Chemistry: The Molecular Nature of Matter and Change

Martin S. Silberberg, Patricia G. Amateis

Chapter 12

Intermolecular Forces: Liquids, Solids, and Phase Changes - all with Video Answers

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Chapter Questions

Problem 1

How does the energy of attraction between particles compare with their energy of motion in a gas and in a solid? As part of your answer, identify two macroscopic properties that differ between a gas and a solid.

Alyssa Iryami

Alyssa Iryami

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Problem 2

(a) Why are gases more easily compressed than liquids?
(b) Why do liquids have a greater ability to flow than solids?

Cathy Geisel

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Problem 3

What type of forces, intramolecular or intermolecular:
(a) Prevent ice cubes from adopting the shape of their container?
(b) Are overcome when ice melts?
(c) Are overcome when liquid water is vaporized?
(d) Are overcome when gaseous water is converted to hydrogen gas and oxygen gas?

Alyssa Iryami

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Problem 4

(a) Why is the heat of fusion $\left(\Delta H_{\text { fus }}\right)$ of a substance smaller than its heat of vaporization $\left(\Delta H_{\mathrm{vap}}\right) ?$
(b) Why is the heat of sublimation $\left(\Delta H_{\text { subl }}\right)$ of a substance greater than its $\Delta H_{\text { vap }} ?$
(c) At a given temperature and pressure, how does the magnitude of the heat of vaporization of a substance compare with that of its heat of condensation?

Cathy Geisel

Numerade Educator

Problem 5

Which forces are intramolecular and which intermolecular?
(a) Those preventing oil from evaporating at room temperature
(b) Those preventing butter from melting in a refrigerator
(c) Those allowing silver to tarnish
(d) Those preventing $\mathrm{O}_{2}$ in air from forming $\mathrm{O}$ atoms

Alyssa Iryami

Numerade Educator

Problem 6

Which forces are intramolecular and which intermolecular?
(a) Those allowing fog to form on a cool, humid evening
(b) Those allowing water to form when $\mathrm{H}_{2}$ is sparked
(c) Those allowing liquid benzene to crystallize when cooled
(d) Those responsible for the low boiling point of hexane

Cathy Geisel

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Problem 7

Name the phase change in each of these events: (a) Dew appears on a lawn in the morning. (b) Icicles change into liquid water. (c) Wet clothes dry on a summer day.

Alyssa Iryami

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Problem 8

Name the phase change in each of these events: (a) A diamond film forms on a surface from gaseous carbon atoms in a vacuum. (b) Mothballs in a bureau drawer disappear over time. (c) Molten iron from a blast furnace is cast into ingots (pigs).

Cathy Geisel

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Problem 9

Liquid propane, a widely used fuel, is produced by compressing gaseous propane. During the process, approximately 15 kJ of energy is released for each mole of gas liquefied. Where does this energy come from?

Alyssa Iryami

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Problem 10

Many heat-sensitive and oxygen-sensitive solids, such as camphor, are purified by warming under vacuum. The solid vaporizes directly, and the vapor crystallizes on a cool surface. What phase changes are involved in this method?

Cathy Geisel

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Problem 11

Describe the changes (if any) in potential energy and in kinetic energy among the molecules when gaseous $\mathrm{PCl}_{3}$ condenses to a liquid at a fixed temperature.

Alyssa Iryami

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Problem 12

When benzene is at its melting point, two processes occur simultaneously and balance each other. Describe these processes on the macroscopic and molecular levels.

Cathy Geisel

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Problem 13

Liquid hexane $\left(b p=69^{\circ} \mathrm{C}\right)$ is placed in a closed container at room temperature. At first, the pressure of the vapor phase increases, but after a short time, it stops changing. Why?

Stephen Ho

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Problem 14

Explain the effect of strong intermolecular forces on each of these parameters: (a) critical temperature; (b) boiling point; (c) vapor pressure; (d) heat of vaporization.

Cathy Geisel

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Problem 15

Match each numbered point in the phase diagram for compound Q with the correct molecular scene below:

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Harini Repaka

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Problem 16

A liquid is in equilibrium with its vapor in a closed vessel at a fixed temperature. The vessel is connected by a stopcock to an evacuated vessel. When the stopcock is opened, will the final pressure of the vapor be different from the initial value if (a) some liquid remains; (b) all the liquid is first removed? Explain

Cathy Geisel

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Problem 17

The phase diagram for substance A has a solid-liquid line with a positive slope, and that for substance B has a solid-liquid line with a negative slope. What macroscopic property can distinguish A from B?

Stephen Ho

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Problem 18

Why does water vapor at $100^{\circ} \mathrm{C}$ cause a more severe burn than liquid water at $100^{\circ} \mathrm{C} ?$

Cathy Geisel

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Problem 19

From the data below, calculate the total heat (in $\mathrm{J}$ needed to convert 22.00 g of ice at $-6.00^{\circ} \mathrm{C}$ to liquid water at $0.500^{\circ} \mathrm{C} :$ $\mathrm{mp}$ at 1 atm: $0.0^{\circ} \mathrm{C}$ $\Delta H_{\mathrm{fus}}^{\circ} : \quad 6.02 \mathrm{kJ} / \mathrm{mol}$ $c_{\text { liquid }} : \qquad 4.21 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C} \quad c_{\mathrm{solid}} : 2.09 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$

Stephen Ho

Numerade Educator

Problem 20

From the data below, calculate the total heat (in $\mathrm{J} )$ needed to convert 0.333 mol of gaseous ethanol at $300^{\circ} \mathrm{C}$ and 1 atm to liquid ethanol at $25.0^{\circ} \mathrm{C}$ and 1 atm:
bp at $1 \mathrm{atm} : \quad 78.5^{\circ} \mathrm{C} \quad \Delta H_{\mathrm{vap}}^{\circ} : 40.5 \mathrm{kJ} / \mathrm{mol}$ $c_{\mathrm{gas}} : \quad 1.43 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C} \quad c_{\mathrm{liquid}} : \quad 2.45 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$

Cathy Geisel

Numerade Educator

Problem 21

A liquid has a $\Delta H_{\text { vap }}^{\circ}$ of 35.5 $\mathrm{kJ} / \mathrm{mol}$ and a boiling point of $122^{\circ} \mathrm{C}$ at 1.00 atm. What is its vapor pressure at $113^{\circ} \mathrm{C} ?$

Stephen Ho

Numerade Educator

Problem 22

Diethyl ether has a $\Delta H_{\mathrm{vap}}^{\circ}$ of 29.1 $\mathrm{kJ} / \mathrm{mol}$ and a vapor pressure of 0.703 atm at $25.0^{\circ} \mathrm{C} .$ What is its vapor pressure at $95.0^{\circ} \mathrm{C} ?$

Freddie Montague

Freddie Montague

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Problem 23

What is the $\Delta H_{\text { vap }}^{\circ}$ of a liquid that has a vapor pressure of 621 torr at $85.2^{\circ} \mathrm{C}$ and a boiling point of $95.6^{\circ} \mathrm{C}$ at 1 $\mathrm{atm} ?$

Stephen Ho

Numerade Educator

Problem 24

Methane $\left(\mathrm{CH}_{4}\right)$ has a boiling point of $-164^{\circ} \mathrm{C}$ at 1 $\mathrm{atm}$ and a vapor pressure of 42.8 atm at $-100^{\circ} \mathrm{C}$ . What is the heat of
vaporization of $\mathrm{CH}_{4} ?$

Freddie Montague

Freddie Montague

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Problem 25

Use these data to draw a qualitative phase diagram for ethylene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right) .$ Is $\mathrm{C}_{2} \mathrm{H}_{4}(s)$ more or less dense than $\mathrm{C}_{2} \mathrm{H}_{4}(l) ?$
$$
\begin{array}{ll}{\text { bp at } 1 \mathrm{atm} :} & {-103.7^{\circ} \mathrm{C}} \\ {\mathrm{mp} \text { at } 1 \mathrm{atm} :} & {-169.16^{\circ} \mathrm{C}}\end{array}
$$
$$
\begin{array}{l}{\text { Critical point: } \quad 9.9^{\circ} \mathrm{C} \text { and } 50.5 \text { atm }} \\ {\text { Triple point: }-169.17^{\circ} \mathrm{C} \text { and } 1.20 \times 10^{-3} \mathrm{atm}}\end{array}
$$

Stephen Ho

Numerade Educator

Problem 26

Use these data to draw a qualitative phase diagram for $\mathrm{H}_{2}$ Does $\mathrm{H}_{2}$ sublime at 0.05 atm? Explain.
$$
\begin{array}{ll}{\mathrm{mp} \text { at } 1 \mathrm{atm} :} & {13.96 \mathrm{K}} \\ {\mathrm{bp} \text { at } 1 \mathrm{atm} :} & {20.39 \mathrm{K}} \\ {\text { Triple point: }} & {13.95 \mathrm{K} \text { and } 0.07 \mathrm{atm}} \\ {\text { Critical point: }} & {33.2 \mathrm{K} \text { and } 13.0 \mathrm{atm}} \\ {\text { Vapor pressure of solid at } 10 \mathrm{K} :} & {0.001 \mathrm{atm}}\end{array}
$$

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Harini Repaka

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Problem 27

The phase diagram for sulfur is shown below.
(a) Give a set of conditions under which it is possible to sublime the rhombic form of solid sulfur.
(b) Describe the phase changes that a sample of sulfur undergoes at 1 atm when it is heated from $90^{\circ} \mathrm{C}$ to $450^{\circ} \mathrm{C}$

HR

Harini Repaka

Numerade Educator

Problem 28

The phase diagram for xenon is shown below.
(a) What phase is xenon in at room temperature and pressure?
(b) Describe the phase changes that a sample of xenon undergoes at $-115^{5} \mathrm{C}$ as it is compressed from 0.5 atm to 25 $\mathrm{atm}$ . (The critical pressure of xenon is 58 $\mathrm{atm} .$ )

Cathy Geisel

Numerade Educator

Problem 29

Sulfur dioxide is produced in enormous amounts for sulfuric acid production. It melts at $-73^{\circ} \mathrm{C}$ and boils at $-10 .^{\circ} \mathrm{C} .$ Its $\Delta H_{\mathrm{fus}}^{\circ}$ is 8.619 $\mathrm{kJ} / \mathrm{mol}$ and its $\Delta H_{\mathrm{vap}}^{\circ}$ is 25.73 $\mathrm{kJ} / \mathrm{mol} .$ The specific heat capacities of the liquid and gas are 0.995 $\mathrm{J} / \mathrm{g} \cdot \mathrm{K}$ and 0.622 $\mathrm{J} / \mathrm{g} \cdot \mathrm{K}$ , respectively. How much heat is required to convert 2.500 $\mathrm{kg}$ of solid $\mathrm{SO}_{2}$ at the melting point to a gas at $60 .^{\circ} \mathrm{C} ?$

Stephen Ho

Numerade Educator

Problem 30

Butane is a common fuel used in cigarette lighters and camping stoves. Normally supplied in metal containers under pressure, the fuel exists as a mixture of liquid and gas, so high temperatures may cause the container to explode. At $25.0^{\circ} \mathrm{C}$ , the vapor pressure of butane is 2.3 atm. What is the pressure in the container at $135^{\circ} \mathrm{C}\left(\Delta H_{\mathrm{vap}}^{\circ}=24.3 \mathrm{kJ} / \mathrm{mol}\right) ?$

Freddie Montague

Freddie Montague

Numerade Educator

Problem 31

Use Figure $12.10, \mathrm{p} .466,$ to answer the following:
(a) Carbon dioxide is sold in steel cylinders under pressures of approximately 20 $\mathrm{atm}$ . Is there liquid $\mathrm{CO}_{2}$ in the cylinder at room temperature $\left(\sim 20^{\circ} \mathrm{C}\right) ?$ At $40^{\circ} \mathrm{C} ? \mathrm{At}-40^{\circ} \mathrm{C} ? \mathrm{At}-120^{\circ} \mathrm{C} ?$
(b) Carbon dioxide is also sold as solid chunks, called dry ice, in insulated containers. If the chunks are warmed by leaving them in an open container at room temperature, will they melt?
(c) If a container is nearly filled with dry ice and then sealed and warmed to room temperature, will the dry ice melt?
(d) If dry ice is compressed at a temperature below its triple point, will it melt?

Rashmi Sinha

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Problem 32

Why are covalent bonds typically much stronger than intermolecular forces?

Cathy Geisel

Numerade Educator

Problem 33

(a) Name the type of force depicted in each scene below.
(b) Rank the forces in order of increasing strength.

Rashmi Sinha

Numerade Educator

Problem 34

Oxygen and selenium are members of Group 6 $\mathrm{A}(16) .$ Water forms $\mathrm{H}$ bonds, but $\mathrm{H}_{2}$ Se does not. Explain.

Cathy Geisel

Numerade Educator

Problem 35

In solid $\mathrm{I}_{2},$ is the distance between the two I nuclei of one $\mathrm{I}_{2}$ molecule longer or shorter than the distance between two I nuclei of adjacent $\mathrm{I}_{2}$ molecules? Explain.

Stephen Ho

Numerade Educator

Problem 36

Polar molecules exhibit dipole-dipole forces. Do they also exhibit dispersion forces? Explain.

Cathy Geisel

Numerade Educator

Problem 37

Distinguish between polarizability and polarity. How does each influence intermolecular forces?

Stephen Ho

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Problem 38

How can one nonpolar molecule induce a dipole in a nearby nonpolar molecule?

Cathy Geisel

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Problem 39

What is the strongest interparticle force in each substance?
(a) $\mathrm{CH}_{3} \mathrm{OH}$
(b) $\mathrm{CCl}_{4}$
(c) $\mathrm{Cl}_{2}$

Alyssa Iryami

Numerade Educator

Problem 40

What is the strongest interparticle force in each substance?
(a) $\mathrm{H}_{3} \mathrm{PO}_{4}$
(b) $\mathrm{SO}_{2}$
(c) $\mathrm{MgCl}_{2}$

Cathy Geisel

Numerade Educator

Problem 41

What is the strongest interparticle force in each substance?
(a) $\mathrm{CH}_{3} \mathrm{Cl}$
(b) $\mathrm{CH}_{3} \mathrm{CH}_{3}$
$(\mathrm{c}) \mathrm{NH}_{3}$

Alyssa Iryami

Numerade Educator

Problem 42

What is the strongest interparticle force in each substance?
(a) Kr
(b) BrF
(c) $\mathrm{H}_{2} \mathrm{SO}_{4}$

Cathy Geisel

Numerade Educator

Problem 43

Which member of each pair of compounds forms intermolecular H bonds? Draw the H-bonded structures in each case:
(a) $\mathrm{CH}_{3} \mathrm{CHCH}_{3}$ or $\mathrm{CH}_{3} \mathrm{SCH}_{3}$ $\mathrm{OH}$
(b) HF or HBr

Alyssa Iryami

Numerade Educator

Problem 44

Which member of each pair of compounds forms intermolecular H bonds? Draw the H-bonded structures in each case:
(a) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}$ or $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N}$
(b) HOCH_ $\mathrm{CH}_{2} \mathrm{OH}$ or $\mathrm{FCH}_{2} \mathrm{CH}_{2} \mathrm{F}$

Freddie Montague

Freddie Montague

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Problem 45

Which forces oppose vaporization of each substance?
(a) Hexane
(b) Water
(c) $\mathrm{SiCl}_{4}$

Alyssa Iryami

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Problem 46

Which forces oppose vaporization of each substance?
(a) $\mathrm{Br}_{2}$
(b) $\mathrm{SbH}_{3}$
(c) $\mathrm{CH}_{3} \mathrm{NH}_{2}$

Cathy Geisel

Numerade Educator

Problem 47

Which has the greater polarizability? Explain.
(a) $\mathrm{Br}^{-}$ or $\mathrm{I}^{-}$
(b) $\mathrm{CH}_{2}=\mathrm{CH}_{2}$ or $\mathrm{CH}_{3}-\mathrm{CH}_{3}$
(c) $\mathrm{H}_{2} \mathrm{O}$ or $\mathrm{H}_{2} \mathrm{Se}$

Stephen Ho

Numerade Educator

Problem 48

Which has the greater polarizability? Explain.
(a) $\mathrm{Ca}^{2+}$ or Ca
(b) $\mathrm{CH}_{3} \mathrm{CH}_{3}$ or $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$
(c) $\mathrm{CCl}_{4}$ or $\mathrm{CF}_{4}$

Cathy Geisel

Numerade Educator

Problem 49

Which member in each pair of liquids has the higher vapor pressure at a given temperature? Explain
(a) $\mathrm{C}_{2} \mathrm{H}_{6}$ or $\mathrm{C}_{4} \mathrm{H}_{10}$
(b) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$ or $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{F}$
(c) $\mathrm{NH}_{3}$ or $\mathrm{PH}_{3}$

Stephen Ho

Numerade Educator

Problem 50

Which member in each pair of liquids has the lower vapor pressure at a given temperature? Explain.
(a) HOCH_ $\mathrm{CH}_{2} \mathrm{OH}$ or $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$
(b) $\mathrm{CH}_{3} \mathrm{COOH}$ or $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{O}$
(c) HF or HCl

Freddie Montague

Freddie Montague

Numerade Educator

Problem 51

Which substance has the lower boiling point? Explain.
(a) LiCl or HCl
(b) $\mathrm{NH}_{3}$ or $\mathrm{PH}_{3}$
(c) $X e$ or $I_{2}$

Alyssa Iryami

Numerade Educator

Problem 52

Which substance has the higher boiling point? Explain
(a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$ or $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$
(b) $\mathrm{NO}$ or $\mathrm{N}_{2}$
(c) $\mathrm{H}_{2} \mathrm{S}$ or $\mathrm{H}_{2} \mathrm{Te}$

Cathy Geisel

Numerade Educator

Problem 53

Which substance has the lower boiling point? Explain
(a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}$ or $\mathrm{CH}_{2}-\mathrm{CH}_{2}$ $\mathrm{CH}_{2}-\mathrm{CH}_{2}$
(b) NaBr or $\mathrm{PBr}_{3}$
(c) $\mathrm{H}_{2} \mathrm{O}$ or $\mathrm{HBr}$

Stephen Ho

Numerade Educator

Problem 54

Which substance has the higher boiling point? Explain
(a) $\mathrm{CH}_{3} \mathrm{OH}$ or $\mathrm{CH}_{3} \mathrm{CH}_{3}$
(b) FNO or CINO
(c)

Freddie Montague

Freddie Montague

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Problem 55

For pairs of molecules in the gas phase, average H-bond dissociation energies are 17 $\mathrm{kJ} / \mathrm{mol}$ for $\mathrm{NH}_{3}, 22 \mathrm{kJ} / \mathrm{mol}$ for $\mathrm{H}_{2} \mathrm{O}$ and 29 $\mathrm{kJ} / \mathrm{mol}$ for $\mathrm{HF}$ . Explain this increase in H-bond strength.

Stephen Ho

Numerade Educator

Problem 56

Dispersion forces are the only intermolecular forces present in motor oil, yet it has a high boiling point. Explain.

Cathy Geisel

Numerade Educator

Problem 57

Why does the antifreeze ingredient ethylene glycol $\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} ; \quad \mathcal{M}=62.07 \mathrm{g} / \mathrm{mol}\right)$ have a boiling point of $197.6^{\circ} \mathrm{C},$ whereas propanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} ; \mathcal{M}=60.09 \mathrm{g} / \mathrm{mol}\right)$
$\mathrm{a}$ compound with a similar molar mass, has a boiling point of only
$97.4^{\circ} \mathrm{C} ?$

Stephen Ho

Numerade Educator

Problem 58

Before the phenomenon of surface tension was understood, physicists described the surface of water as being covered with a skin. What causes this skinlike phenomenon?

Cathy Geisel

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Problem 59

Small, equal-sized drops of oil, water, and mercury lie on a waxed floor. How does each liquid behave? Explain.

Stephen Ho

Numerade Educator

Problem 60

Why does an aqueous solution of ethanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$ have a lower surface tension than water?

Cathy Geisel

Numerade Educator

Problem 61

Why are units of energy per area $\left(\mathrm{J} / \mathrm{m}^{2}\right)$ used for surface tension values?

Victoria Jones

Numerade Educator

Problem 62

Does the strength of the intermolecular forces in a liquid change as the liquid is heated? Explain. Why does liquid viscosity decrease with rising temperature?

Cathy Geisel

Numerade Educator

Problem 63

Rank the following in order of increasing surface tension at a given temperature, and explain your ranking:
(a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$
(b) $\mathrm{HOCH}_{2} \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}$
(c) HOCH_ $_{2} \mathrm{CH}_{2} \mathrm{OH}$

Stephen Ho

Numerade Educator

Problem 64

Rank the following in order of decreasing surface tension at a given temperature, and explain your ranking
(a) $\mathrm{CH}_{3} \mathrm{OH}$
(b) $\mathrm{CH}_{3} \mathrm{CH}_{3}$
(c) $\mathrm{H}_{2} \mathrm{C}=\mathrm{O}$

Cathy Geisel

Numerade Educator

Problem 65

Rank the compounds in Problem 12.63 in order of decreasing viscosity at a given temperature; explain your ranking.

Rashmi Sinha

Numerade Educator

Problem 66

Rank the compounds in Problem 12.64 in order of increasing viscosity at a given temperature; explain your ranking.

Freddie Montague

Freddie Montague

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Problem 67

Soil vapor extraction (SVE) is used to remove volatile organic pollutants, such as chlorinated solvents, from soil at hazardous waste sites. Vent wells are drilled, and a vacuum pump is applied to the subsurface. (a) How does this remove pollutants? (b) Why does heating combined with SVE speed the process?

Stephen Ho

Numerade Educator

Problem 68

Use Figure $12.2, \mathrm{p} .457$ to answer the following: (a) Does it take more heat to melt 12.0 $\mathrm{g}$ of $\mathrm{CH}_{4}$ or 12.0 $\mathrm{g}$ of $\mathrm{Hg} ?$ (b) Does
it take more heat to vaporize 12.0 $\mathrm{g}$ of $\mathrm{CH}_{4}$ or 12.0 $\mathrm{g}$ of $\mathrm{Hg} ?$ (c) What is the principal intermolecular force in each sample?

Freddie Montague

Freddie Montague

Numerade Educator

Problem 69

Pentanol $\left(\mathrm{C}_{5} \mathrm{H}_{11}, \mathrm{OH} ; \quad \mathscr{M}=88.15 \mathrm{g} / \mathrm{mol}\right)$ has nearly the same molar mass as hexane $\left(\mathrm{C}_{6} \mathrm{H}_{14} ; \mathscr{M}=86.17 \mathrm{g} / \mathrm{mol}\right)$ but is more than 12 times as viscous at $20^{\circ} \mathrm{C}$ . Explain.

Stephen Ho

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Problem 70

For what types of substances is water a good solvent? For what types is it a poor solvent? Explain

Cathy Geisel

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Problem 71

A water molecule can engage in as many as four H bonds. Explain.

Stephen Ho

Numerade Educator

Problem 72

Warm-blooded animals have a narrow range of body temperature because their bodies have a high water content. Explain.

Cathy Geisel

Numerade Educator

Problem 73

What property of water keeps plant debris on the surface of lakes and ponds? What is the ecological significance of this?

Stephen Ho

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Problem 74

A drooping plant can be made upright by watering the ground around it. Explain.

Cathy Geisel

Numerade Educator

Problem 75

Describe the molecular basis of the property of water responsible for the presence of ice on the surface of a frozen lake.

Stephen Ho

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Problem 76

Describe in molecular terms what occurs when ice melts

Cathy Geisel

Numerade Educator

Problem 77

What is the difference between an amorphous solid and a crystalline solid on the macroscopic and molecular levels? Give an example of each.

Rashmi Sinha

Numerade Educator

Problem 78

How are a solid’s unit cell and crystal structure related?

Cathy Geisel

Numerade Educator

Problem 79

For structures consisting of identical atoms, how many atoms are contained in the simple, body-centered, and facecentered cubic unit cells? Explain how you obtained the values.

Rashmi Sinha

Numerade Educator

Problem 80

An element has a crystal structure in which the width of the cubic unit cell equals the diameter of an atom. What type of unit cell does it have?

Cathy Geisel

Numerade Educator

Problem 81

What specific difference in the positioning of spheres gives a crystal structure based on the face-centered cubic unit cell less empty space than one based on the body-centered cubic unit cell?

Rashmi Sinha

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Problem 82

Both solid Kr and solid Cu consist of individual atoms. Why do their physical properties differ so much?

Cathy Geisel

Numerade Educator

Problem 83

What is the energy gap in band theory? Compare its size in superconductors, conductors, semiconductors, and insulators.

Stephen Ho

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Problem 84

Predict the effect (if any) of an increase in temperature on the electrical conductivity of (a) a conductor; (b) a semiconductor; (c) an insulator.

Freddie Montague

Freddie Montague

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Problem 85

Besides the type of unit cell, what information is needed to find the density of a solid consisting of identical atoms?

Stephen Ho

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Problem 86

What type of crystal lattice does each metal form? (The number of atoms per unit cell is given in parentheses.)
(a) $\mathrm{Ni}(4)$
(b) $\operatorname{Cr}(2)$
(c) $\mathrm{Ca}(4)$

Cathy Geisel

Numerade Educator

Problem 87

What is the number of atoms per unit cell for each metal?
(a) Polonium, Po
(b) Manganese, Mn
(c) Silver, Ag

Rashmi Sinha

Numerade Educator

Problem 88

Calcium crystallizes through cubic closest packing. If the atomic radius of calcium is 197 pm, find the density of the solid.

Freddie Montague

Freddie Montague

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Problem 89

Chromium adopts the body-centered cubic unit cell in its crystal structure. If the density of chromium is $7.14 \mathrm{g} / \mathrm{cm}^{3},$ find its atomic radius.

Stephen Ho

Numerade Educator

Problem 90

When cadmium oxide reacts to form cadmium selenide, a change in unit cell occurs, as depicted below:
(a) What is the change in unit cell?
(b) Does the coordination number of cadmium change? Explain.

Rashmi Sinha

Numerade Educator

Problem 91

As molten iron cools to 1674 K, it adopts one type of cubic unit cell; then, as the temperature drops below 1181 K, it changes to another, as depicted below:
(a) What is the change in unit cell?
(b) Which crystal structure has the greater packing efficiency?

Stephen Ho

Numerade Educator

Problem 92

Potassium adopts the body-centered cubic unit cell in its crystal structure. If the atomic radius of potassium is 227 pm, find the edge length of the unit cell.

Freddie Montague

Freddie Montague

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Problem 93

Lead adopts the face-centered cubic unit cell in its crystal structure. If the edge length of the unit cell is 495 pm, find the atomic radius of lead.

Stephen Ho

Numerade Educator

Problem 94

Of the five major types of crystalline solid, which does each of the following form, and why: (a) Ni; (b) $\mathrm{F}_{2} ;(\mathrm{c}) \mathrm{CH}_{3} \mathrm{OH} ;$ (d) $\mathrm{Sn} ;(\mathrm{e}) \mathrm{Si} ;(\mathrm{f}) \mathrm{Xe} ?$

Cathy Geisel

Numerade Educator

Problem 95

Of the five major types of crystalline solid, which does each of the following form, and why: (a) SiC; (b) $\mathrm{Na}_{2} \mathrm{SO}_{4} ;(\mathrm{c}) \mathrm{SF}_{6}$ ; (d) cholesterol $\left(\mathrm{C}_{27} \mathrm{H}_{45} \mathrm{OH}\right) ;(\mathrm{e}) \mathrm{KCl} ;(\mathrm{f}) \mathrm{BN}$ ?

Rashmi Sinha

Numerade Educator

Problem 96

Zinc oxide adopts the zinc blende crystal structure (Figure P12.96). How many $\mathrm{Zn}^{2+}$ ions are in the ZnO unit cell?

Cathy Geisel

Numerade Educator

Problem 97

Calcium sulfide adopts the sodium chloride crystal structure (Figure $\mathrm{P} 12.97 ) .$ How many $\mathrm{S}^{2-}$ ions are in the CaS unit cell?

Rashmi Sinha

Numerade Educator

Problem 98

Zinc selenide (ZnSe) crystallizes in the zinc blende structure (see Figure $\mathrm{P} 12.96 )$ and has a density of 5.42 $\mathrm{g} / \mathrm{cm}^{3}$
(a) How many Zn and Se ions are in each unit cell?
(b) What is the mass of a unit cell?
(c) What is the volume of a unit cell?
(d) What is the edge length of a unit cell?

Freddie Montague

Freddie Montague

Numerade Educator

Problem 99

An element crystallizes in a face-centered cubic lattice and it has a density of 1.45 $\mathrm{g} / \mathrm{cm}^{3} .$ The edge of its unit cell is $4.52 \times 10^{-8} \mathrm{cm} .$
(a) How many atoms are in each unit cell?
(b) What is the volume of a unit cell?
(c) What is the mass of a unit cell?
(d) Calculate an approximate atomic mass for the element.

Stephen Ho

Numerade Educator

Problem 100

Classify each of the following as a conductor, insulator, or semiconductor: (a) phosphorus; (b) mercury; (c) germanium.

Cathy Geisel

Numerade Educator

Problem 101

Classify each of the following as a conductor, insulator, or semiconductor: (a) carbon (graphite); (b) sulfur; (c) platinum.

Stephen Ho

Numerade Educator

Problem 102

Predict the effect (if any) of an increase in temperature on the electrical conductivity of (a) antimony; (b) tellurium; (c) bismuth.

Cathy Geisel

Numerade Educator

Problem 103

Predict the effect (if any) of a decrease in temperature on the electrical conductivity of (a) silicon; (b) lead; (c) germanium.

Stephen Ho

Numerade Educator

Problem 104

Polonium, the Period 6 member of Group $6 \mathrm{A}(16),$ is a rare radioactive metal that is the only element with a crystal structure based on the simple cubic unit cell. If its density is 9.142 $\mathrm{g} / \mathrm{cm}^{3}$ , calculate an approximate atomic radius for polonium.

Freddie Montague

Freddie Montague

Numerade Educator

Problem 105

The coinage metals - copper, silver, and gold- crystallize in a cubic closest packed structure. Use the density of copper $\left(8.95 \mathrm{g} / \mathrm{cm}^{3}\right)$ and its molar mass $(63.55 \mathrm{g} / \mathrm{mol})$ to calculate an approximate atomic radius for copper.

Stephen Ho

Numerade Educator

Problem 106

One of the most important enzymes in the world-nitrogenase, the plant protein that catalyzes nitrogen fixation-contains active clusters of iron, sulfur, and molybdenum atoms. Crystalline molybdenum (Mo) has a body-centered cubic unit cell $\left(d \text { of Mo }=10.28 \mathrm{g} / \mathrm{cm}^{3}\right) .$ (a) Determine the edge length of the unit cell. (b) Calculate the atomic radius of Mo.

Freddie Montague

Freddie Montague

Numerade Educator

Problem 107

Tantalum $\left(\mathrm{Ta} ; d=16.634 \mathrm{g} / \mathrm{cm}^{3} \text { and } \mathcal{M}=180.9479 \mathrm{g} / \mathrm{mol}\right)$ has a body-centered cubic structure with a unit-cell edge length of 3.3058 A. Use these data to calculate Avogadro's number.

Rashmi Sinha

Numerade Educator

Problem 108

When tin is added to copper, the resulting alloy (bronze) is much harder than copper. Explain.

Cathy Geisel

Numerade Educator

Problem 109

In the process of doping a semiconductor, certain impurities are added to increase the electrical conductivity. Explain this process for an n-type and a p-type semiconductor.

Stephen Ho

Numerade Educator

Problem 110

State two molecular characteristics of substances that typically form liquid crystals. How is each related to function?

Rashmi Sinha

Numerade Educator

Problem 111

Distinguish between isotropic and anisotropic substances. To which category do liquid crystals belong?

Stephen Ho

Numerade Educator

Problem 112

How are the properties of high-tech ceramics the same as those of traditional clay ceramics, and how are they different? Refer to specific substances in your answer.

Cathy Geisel

Numerade Educator

Problem 113

Why is the average molar mass of a polymer sample different from the molar mass of an individual chain?

Stephen Ho

Numerade Educator

Problem 114

How does the random coil shape relate to the radius of gyration of a polymer chain?

Rashmi Sinha

Numerade Educator

Problem 115

What factor(s) influence the viscosity of a polymer solution? What factor(s) influence the viscosity of a molten polymer? What is a polymer glass?

Stephen Ho

Numerade Educator

Problem 116

Use an example to show how branching and crosslinking can affect the physical behavior of a polymer.

Cathy Geisel

Numerade Educator

Problem 117

Silicon and germanium are both semiconducting elements from Group 4A(14) that can be doped to improve their conductivity. Would each of the following form an n-type or a p-type semiconductor: (a) Ge doped with P; (b) Si doped with In?

Stephen Ho

Numerade Educator

Problem 118

Would each of the following form an n-type or a p-type semiconductor: (a) Ge doped with As; (b) Si doped with B?

Rashmi Sinha

Numerade Educator

Problem 119

The repeat unit in a polystyrene coffee cup has the formula $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHCH}_{2}$ . If the molar mass of the polymer is $3.5 \times 10^{5} \mathrm{g} / \mathrm{mol}$ , what is the degree of polymerization?

Stephen Ho

Numerade Educator

Problem 120

The monomer of poly(vinyl chloride) has the formula $\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}$ . If there are 1565 repeat units in a single chain of the polymer, what is the molecular mass ( in amu) of that chain?

Freddie Montague

Freddie Montague

Numerade Educator

Problem 121

The polypropylene (repeat unit $\mathrm{CH}_{3} \mathrm{CHCH}_{2} )$ in a plastic toy has a molar mass of $2.8 \times 10^{5} \mathrm{g} / \mathrm{mol}$ and a repeat unit length of 0.252 $\mathrm{pm}$ . Calculate the radius of gyration.

Stephen Ho

Numerade Educator

Problem 122

The polymer that is used to make $2-\mathrm{L}$ soda bottles [poly(ethylene terephthalate)] has a repeat unit with molecular formula $\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{O}_{4}$ and length 1.075 $\mathrm{nm} .$ Calculate the radius of gyration of a chain with a molar mass of $2.30 \times 10^{4} \mathrm{g} / \mathrm{mol}$ .

Crystal Wang

Numerade Educator

Problem 123

A $0.75-\mathrm{L}$ bottle is cleaned, dried , and closed in a room where the air is $22^{\circ} \mathrm{C}$ and has 44$\%$ relative humidity (that is, the water vapor in the air is 0.44 of the equilibrium vapor pressure at $22^{\circ} \mathrm{C} ) .$ The bottle is then brought outside and stored at $0.0^{\circ} \mathrm{C} .$ (a) What mass of liquid water condenses inside the bottle? (b) Would liquid liquid water condense at $10^{\circ} \mathrm{C} ?$ (See Table $5.2, \mathrm{p} .220 . )$

Prashant Bana

Numerade Educator

Problem 124

In an experiment, 5.00 $\mathrm{L}$ of $\mathrm{N}_{2}$ is saturated with water vapor at $22^{\circ} \mathrm{C}$ and then compressed to half its volume at constant $T$ (a) What is the partial pressure of $\mathrm{H}_{2} \mathrm{O}$ in the compressed gas mixture? (b) What mass of water vapor condenses to liquid?

Cathy Geisel

Numerade Educator

Problem 125

Barium is the largest nonradioactive alkaline earth metal. It has a body-centered cubic unit cell and a density of 3.62 $\mathrm{g} / \mathrm{cm}^{3} .$ What is the atomic radius of barium? (Volume of a
sphere: $V=\frac{4}{3} \pi r^{3} . )$

Stephen Ho

Numerade Educator

Problem 126

Two important characteristics used to evaluate the risk of fire or explosion are a compound's lower flammable limit (LFL) and flash point. The LFL is the minimum percentage by volume in air that is ignitable. Below that, the mixture is too lean to burn. The flash point is the temperature at which the air over a confined liquid becomes ignitable. $n$ -Hexane boils at $68.7^{\circ} \mathrm{C}$ at 1 atm. At
$20.0^{\circ} \mathrm{C},$ its vapor pressure is 121 $\mathrm{mm} \mathrm{Hg}$ . The LFL of $n$ -hexane is 1.1$\%$ . Calculate the flash point of $n$ -hexane.

Kaylee Rushlau

Numerade Educator

Problem 127

Bismuth is used to calibrate instruments employed in high-pressure studies because it has several well-characterized crystalline phases. Its phase diagram (right) shows the liquid phase and five solid phases
that are stable above 1 katm $(1000 \text { atm })$ and up to $300^{\circ} \mathrm{C}$ . (a) Which solid phases are stable at $25^{\circ} \mathrm{C} ?$ (b) Which phase is stable at 50 katm and $175^{\circ} \mathrm{C}$ ? (c) As the pressure is reduced from 100 to 1 katm at $200^{\circ} \mathrm{C},$ what
phase transitions does bismuth undergo? (d) What phases are present at each of the triple points?

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 128

In making computer chips, a 4.00 -kg cylindrical ingot of ultrapure n-type doped silicon that is 5.20 inches in diameter is sliced into wafers $1.12 \times 10^{-4} \mathrm{m}$ thick.
(a) Assuming no waste, how many wafers can be made?
(b) What is the mass of a wafer $\left(d \text { of } \mathrm{Si}=2.34 \mathrm{g} / \mathrm{cm}^{3} ; V \text { of a }\right.$ cylinder $=\pi r^{2} h ) ?$
(c) A key step in making p-n junctions for the chip is chemical removal of the oxide layer on the wafer through treatment with gaseous $\mathrm{HF}$ . Write a balanced equation for this reaction.
(d) If 0.750$\%$ of the Si atoms are removed during the treatment in part (c), how many moles of HF are required per wafer, assuming 100$\%$ reaction yield?

Crystal Wang

Numerade Educator

Problem 129

Methyl salicylate, $\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3},$ the odorous constituent of oil of wintergreen, has a vapor pressure of 1.00 torr at $54.3^{\circ} \mathrm{C}$ and 10.0 torr at $95.3^{\circ} \mathrm{C}$ (a) What is its vapor pressure at $25^{\circ} \mathrm{C}$ ? (b) What is the minimum number of liters of air that must pass over a sample of the compound at $25^{\circ} \mathrm{C}$ to vaporize 1.0 $\mathrm{mg}$ of it?

David Collins

Numerade Educator

Problem 130

Mercury (Hg) vapor is toxic and readily absorbed from the lungs. At $20 .^{\circ} \mathrm{C}$ , mercury $\left(\Delta H_{\mathrm{vap}}=59.1 \mathrm{kJ} / \mathrm{mol}\right)$ has a vapor pressure of $1.20 \times 10^{-3}$ torr, which is high enough to be hazardous. To reduce the danger to workers in processing plants, Hg is cooled to lower its vapor pressure. At what temperature would the vapor pressure of Hg be at the safer level of $5.0 \times 10^{-5}$ torr?

Freddie Montague

Freddie Montague

Numerade Educator

Problem 131

Polytetrafluoroethylene (Teflon) has a repeat unit with the formula $\mathrm{F}_{2} \mathrm{C}-\mathrm{CF}_{2}$ . A sample of the polymer consists of fractions with the following distribution of chains:
(a) Determine the molar mass of each fraction.
(b) Determine the number-average molar mass of the sample.
(c) Another type of average molar mass of a polymer sample is called the weight-average molar mass, $\mathscr{M}_{\mathrm{w}}$ :
$$
\mathcal{M}_{\mathrm{w}}=\frac{\Sigma(\mathscr{M} \text { of fraction } \times \text { mass of fraction })}{\text { total mass of all fractions }}
$$
Calculate the weight-average molar mass of the above sample.

Crystal Wang

Numerade Educator

Problem 132

A greenhouse contains 256 $\mathrm{m}^{3}$ of air at a temperature of $26^{\circ} \mathrm{C},$ and a humidifier in it vaporizes 4.20 $\mathrm{L}$ of water. (a) What is the pressure of water vapor in the greenhouse, assuming that none escapes and that the air was originally completely dry $\left(d \text { of } \mathrm{H}_{2} \mathrm{O}=\right.$ 1.00 $\mathrm{g} / \mathrm{mL} ) ?(\mathrm{b})$ What total volume of liquid water would have to be vaporized to saturate the air (that is, achieve 100$\%$ relative
humidity)? ( See Table 5.2, p. 220 )

Crystal Wang

Numerade Educator

Problem 133

Like most transition metals, tantalum (Ta) exhibits several oxidation states. Give the formula of each tantalum compound whose unit cell is depicted below:

Madi Sousa

Numerade Educator

Problem 134

KF has the same type of crystal structure as NaCl. The unit cell of KF has an edge length of 5.39 Å. Find the density of KF.

Freddie Montague

Freddie Montague

Numerade Educator

Problem 135

Furfural, which is prepared from corncobs, is an important solvent in synthetic rubber manufacturing, and it is reduced to furfuryl alcohol, which is used to make polymer resins. Furfural can also be oxidized to 2-furoic acid.
(a) Which of these compounds can form H bonds? Draw structures in each case.
(b) The molecules of some substances can form an internal H bond, that is, an H bond within a molecule. This takes the form of a polygon with atoms as corners and bonds as sides and an H bond as one of the sides. Which of these molecules is (are) likely to form a stable internal H bond? Draw the structure. (Hint:
Structures with 5 or 6 atoms as corners are most stable.)

Crystal Wang

Numerade Educator

Problem 136

On a humid day in New Orleans, the temperature is $22.0^{\circ} \mathrm{C},$ and the partial pressure of water vapor in the air is 31.0 torr. The 9000 -ton air-conditioning system in the Louisiana Superdome maintains an inside air temperature of $22.0^{\circ} \mathrm{C}$ also, but a partial pressure of water vapor of 10.0 torr. The volume of air in the dome is $2.4 \times 10^{6} \mathrm{m}^{3},$ and the total pressure is 1.0 atm both inside and outside the dome.
(a) What mass of water (in metric tons) must be removed every time the inside air is completely replaced with outside air? (Hint How many moles of gas are in the dome? How many moles of water vapor? How many moles of dry air? How many moles of outside air must be added to the air in the dome to simulate the composition of outside air?):
(b) Find the heat released when this mass of water condenses.

Mahnoor Amin

Numerade Educator

Problem 137

The boiling point of amphetamine, $\mathrm{C}_{9} \mathrm{H}_{13} \mathrm{N},$ is $201^{\circ} \mathrm{C}$ at 760 torr and $83^{\circ} \mathrm{C}$ at 13 torr. What is the concentration (in $\mathrm{g} / \mathrm{m}^{3} )$ of amphetamine when it is in contact with $20 .^{\circ} \mathrm{C}$ air?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 138

Diamond has a face-centered cubic unit cell, with four more $\mathrm{C}$ atoms in tetrahedral holes within the cell. Densities of diamonds vary from 3.01 $\mathrm{g} / \mathrm{cm}^{3}$ to 3.52 $\mathrm{g} / \mathrm{cm}^{3}$ because $\mathrm{C}$ atoms are missing from some holes. (a) Calculate the unit-cell edge length of the densest diamond. (b) Assuming the cell dimensions are fixed, how many $\mathrm{C}$ atoms are in the unit cell of the diamond with the lowest density?

Crystal Wang

Numerade Educator

Problem 139

Is it possible for a salt of formula $\mathrm{AB}_{3}$ to have a face-centered cubic unit cell of anions with cations in all eight of the available holes? Explain.

Stephen Ho

Numerade Educator

Problem 140

The density of solid gallium at its melting point is 5.9 $\mathrm{g} / \mathrm{cm}^{3}$ , whereas that of liquid gallium is 6.1 $\mathrm{g} / \mathrm{cm}^{3} .$ Is the temperature at the triple point higher or lower than the normal melting point? Is the slope of the solid-liquid line for gallium positive or negative?

Cathy Geisel

Numerade Educator

Problem 141

A 4.7 -L sealed bottle containing 0.33 g of liquid ethanol, $\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O},$ is placed in a refrigerator and reaches equilibrium with its vapor at $-11^{\circ} \mathrm{C} .(\mathrm{a})$ What mass of ethanol is present in the vapor? (b) When the container is removed and warmed to room temperature, $20 .^{\circ} \mathrm{C},$ will all the ethanol vaporize? (c) How much liquid ethanol would be present at $0.0^{\circ} \mathrm{C}$ ? The vapor pressure of ethanol is 10 . torr at $-2.3^{\circ} \mathrm{C}$ and 40 . torr at $19^{\circ} \mathrm{C} .$

Nicholas Mogoi

Numerade Educator

Problem 142

Substance A has the following properties.
At 1 atm, a 25 -g sample of A is heated from $-40 .^{\circ} \mathrm{C}$ to $100 .^{\circ} \mathrm{C}$ at a constant rate of $450 . \mathrm{J} / \mathrm{min.}$ (a) How many minutes does it take to heat the sample to its melting point? (b) How many minutes does it take to melt the sample? (c) Perform any other necessary calculations, and draw a curve of temperature vs. time for the entire heating process.

TP

Tuan Pham

University of Wisconsin - Madison

Problem 143

An aerospace manufacturer is building a prototype experimental aircraft that cannot be detected by radar. Boron nitride is chosen for incorporation into the body parts, and the boric acid/ ammonia method is used to prepare the ceramic material. Given 85.5$\%$ and 86.8$\%$ yields for the two reaction steps, how much boron nitride can be prepared from 1.00 metric ton of boric acid and 12.5 $\mathrm{m}^{3}$ of ammonia at 275 $\mathrm{K}$ and $3.07 \times 10^{3} \mathrm{kPa}$ ? Assume that ammonia does not behave ideally under these conditions and is recycled completely in the reaction process.

David Collins

Numerade Educator

Problem 144

The ball-and-stick models below represent three compounds with the same molecular formula, $\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}$
(a) Which compound(s) can form intermolecular H bonds?
(b) Which has the highest viscosity?

Freddie Montague

Freddie Montague

Numerade Educator

Problem 145

The $\Delta H_{\mathrm{f}}^{\circ}$ of gaseous dimethyl ether $\left(\mathrm{CH}_{3} \mathrm{OCH}_{3}\right)$ is $-185.4 \mathrm{kJ} / \mathrm{mol} ;$ the vapor pressure is 1.00 $\mathrm{atm}$ at $-23.7^{\circ} \mathrm{C}$ and 0.526 $\mathrm{atm}$ at $-37.8^{\circ} \mathrm{C} .$ (a) Calculate $\Delta H_{\mathrm{vap}}^{\circ}$ of dimethyl ether. (b) Calculate $\Delta H_{\mathrm{f}}^{\circ}$ of liquid dimethyl ether.

Stephen Ho

Numerade Educator

Problem 146

The crystal structure of sodium is based on the bodycentered cubic unit cell. What is the mass of one unit cell of Na?

Freddie Montague

Freddie Montague

Numerade Educator

Problem 147

The intrinsic viscosity of a polymer solute in a solvent, $[\eta]_{\text { solvent }}$ is the portion of the total viscosity due to the solute and is related to solute shape. It has also been found to relate to intermolecular interactions between solvent and polymer: higher $[\eta]_{\text { solvent }}$ means stronger interaction. The $[\eta]_{\text { solvent }}$ values of polymers in solution are given by the Mark-Houwink equation, $[\eta]_{\text { solvent }}=K M^{a}$ where $\mathscr{M}$ is the molar mass of the polymer and $K$ and $a$ are constants specific to the polymer and solvent. Use the data below for substances at $25^{\circ} \mathrm{C}$ to answer the following questions:
(a) A polystyrene sample has a molar mass of $104,160 \mathrm{g} / \mathrm{mol}$ . Calculate the intrinsic viscosity in benzene and in cyclohexane. Which solvent has stronger interactions with the polymer?
(b) A different polystyrene sample has a molar mass of $52,000 \mathrm{g} / \mathrm{mol}$ . Calculate its $[\eta]_{\text { benzene }}$ Given a polymer standard of known $\mathcal{M}$ , how could you use its measured $[\eta]$ in a given solvent to determine the molar mass of any sample of that polymer?
(c) Compare $[\eta]$ of a polyisobutylene sample [repeat unit $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CCH}_{2} ]$ with a molar mass of $104,160 \mathrm{g} / \mathrm{mol}$ with that of the polystyrene in part (a). What does this suggest about the solvent-polymer interactions of the two samples?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 148

One way of purifying gaseous $\mathrm{H}_{2}$ is to pass it under high pressure through the holes of a metal's crystal structure. Palladium, which adopts a cubic closest packed structure, absorbs more $\mathrm{H}_{2}$ than any other element and is one of the metals used for this purpose. How the metal and $\mathrm{H}_{2}$ interact is unclear, but it is estimated that the density of absorbed $\mathrm{H}_{2}$ approaches that of liquid hydrogen $(70.8 \mathrm{g} / \mathrm{L}) .$ What volume (in $\mathrm{L} )$ of gaseous $\mathrm{H}_{2}(\text { at } \mathrm{STP})$ can be packed into the spaces of 1 $\mathrm{dm}^{3}$ of palladium metal?

Madi Sousa

Numerade Educator