calculate the percent volume occupied by the spheres in a body-centered cubic unit cell.

Ahmed Ali

Numerade Educator

Problem 125

Iron crystallizes in a body-centered cubic unit cell with an edge length of 287 $\mathrm{pm}$ . What is the radius of an iron atom in picometers?

Ahmed Ali

Numerade Educator

Problem 126

Iron metal has a density of 7.86 $\mathrm{g} / \mathrm{cm}^{3}$ and a molar mass of 55.85 $\mathrm{g} .$ Use this information together with the data in Problem 10.125 to calculate a value for Avogadro's number.

Ahmed Ali

Numerade Educator

Problem 127

Silver metal crystallizes in a face-centered cubic unit cell with an edge length of 408 $\mathrm{pm}$ . The molar mass of silver is $107.9 \mathrm{g} / \mathrm{mol},$ and its density is 10.50 $\mathrm{g} / \mathrm{cm}^{3} .$ Use these data to calculate a value for Avogadro's number.

Ahmed Ali

Numerade Educator

Problem 128

A drawing of the NaCl unit cell is shown in Figure 10.24 .
(a) What is the edge length in picometers of the NaCl unit cell? The ionic radius of $\mathrm{Na}^{+}$ is $97 \mathrm{pm},$ and the ionic radius of $\mathrm{Cl}^{-}$ is 181 $\mathrm{pm} .$
(b) What is the density of NaCl in g/ $\mathrm{cm}^{3}$ ?

Ahmed Ali

Numerade Educator

Problem 129

Niobium oxide crystallizes in the following cubic unit cell:
(a) How many niobium atoms and how many oxygen atoms are in each unit cell?
(b) What is the formula of niobium oxide?
(c) What is the oxidation state of niobium?

Ahmed Ali

Numerade Educator

Problem 130

For each of the following substances, identify the inter molecular force or forces that predominate. Using your knowledge of the relative strengths of the various forces, rank the substances in order of their normal boiling points.
$\mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{F}_{2}, \mathrm{H}_{2} \mathrm{O}, \mathrm{Br}_{2}, \mathrm{ICl}, \mathrm{NaCl}$

Ahmed Ali

Numerade Educator

Problem 131

One form of silver telluride $\left(\mathrm{Ag}_{2} \text { Te) crystallizes with a }\right.$ cubic unit cell and a density of 7.70 $\mathrm{g} / \mathrm{cm}^{3} . \mathrm{X}$ -ray crystalography shows that the edge of the cubic unit cell has a length of 529 $\mathrm{pm}$ . How many Ag atoms are in the unit
cell?

Ahmed Ali

Numerade Educator

Problem 132

Substance $X$ has a vapor pressure of 100 $\mathrm{mm}$ Hg at its triple point $\left(48^{\circ} \mathrm{C}\right) .$ When 1 $\mathrm{mol}$ of $\mathrm{X}$ is heated at 1 atm pressure with a constant rate of heat input, the following heating curve is obtained:
(a) Sketch the phase diagram for $X,$ including labels for different phases, triple point, melting point, and boiling point.
(b) For each of the following, choose which phase of $X$ (solid, liquid, or gas) fits the description:
(i) Is the most dense at $50^{\circ} \mathrm{C}$
(ii) Is the least dense at $50^{\circ} \mathrm{C}$
(iii) Has the greatest specific heat
(iv) Predominates at $80^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$
(v) Can have a vapor pressure of 20 $\mathrm{mm} \mathrm{Hg}$

Ronald Prasad

Numerade Educator

Problem 133

Look up thermodynamic data for ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ in
Appendix $\mathrm{B},$ estimate the normal boiling point of ethanol, and calculate the vapor pressure of ethanol at $25^{\circ} \mathrm{C} .$

Farhana Sharmin

Farhana Sharmin

Numerade Educator

Problem 134

The mineral magnetite is an iron oxide ore that has a density of 5.20 $\mathrm{g} / \mathrm{cm}^{3} .$ At high temperature, magnetite reacts with carbon monoxide to yield iron metal and carbon dioxide. When 2.660 $\mathrm{g}$ of magnetite is allowed to react with sufficient carbon monoxide, the $\mathrm{CO}_{2}$ product is found to have a volume of 1.136 $\mathrm{L}$ at 298 $\mathrm{K}$ and 751 $\mathrm{mm}$ Hg pressure.
(a) What mass of iron in grams is formed in the reaction?
(b) What is the formula of magnetite?
(c) Magnetite has a somewhat complicated cubic unit cell with an edge length of 839 $\mathrm{pm}$ . How many Fe and O atoms are present in each unit cell?

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 135

A group 3 $\mathrm{A}$ metal has a density of 2.70 $\mathrm{g} / \mathrm{cm}^{3}$ and a cubic
unit cell with an edge length of 404 $\mathrm{pm}$ . Reaction of a 1.07 $\mathrm{cm}^{3}$ chunk of the metal with an excess of hydrochloric acid gives a colorless gas that occupies 4.00 $\mathrm{L}$ at $23.0^{\circ} \mathrm{C}$ and a pressure of 740 $\mathrm{mm}$ Hg.
(a) Identify the metal.
(b) Is the unit cell primitive, body-centered, or face-centered?
(c) What is the atomic radius of the metal atom in picometers?

Matthew Confer

Numerade Educator

Problem 136

A cube-shaped crystal of an alkali metal, 1.62 $\mathrm{mm}$ on an edge, was vaporized in a 500.0 $\mathrm{mL}$ evacuated flask. The resulting vapor pressure was 12.5 $\mathrm{mm} \mathrm{Hg}$ at $802^{\circ} \mathrm{C} .$ The structure of the solid metal is known to be body-centered cubic.
(a) What is the atomic radius of the metal atom in picometers?
(b) Use the data in Figure 5.18 on page 177 to identify the alkali metal.
(c) What are the densities of the solid and the vapor in $\mathrm{g} / \mathrm{cm}^{3}$ ?

Jake Rempel

Numerade Educator

Problem 137

Assume that 1.588 g of an alkali metal undergoes complete reaction with the amount of gaseous halogen contained in a 0.500 L flask at 298 $\mathrm{K}$ and 755 $\mathrm{mm}$ Hg pressure. In the reaction, 22.83 $\mathrm{kJ}$ is released $(\Delta H=-22.83 \mathrm{kJ})$ ). The product, a binary ionic compound, crystallizes in a unit cell with anions in a face-centered cubic arrangement and with cations centered along each edge between anions. In addition, there is a cation in the center of the cube.
(a) What is the identity of the alkali metal?
(b) The edge length of the unit cell is 535 $\mathrm{pm}$ . Find the radius of the alkali metal cation from the data in Figure 6.1 on page $189,$ and then calculate the radius of the halide anion. Identify the anion from the data in Figure 6.2 on page 189 .
(c) Sketch a space-filling, head-on view of the unit cell, labeling the ions. Are the anions in contact with one another?
(d) What is the density of the compound in $\mathrm{g} / \mathrm{cm}^{3}$ ?
(e) What is the standard heat of formation for the compound?

Susan Hallstrom

Susan Hallstrom

Numerade Educator