CHAPTER TEN LIQUIDS AND SOLIDS · CHAPTER TEN LIQUIDS AND SOLIDS Questions 12. ... 20. Evaporation...

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CHAPTER TEN

LIQUIDS AND SOLIDS

Questions

12. Dipole forces are the forces that act between polar molecules. The electrostatic attraction between thepositive end of one polar molecule and the negative end of another is the dipole force. Dipole forcesare generally weaker than hydrogen bonding. Both of these forces are due to dipole moments inmolecules. Hydrogen bonding is given a separate name from dipole forces because hydrogen bondingis a particularly strong dipole force.

London dispersion forces can be referred to as accidental-induced dipole forces. As the size of themolecule increases, the strength of the London dispersion forces increases. This is because, as theelectron cloud about a molecule gets larger, it is easier for the electrons to be drawn away from thenucleus. The molecule is said to be more polarizable.

13. London dispersion (LD) < dipole-dipole < H bonding < metallic bonding, covalent network, ionic.

Yes, there is considerable overlap. Consider some of the examples in Exercise 10.92. Benzene (onlyLD forces) has a higher boiling point than acetone (dipole-dipole forces). Also, there is even moreoverlap among the stronger forces (metallic, covalent, and ionic).

14. As the strengths of intermolecular forces increase: surface tension, viscosity, melting point and boilingpoint increase, while vapor pressure decreases.

15. a. Polarizability of an atom refers to the ease of distorting the electron cloud. It can also refer todistorting the electron clouds in molecules or ions. Polarity refers to the presence of a permanentdipole moment in a molecule.

b. London dispersion (LD) forces are present in all substances. LD forces can be referred to asaccidental dipole-induced dipole forces. Dipole-dipole forces involve the attraction of moleculeswith permanent dipoles for each other.

2c. inter: between; intra: within; For example, in Br the covalent bond is an intramolecular forceholding the two Br atoms together in the molecule. The much weaker London dispersion forces

2are the intermolecular forces of attraction which hold different molecules of Br together in theliquid phase.

16. Liquids and solids both have characteristic volume and are not very compressible. Liquids and gasesflow and assume the shape of their container.

17. Atoms have an approximately spherical shape (on the average). It is impossible to pack spheres

CHAPTER 10 LIQUIDS AND SOLIDS 239

together without some empty space among the spheres.

18. Critical temperature: The temperature above which a liquid cannot exist, i.e., the gas cannot beliquified by increased pressure.

Critical pressure: The pressure that must be applied to a substance at its critical temperature toproduce a liquid.

4 c 3 2 1The kinetic energy distribution changes as one raises the temperature (T > T > T > T > T ).

cAt the critical temperature, T , all molecules have kinetic energies greater than the intermolecularforces, F, and a liquid can't form. Note: The distributions above are not to scale.

19. As the intermolecular forces increase, the critical temperature increases.

20. Evaporation takes place when some molecules at the surface of a liquid have enough energy to breakthe intermolecular forces holding them in the liquid phase. When a liquid evaporates, the moleculesthat escape have high kinetic energies. The average kinetic energy of the remaining molecules is lower,thus, the temperature of the liquid is lower.

21. a. Crystalline solid: Regular, repeating structure

Amorphous solid: Irregular arrangement of atoms or molecules

b. Ionic solid: Made up of ions held together by ionic bonding.

Molecular solid: Made up of discrete covalently bonded molecules held together inthe solid phase by weaker forces (LD, dipole or hydrogen bonds).

c. Molecular solid: Discrete, individual molecules

Network solid: No discrete molecules; A network solid is one large molecule. Theintermolecular forces are the covalent bonds between atoms.

d. Metallic solid: Completely delocalized electrons, conductor of electricity (ions in asea of electrons)

Network solid: Localized electrons; Insulator or semiconductor

22. A crystalline solid will because a regular, repeating arrangement is necessary to produce planes of

CHAPTER 10 LIQUIDS AND SOLIDS240

atoms that will diffract the X-rays in regular patterns. An amorphous solid does not have a regularrepeating arrangement and will produce a complicated diffraction pattern.

23. Conductor: The energy difference between the filled and unfilled molecular orbitals is minimal.We call this energy difference the band gap. Since the band gap is minimal, electronscan easily move into the conduction bands (the unfilled molecular orbitals).

Insulator: Large band gap; Electrons do not move from the filled molecular orbitals to theconduction bands since the energy difference is large.

Semiconductor: Small band gap; Since the energy difference between the filled and unfilled molecularorbitals is smaller than in insulators, some electrons can jump into the conductionbands. The band gap, however, is not as small as with conductors, so semiconductorshave intermediate conductivity.

a. As the temperature is increased, more electrons in the filled molecular orbitals have sufficientkinetic energy to jump into the conduction bands (the unfilled molecular orbitals).

b. A photon of light is absorbed by an electron which then has sufficient energy to jump into theconduction bands.

c. An impurity either adds electrons at an energy near that of the conduction bands (n-type) orcreates holes (unfilled energy levels) at energies in the previously filled molecular orbitals (p-type).

24. In conductors, electrical conductivity is inversely proportional to temperature. Increases intemperature increase the motions of the atoms, which gives rise to increased resistance (decreasedconductivity). In a semiconductor, electrical conductivity is directly proportional to temperature. Anincrease in temperature provides more electrons with enough kinetic energy to jump from the filledmolecular orbitals to the conduction bands, increasing conductivity.

25. To produce an n-type semiconductor, dope Ge with a substance that has more than 4 valence electrons,e.g., a group 5A element. Phosphorus or arsenic are two substances which will produce n-typesemiconductors when they are doped into germanium. To produce a p-type semiconductor, dope Gewith a substance that has fewer than 4 valence electrons, e.g., a group 3A element. Gallium or indiumare two substances which will produce p-type semiconductors when they are doped into germanium.

26. An alloy is a substance that contains a mixture of elements and has metallic properties. In asubstitutional alloy, some of the host metal atoms are replaced by other metal atoms of similar size,e.g., brass, pewter, plumber’s solder. An interstitial alloy is formed when some of the interstices(holes) in the closest packed metal structure are occupied by smaller atoms, e.g., carbon steels.

27. a. Condensation: vapor ÷ liquid b. Evaporation: liquid ÷ vapor

c. Sublimation: solid ÷ vapor

d. A supercooled liquid is a liquid which is at a temperature below its freezing point.

28. Equilibrium: There is no change in composition; the vapor pressure is constant.


Dynamic: Two processes, vapor ÷ liquid and liquid ÷ vapor, are both occurring but with equalrates so the composition of the vapor is constant.

29. a. As the intermolecular forces increase, the rate of evaporation decreases.

b. As temperature increases, the rate of evaporation increases.

c. As surface area increases, the rate of evaporation increases.

30. A volatile liquid is one that evaporates relatively easily. Volatile liquids have large vapor pressuresbecause the intermolecular forces that prevent evaporation are relatively weak.

2 5 2 531. C H OH(l) ÷ C H OH(g) is an endothermic process. Heat is absorbed when liquid ethanol vaporizes;the internal heat from the body provides this heat which results in the cooling of the body.

232. Sublimation will occur allowing water to escape as H O(g).

2 233. The phase change, H O(g) ÷ H O(l), releases heat that can cause additional damage. Also steam canbe at a temperature greater than 100°C.

34. Fusion refers to a solid converting to a liquid, and vaporization refers to a liquid converting to a gas.Only a fraction of the hydrogen bonds are broken in going from the solid phase to the liquid phase.Most of the hydrogen bonds are still present in the liquid phase and must be broken during the liquidto gas phase transition. Thus, the enthalpy of vaporization is much larger than the enthalpy of fusionsince more intermolecular forces are broken during the vaporization process.

Exercises

Intermolecular Forces and Physical Properties

35. Ionic compounds have ionic forces. Covalent compounds all have London Dispersion (LD) forces,while polar covalent compounds have dipole forces and/or hydrogen bonding forces. For H bondingforces, the covalent compound must have either a N&H, O&H or F&H bond in the molecule.

a. LD only b. dipole, LD c. H bonding, LD

4d. ionic e. LD only (CH in a nonpolar covalent compound.)

f. dipole, LD g. ionic

36. a. ionic

b. LD mostly; C S F bonds are polar, but polymers like teflon are so large the LD forces are thepredominant intermolecular forces.

c. LD d. dipole, LD e. H bonding, LD


f. dipole, LD g. LD

37. a. OCS; OCS is polar and has dipole-dipole forces in addition to London dispersion (LD) forces.

2All polar molecules have dipole forces. CO is nonpolar and only has LD forces. To predictpolarity, draw the Lewis structure and deduce whether the individual bond dipoles cancel.

2 2 2b. SeO ; Both SeO and SO are polar compounds, so they both have dipole forces as well as LD

2forces. However, SeO is a larger molecule, so it would have stronger LD forces.

2 2 2 2c. H NCH CH NH ; More extensive hydrogen bonding is possible.

2 2 3 3 2d. H CO; H CO is polar while CH CH is nonpolar. H CO has dipole forces in addition to LDforces.

3 3 2e. CH OH; CH OH can form relatively strong H bonding interactions, unlike H CO.

38. a. Neopentane is more compact than n-pentane. There is less surface area contact among neopentanemolecules. This leads to weaker LD forces and a lower boiling point.

b. Ethanol is capable of H bonding; dimethyl ether is not.

c. HF is capable of H bonding; HCl is not.

d. LiCl is ionic, and HCl is a molecular solid with only dipole forces and LD forces. Ionic forces aremuch stronger than the forces for molecular solids.

e. n-pentane is a larger molecule so has stronger LD forces.

f. Dimethyl ether is polar so has dipole forces in addition to LD forces, unlike n-propane which hasonly LD forces.

39. See Question 10.14 to review the dependence of some physical properties on the strength of theintermolecular forces.

2 2a. HCl; HCl is polar while Ar and F are nonpolar. HCl has dipole forces unlike Ar and F .

b. NaCl; Ionic forces are much stronger than molecular forces.

2 2c. I ; All are nonpolar, so the largest molecule (I ) will have the strongest LD forces and the lowestvapor pressure.

2d. N ; Nonpolar and smallest, so has the weakest intermolecular forces.

4e. CH ; Smallest, nonpolar molecule so has the weakest LD forces.

f. HF; HF can form relatively strong H bonding interactions unlike the others.

3 2 2g. CH CH CH OH; H bonding, unlike the others, so has strongest intermolecular forces.


440. a. CBr ; Largest of these nonpolar molecules so has strongest LD forces.

2 2b. Cl ; Ionic forces in LiF are much stronger than the covalent forces in Cl and HBr. HBr has

2 2dipole forces that the nonpolar Cl does not exhibit; so Cl has the weakest intermolecular forces.

3 2c. CH CH OH; Can form H bonding interactions unlike the others.

2 2d. H O ; H&O&O&H structure produces stronger H bonding interactions than HF, so hasgreatest viscosity.

2 2e. H CO; H CO is polar so has dipole forces, unlike the other nonpolar covalent compounds.

2 2 2f. I ; I has only LD forces while CsBr and CaO have much stronger ionic forces. I has

fusionweakest intermolecular forces so has smallest )H .

Properties of Liquids

2 2 241. The attraction of H O for glass is stronger than the H O S H O attraction. The miniscus is concave

2to increase the area of contact between glass and H O. The Hg S Hg attraction is greater than the HgS glass attraction. The miniscus is convex to minimize the Hg S glass contact.

42. A molecule at the surface of a waterdrop is subject to attractions only by molecules below it and toeach side. The effect of this uneven pull on the surface molecules tends to draw them into the bodyof the liquid and causes the droplet to assume the shape that has the minimum surface area, a sphere.

2 243. The structure of H O is H S O S O S H, which produces greater hydrogen bonding than water. Long

2 2chains of hydrogen bonded H O molecules then get tangled together.

244. CO is a gas at room temperature. As mp and bp increase, the strength of the intermolecular forces

2 2 2also increases. Therefore, the strength of forces is CO < CS < CSe . From a structural standpointthis is expected. All three are linear, nonpolar molecules. Thus, only London dispersion forces are

2 2 2present. Since the molecules increase in size from CO < CS < CSe , the strength of theintermolecular forces will increase in the same order.

Structures and Properties of Solids

45. n8 = 2d sin 2, d = = 3.13 D = 3.13 × 10 m = 313 pm-10

46. n8 = 2d sin 2, d = = 4.91 D = 4.91 × 10 m = 491 pm-10

sin 2 = = 0.536, 2 = 32.4°


47. A cubic closest packed structure has a face-centered cubic unit cell. In a face-centered cubic unit,there are:

8 corners × + 6 faces × = 4 atoms

The atoms in a face-centered cubic unit cell touch along the face diagonal of the cubic unit cell. Usingthe Pythagorean formula where l = length of the face diagonal and r = radius of the atom:

l + l = (4r)2 2 2

2 l = 16 r2 2

l = r

l = r = 197 × 10 m × = 5.57 × 10 m = 5.57 × 10 cm-12 -10 -8

Volume of a unit cell = l = (5.57 × 10 cm) = 1.73 × 10 cm3 -8 3 -22 3

Mass of a unit cell = 4 Ca atoms × = 2.662 × 10 g Ca-22

density = = 1.54 g/cm3

48. There are 4 Ni atoms in each unit cell: For a unit cell:

density = = 6.84 g/cm = 3

Solving: l = 3.85 × 10 cm = cube edge length-8

For a face centered cube:

(4r) = l + l = 2 l2 2 2 2

r = l, r = l/

r = 3.85 × 10 cm/-8

r = 1.36 × 10 cm = 136 pm-8

49. The volume of a unit cell is:


V = l = (383.3 × 10 cm) = 5.631 × 10 cm3 -10 3 -23 3

There are 4 Ir atoms in the unit cell, as is the case for all face-centered cubic unit cells. The mass ofatoms in a unit cell is:

mass = 4 Ir atoms × = 1.277 × 10 g-21


50. A face-centered cubic unit cell contains 4 atoms. For a unit cell:

mass of X = volume × density = (4.09 × 10 cm) × 10.5 g/cm = 7.18 × 10 g-8 3 3 -22

mol X = 4 atoms X × = 6.642 × 10 mol X-24

Molar mass = = 108 g/mol; The metal is silver (Ag).

51. For a body-centered unit cell: 8 corners × + Ti at body center = 2 Ti atoms

All body-centered unit cells have 2 atoms per unit cell. For a unit cell:

density = 4.50 g/cm = , l = cube edge length3

Solving: l = edge length of unit cell = 3.28 × 10 cm = 328 pm-8

Assume Ti atoms just touch along the body diagonal of the cube, so body diagonal = 4 × radiusof atoms = 4r.

The triangle we need to solve is:

(4r) = (3.28 × 10 cm) + [(3.28 × 10 cm) ] , r = 1.42 × 10 cm = 142 pm 2 -8 2 -8 2 -8

For a body-centered unit cell (bcc), the radius of the atom is related to the cube edge length by4r = l or l = 4r/ .


52. From Exercise 10.51:

16 r = l + 2 l2 2 2

l = 4r/ = 2.309 r

l = 2.309 (222 pm) = 513 pm = 5.13 × 10 cm-8

In a bcc, there are 2 atoms/unit cell. For a unit cell:

density =

53. In a face-centered unit cell (ccp structure), the atoms touch along the face diagonal:

(4r) = l + l2 2 2

l = r

cubeV = l = (r ) = 22.63 r3 3 3

There are four atoms in a face-centered cubic cell (see Exercise 10.47). Each atom has a volume of4/3 Br .3

atomsV = 4 × Br = 16.76 r3 3

So, = 0.7406 or 74.06% of the volume of each unit cell is occupied by atoms.

In a simple cubic unit cell, the atoms touch along the cube edge (l):

2(radius) = 2r = l

cubeV = l = (2r) = 8 r3 3 3

There is one atom per simple cubic cell (8 corner atoms × 1/8 atom per corner = 1 atom/unit cell).Each atom has an assumed volume of 4/3 Br = volume of a sphere.3

atomV = Br = 4.189 r3 3


So, = 0.5236 or 52.36% of the volume of each unit cell is occupied by atoms.

A cubic closest packed structure packs the atoms much more efficiently than a simple cubic structure.

54. From Exercise 10.51, a body-centered unit cell contains 2 atoms, and the length of a cube edge (l) isrelated to the radius of the atom (r) by the equation l = 4r/ .

Volume of unit cell = l = (4 r/ ) = 12.32 r3 3 3

Volume of atoms in unit cell = 2 × B r = 8.378 r3 3

So, = 0.6800 = 68.00% occupied

To determine the radius of the Fe atoms, we need to determine the cube edge length (l).

Volume of unit cell =

= 2.36 × 10 cm-23 3

Volume = l = 2.36 × 10 cm , l = 2.87 × 10 cm3 -23 3 -8

l = 4r/ , r = l /4 = 2.87 × 10 cm × /4 = 1.24 × 10 cm-8 -8

55. In has fewer valence electrons than Se, thus, Se doped with In would be a p-type semiconductor.

56. To make a p-type semiconductor we need to dope the material with atoms that have fewer valenceelectrons. The average number of valence electrons is four when 50-50 mixtures of group 3A andgroup 5A elements are considered. We could dope with more of the Group 3A element or with atomsof Zn or Cd. Cadmium is the most common impurity used to produce p-type GaAs semiconductors.To make an n-type GaAs semiconductor, dope with an excess group 5A element or dope with a Group6A element such as sulfur.

gap gap light57. E = 2.5 eV × 1.6 × 10 J/eV = 4.0 × 10 J; We want E = E , so:-19 -19

lightE = = 5.0 × 10 m = 5.0 × 10 nm-7 2

58. E = = 2.72 × 10 J = energy of band gap-19

59. a. 8 corners × + 6 faces × = 4 Cl ions

12 edges × + 1 Na at body center = 4 Na ions; NaCl is the formula.

b. 1 Cs ion at body center; 8 corners × = 1 Cl ion; CsCl is the formula.


c. There are 4 Zn ions inside the cube.

8 corners × + 6 faces × = 4 S ions; ZnS is the formula.

d. 8 corners × + 1 Ti at body center = 2 Ti ions

24 faces × + 2 O inside cube = 4 O ions; TiO is the formula.

60. Both As ions are inside the unit cell. 8 corners × + 4 edges × = 2 Ni ions

The unit cell contains 2 ions of Ni and 2 ions of As which gives a formula of NiAs.

61. There is one octahedral hole per closest packed anion in a closest packed structure. If half of theoctahedral holes are filled, there is a 2:1 ratio of fluoride ions to cobalt ions in the crystal. The formula

2is CoF .

62. There are 2 tetrahedral holes per closest packed anion. Let f = fraction of tetrahedral holes filled bythe cations.

2Na O: cation to anion ratio = , f = 1; All of the tetrahedral holes are filled by Na+

cations.

CdS: cation to anion ratio = , f = ; of the tetrahedral holes are filled by Cd cations.2+

4ZrI : cation to anion ratio = , f = ; of the tetrahedral holes are filled by Zr cations.4+

63. 8 F ions at corners × = 1 F ion per unit cell; Since there is one cubic hole per cubic unit - -

2cell, there is a 2:1 ratio of F ions to metal ions in the crystal. The formula is MF where-

M is the metal ion.2+

64. Mn ions at 8 corners: 8(1/8) = 1 Mn ion; F ions at 12 edges: 12(1/4) = 3 F ions

3Formula is MnF . Assuming fluoride is -1 charged, the charge on Mn is +3.

65. Since magnesium oxide has the same structure as NaCl, each unit cell contains 4 Mg ions and 4 O2+ 2-

ions. The mass of a unit cell is:

4 MgO formula units = 2.678 × 10 g MgO-22

Volume of unit cell = 2.678 × 10 g MgO = 7.48 × 10 cm-22 -23 3


Volume of unit cell = l , l = cube edge length; l = (7.48 × 10 cm ) = 4.21 × 10 cm = 421 pm3 -23 3 1/3 -8

From the NaCl structure in Figure 10.35 of the text, Mg and O ions should touch along the cube2+ 2-

edge, l:

l = = 2 (65 pm) + 2 (140. pm) = 410. pm

The two values agree within 3%. In the actual crystals, the Mg and O ions may not touch, which2+ 2-

is assumed in calculating the 410. pm value.

66. CsCl is a simple cubic array of Cl ions with Cs in the middle of each unit cell. There is one Cs dna- + +

one Cl ion in each unit cell. Cs and Cl touch along the body diagonal.- + -

body diagonal = , l = length of cube edge

In each unit cell:

mass = 1 CsCl formula unit = 2.796 × 10 g -22

volume = l = 2.796 × 10 g CsCl × = 7.04 × 10 cm3 -22 -23 3

l = 7.04 × 10 cm , l = 4.13 × 10 cm = 413 pm = length of cube edge3 -23 3 -8

The distance between ion centers =

From ionic radius: = 169 pm and

The actual distance is 8 pm (2.3%) greater than that calculated from values of ionic radii.

2 267. a. CO : molecular b. SiO : network c. Si: atomic, network

4 2d. CH : molecular e. Ru: atomic, metallic f. I : molecular

2g. KBr: ionic h. H O: molecular i. NaOH: ionic

3 3j. U: atomic, metallic k. CaCO : ionic l. PH : molecular

3 268. a. diamond: atomic, network b. PH : molecular c. H : molecular

d. Mg: atomic, metallic e. KCl: ionic f. quartz: network

4 3 2g. NH NO : ionic h. SF : molecular i. Ar: atomic, group 8A

6 12 6j. Cu: atomic, metallic k. C H O : molecular


69. a. The unit cell consists of Ni at the cube corners and Ti at the body center, or Ti at the cube cornersand Ni at the body center.

b. 8 × 1/8 = 1 atom from corners + 1 atom at body center; Empirical formula = NiTi

c. Both have a coordination number of 8 (both are surrounded by 8 atoms).

70. 8 corners × + 1 Xe inside cell = 2 Xe; 8 edges × + 2 F inside cell = 4 F

2Empirical formula is XeF . This is also the molecular formula.

71. Structure 1 Structure 2

8 corners × = 1 Ca atom 8 corners × = 1 Ti atom

6 faces × = 3 O atoms 12 edges × = 3 O atoms

3 31 Ti at body center. Formula = CaTiO 1 Ca at body center. Formula = CaTiO

In the extended lattice of both structures, each Ti atom is surrounded by six O atoms.

72. There are four sulfur ions per unit cell since the sulfur ions are cubic closest packed (face-centered cubic unit cell). Since there are one octahedral hole and two tetrahedral holes per closestpacked ion, each unit cell has 4 octahedral holes and 8 tetrahedral holes. This gives 4 (1/2) = 2 Al ions

2 4per unit cell and 8 (1/8) = 1 Zn ion per unit cell. The formula of the mineral is Al ZnS .

73. a. Y: 1 Y in center; Ba: 2 Ba in center

Cu: 8 corners × = 1 Cu, 8 edges × = 2 Cu, total = 3 Cu atoms

O: 20 edges × = 5 oxygen, 8 faces × = 4 oxygen, total = 9 O atoms

2 3 9Formula: YBa Cu O

b. The structure of this superconductor material follows the second perovskite structure described

2 3 9in Exercise 10.71. The YBa Cu O structure is three of these cubic perovskite unit cells stackedon top of each other. The oxygen atoms are in the same places, Cu takes the place of Ti, two ofthe calcium atoms are replaced by two barium atoms, and one Ca is replaced by Y.

c. Y, Ba, and Cu are the same. Some oxygen atoms are missing.


12 edges × = 3 O, 8 faces × = 4 O, total = 7 O atoms

2 3 7Superconductor formula is YBa Cu O .

74. a. Structure (a):

Ba: 2 Ba inside unit cell; Tl: 8 corners × = 1 Tl; Cu: 4 edges × = 1 Cu

2 5O: 6 faces × + 8 edges × = 5 O; Formula = TlBa CuO

Structure (b):

Tl and Ba are the same as in structure (a).

Ca: 1 Ca inside unit cell; Cu: 8 edges × = 2 Cu

2 2 7O: 10 faces × + 8 edges × = 7 O; Formula = TlBa CaCu O

Structure (c):

Tl and Ba are the same, and two Ca are located inside the unit cell.

Cu: 12 edges × = 3 Cu; O: 14 faces × + 8 edges × = 9 O

2 2 3 9Formula: TlBa Ca Cu O

2 3 4 11Structure (d): Following similar calculations, formula = TlBa Ca Cu O

b. Structure (a) has one planar sheet of Cu and O atoms, and the number increases by one for eachof the remaining structures. The order of superconductivity temperature from lowest to highesttemperature is: (a) < (b) < (c) < (d).

2 5c. TlBa CuO : 3 + 2(2) +x + 5(-2) = 0, x = +3Only Cu is present in each formula unit.3+

2 2 7TlBa CaCu O : 3 + 2(2) + 2 + 2(x) + 7(-2) = 0, x = +5/2Each formula unit contains 1 Cu and 1 Cu .2+ 3+


2 2 3 9TlBa Ca Cu O : 3 + 2(2) + 2(2) + 3(x) + 9(-2) = 0, x = +7/3Each formula unit contains 2 Cu and 1 Cu .2+ 3+

2 3 4 11TlBa Ca Cu O : 3 + 2(2) + 3(2) + 4(x) + 11(-2) = 0, x = +9/4Each formula unit contains 3 Cu and 1 Cu .2+ 3+

d. This superconductor material achieves variable copper oxidation states by varying the numbersof Ca, Cu and O in each unit cell. The mixtures of copper oxidation states are discussed above.The superconductor material in Exercise 10.73 achieves variable copper oxidation states byomitting oxygen at various sites in the lattice.

Phase Changes and Phase Diagrams

vap vap75. If we graph ln P vs 1/T, the slope of the resulting straight line will be -)H /R.

vap vapP ln P T (Li) 1/T T (Mg) 1/T

1 torr 0 1023 K 9.775 × 10 K 893 K 11.2 × 10 K-4 -1 -4 -1

10. 2.3 1163 8.598 × 10 1013 9.872 × 10 -4 -4

100. 4.61 1353 7.391 × 10 1173 8.525 × 10-4 -4

400. 5.99 1513 6.609 × 10 1313 7.616 × 10-4 -4

760. 6.63 1583 6.317 × 10 1383 7.231 × 10-4 -4

For Li:

We get the slope by taking two points (x, y) that are on the line we draw. For a line:

slope =


or we can determine the straight line equation using a computer or calculator. The general straightline equation is y = mx + b where m = slope and b = y-intercept.

vapThe equation of the Li line is: ln P = -1.90 × 10 (1/T) + 18.6, slope = -1.90 × 10 K4 4

vap vapSlope = -)H /R, )H = -slope × R = 1.90 × 10 K × 8.3145 J/KCmol4

vap)H = 1.58 × 10 J/mol = 158 kJ/mol5

For Mg:

vapThe equation of the line is: ln P = -1.67 × 10 (1/T) + 18.7, slope = -1.67 × 10 K4 4

vap vap)H = -slope × R = 1.67 × 10 K × 8.3145 J/KCmol, )H = 1.39 × 10 J/mol = 139 kJ/mol4 5

vapThe bonding is stronger in Li since )H is larger for Li.

vap vap76. Again we graph ln P vs 1/T. The slope of the line equals -)H /R.

vap vapT(K) 10 /T (K ) P (torr) ln P3 -1

273 3.66 14.4 2.67283 3.53 26.6 3.28293 3.41 47.9 3.87303 3.30 81.3 4.40313 3.19 133 4.89323 3.10 208 5.34353 2.83 670. 6.51

slope =

-4600 K =

vap)H = 38 kJ/mol

To determine the normal boiling point, we can use the following formula:


At the normal boiling point, the vapor pressure equals 1.00 atm or 760. torr. At 273 K, the vaporpressure is 14.4. torr (from data in the problem).

2, -3.97 = 4.6 × 10 (1/T - 3.66 × 10 )3 -3

2 2- 8.6 × 10 + 3.66 × 10 = 1/T = 2.80 × 10 , T = 357 K = normal boiling point-4 -3 -3

277. At 100.°C (373 K), the vapor pressure of H O is 1.00 atm = 760. torr.

vapFor water, )H = 40.7 kJ/mol.

or

, -7.75 × 10 = -5

2-7.75 × 10 = 2.68 × 10 - = 2.76 × 10 , T = = 362 K or 89°C-5 -3 -3

2 278. , ln P = 5.27, P = e = 194 atm5.27

1 1 2 279. ln = ; P = 760. torr, T = 630. K; P = ?, T = 298 K

ln = = 12.6

2 2760./ P = e , P = 760./ (2.97 × 10 ) = 2.56 × 10 torr12.6 5 -3

80.

1 1 2 2P = 760. torr, T = 56.5°C + 273.2 = 329.7 K; P = 630. torr, T = ?

, 0.188 = 3.85 × 10 3

2 - 3.033 × 10 = 4.88 × 10 , = 3.082 × 10 , T = 324.5 K = 51.3°C-3 -5 -3


2, ln 630. - ln P = 1.05

2 2ln P = 5.40, P = e = 221 torr5.40

81.

82. X(g, 100.°C) ÷ X(g, 75°C), )T = -25°C

1 gasq = s × m × )T = × 250. g × (-25°C) = -6300 J = -6.3 kJ

2X(g, 75°C) ÷ X(l, 75°C), q = 250. g × = -67 kJ

3X(l, 75°C) ÷ X(l, -15°C), q = × 250. g × (-90.°C) = -56,000 J = -56 kJ

4X(l, -15°C) ÷ X(s, -15°C), q = 250. g × = -17 kJ

5X(s, -15°C) ÷ X(s, -50.°C), q = × 250. g × (-35°C) = -26,000 J = -26 kJ

total 1 2 3 4 5q = q + q + q + q + q = -6.3 - 67 - 56 - 17 - 26 = -172 kJ

2 283. H O(s, -20.°C) ÷ H O(s, 0°C), )T = 20.°C

1 iceq = s × m × )T = × 5.00 × 10 g × 20.°C = 2.1 × 10 J = 21 kJ2 4

2 2 2 2H O(s, 0°C) ÷ H O(l, 0°C), q = 5.00 × 10 g H O × × = 167 kJ2

2 2 3H O(l, 0°C) ÷ H O(l, 100°C), q = × 5.00 × 10 g × 100.°C = 2.1 × 10 J = 210 kJ2 5

2 2 4H O(l, 100°C) ÷ H O(g, 100°C), q = 5.00 × 10 g × = 1130 kJ2


2 2 5H O(g, 100°C) ÷ H O(g, 250°C), q = × 5.00 × 10 g × 150.°C = 1.5 × 10 J = 150 kJ2 5

total 1 2 3 4 5q = q + q + q + q + q = 21 + 167 + 210 + 1130 + 150 = 1680 kJ

2 2 184. H O(g, 125°C) ÷ H O(g, 100.°C), q = 2.0 J/g C°C × 75.0 g × (-25°C) = -3800 J = -3.8 kJ

2 2 2H O(g, 100.°C) ÷ H O(l, 100.°C), q = 75.0 g × = -169 kJ

2 2 3H O(l, 100.°C) ÷ H O(l, 0°C), q = 4.2 J/g C°C × 75.0 g × (-100.°C) = -32,000 J = -32 kJ

2 2To convert H O(g) at 125°C to H O(l) at 0°C requires (-3.8 kJ - 169 kJ - 32 kJ =) -205 kJ of heat

2 2removed. To convert from H O(l) at 0°C to H O(s) at 0°C requires:

4q = 75.0 g × = -25 kJ

This amount of energy puts us over the -215 kJ limit (-205 kJ - 25 kJ = -230. kJ). Therefore, a

2 2mixture of H O(s) and H O(l) will be present at 0°C when 215 kJ of heat are removed from the gassample.

2 2 285. Total mass H O = 18 cubes × = 540. g; 540. g H O × = 30.0 mol H O

Heat removed to produce ice at -5.0°C:

× 540. g × 22.0 °C + × 30.0 mol + × 540. g × 5.0 °C

= 4.97 × 10 J + 1.81 × 10 J + 5.6 × 10 J = 2.36 × 10 J4 5 3 5

2 22.36 × 10 J × = 1.49 × 10 g CF Cl must be vaporized.5 3

86. Heat released = 0.250 g Na × = 2.00 kJ

To melt 50.0 g of ice requires: 50.0 g ice × = 16.7 kJ

The reaction doesn't release enough heat to melt all of the ice. The temperature will remain at 0°C.

87. A: solid B: liquid C: vapor

D: solid + vapor E: solid + liquid + vapor

F: liquid + vapor G: liquid + vapor H: vapor

triple point: E critical point: G

normal freezing point: temperature at which solid - liquid line is at 1.0 atm (see plot below).


normal boiling point: temperature at which liquid - vapor line is at 1.0 atm (see plot below).

Since the solid-liquid line has a positive slope, the solid phase is denser than the liquid phase.

88. a. 3

b. Triple point at 95.31°C: rhombic, monoclinic, gasTriple point at 115.18°C: monoclinic, liquid, gasTriple point at 153°C: rhombic, monoclinic, liquid

c. From the phase diagram, the monoclinic solid phase is stable at T = 100°C and P = 1 atm.

d. Normal melting point = 115.21°C; normal boiling point = 444.6°C; The normal melting andboiling points occur at P = 1.0 atm.

e. Rhombic is the densest phase since the rhombic-monoclinic equilibrium line has a positiveslope and since the solid-liquid lines also have positive slopes.

f. No; P = 1.0 × 10 atm is at a pressure somewhere between the 95.31°C and 115.18°C-5

triple points. At this pressure, the rhombic and gas phases are never in equilibrium with eachother, so rhombic sulfur cannot sublime at P = 1.0 × 10 atm. However, monoclinic sulfur can-5

sublime at this pressure.

g. From the phase diagram, we would start off with gaseous sulfur. At 100°C and ~1 × 10 atm,-5

S(g) would convert to the solid monoclinic form of sulfur. Finally at 100°C and some largepressure less than 1420 atm, S(s, monoclinic) would convert to the solid rhombic form of sulfur.Summarizing, the phase changes are S(g) ö S(monoclinic) ö S(rhombic).

89. a. two

b. Higher pressure triple point: graphite, diamond and liquid; Lower pressure triple point: graphite,liquid and vapor

c. It is converted to diamond (the more dense solid form).

d. Diamond is more dense, which is why graphite can be converted to diamond by applying pressure.

2 290. The following sketch of the Br phase diagram is not to scale. Since the triple point of Br is at a

2temperature below the freezing point of Br , the slope of the solid-liquid line is positive.


2 2The positive slopes of all the lines indicate that Br (s) is more dense than Br (l) which is more dense than

2 2 2Br (g). At room temperature (~22°C) and 1 atm, Br (l) is the stable phase. Br (l) cannot exist at a temperaturebelow the triple point temperature of -7.3°C and at a temperature above the critical point temperature of 320°C.The phase changes that occur as temperature is increased at 0.10 atm are solid ö liquid ö gas.

Additional Exercises

25 5291. C H has the stronger intermolecular forces because it has the higher boiling point. Even though

25 52C H is nonpolar, it is so large that its London dispersion forces are much stronger than the sum of

2the London dispersion and hydrogen bonding interactions found in H O.

92. Benzene Naphthalene

LD forces only LD forces only

Note: London dispersion forces in molecules like benzene and naphthalene are fairly large. Themolecules are flat, and there is efficient surface area contact among molecules. Large surface areacontact leads to stronger London dispersion forces.

4Carbon tetrachloride (CCl ) has polar bonds but is a nonpolar molecule.

4CCl only has LD forces.

4 6 6 10 8In terms of size and shape: CCl < C H < C H

4The strengths of the LD forces are proportional to size and are related to shape. Although CCl is


fairly large, its overall spherical shape gives rise to relatively weak LD forces as compared to flatmolecules like benzene and naphthalene. The physical properties given in the problem are consistentwith the order listed above. Each of the physical properties will increase with an increase inintermolecular forces.

Acetone Acetic Acid

LD, dipole LD, dipole, H bonding

Benzoic Acid

LD, dipole, H bonding

We would predict the strength of intermolecular forces for the last three molecules to be:

acetone < acetic acid < benzoic acid

polar H bonding H bonding, but large LD forces because of greater size and shape.

vapThis ordering is consistent with the values given for bp, mp, and )H .

The overall order of the strengths of intermolecular forces based on physical properties are:

4 6 6acetone < CCl < C H < acetic acid < naphthalene < benzoic acid

The order seems reasonable except for acetone and naphthalene. Since acetone is polar, we would notexpect it to boil at the lowest temperature. However, in terms of size and shape, acetone is the smallestmolecule, and the LD forces in acetone must be very small compared to the other molecules.Naphthalene must have very strong LD forces because of its size and flat shape.

93. At any temperature, the plot tells us that substance A has a higher vapor pressure than substance B,with substance C having the lowest vapor pressure. Therefore, the substance with the weakestintermolecular forces is A, and the substance with the strongest intermolecular forces is C.

3 3NH can form hydrogen bonding interactions while the others cannot. Substance C is NH . The other


4 4two are nonpolar compounds with only London dispersion forces. Since CH is smaller than SiH ,

4 4CH will have weaker LD forces and is substance A. Therefore, substance B is SiH .

94. As the electronegativity of the atoms covalently bonded to H increases, the strength of the hydrogenbonding interaction increases.

N @@@ H S N < N @@@ H S O < O @@@ H S O < O @@@ H S F < F @@@ H S F

weakest strongest

95. n8 = 2d sin 2, 8 = , 8 = 229 pm = 2.29 × 10 m = 0.229 nm-10

96. If a face-centered cubic structure, then 4 atoms/unit cell and from Exercise 10.47:

2 l = 16 r2 2

l = r = 144 pm = 407 pm

l = 407 × 10 m = 407 × 10 cm-12 -10


If a body-centered cubic structure, then 2 atoms/unit cell and from Exercise 10.51:

16 r = l + 2 l2 2 2

l = 4r/ = 333 pm = 333 × 10 m-12

l = 333 × 10 cm = 3.33 × 10 cm-10 -8


The measured density is consistent with a face-centered cubic unit cell.

2 297. If TiO conducts electricity as a liquid, then it is an ionic solid; if not, then TiO is a network solid.

98. One B atom and one N atom together have the same number of electrons as two C atoms. Thedescription of physical properties sounds a lot like the properties of graphite and diamond, the twosolid forms of carbon. The two forms of BN have structures similar to graphite and diamond.


2 699. B H : This compound contains only nonmetals so it is probably a molecular solid with covalentbonding. The low boiling point confirms this.

2SiO : This is the empirical formula for quartz, which is a network solid.

CsI: This is a metal bonded to a nonmetal, which generally form ionic solids. The electricalconductivity in aqueous solution confirms this.

W: Tungsten is a metallic solid as the conductivity data confirms.

100. In order to set up an equation, we need to know what phase exists at the final temperature. Toheat 20.0 g of ice from -10.0°C to 0.0°C requires:

To convert ice to water at 0.0°C requires:

q = 20.0 g × = 6.68 kJ = 6680 J

To chill 100.0 g of water from 80.0°C to 0.0° requires:

q = × 100.0 g × 80.0°C = 33,400 J of heat removed

From the heat values above, the liquid phase exists once the final temperature is reached (a lotmore heat is lost when the 100.0 g of water is cooled to 0.0°C than the heat required to convertthe ice into water). To calculate the final temperature, we will equate the heat gain by the ice to theheat loss by the water. We will keep all quantities positive in order to avoid sign errors. Theheat gain by the ice will be the 416 J required to convert the ice to 0.0°C plus the 6680 J required toconvert the ice at 0.0°C into water at 0.0°C plus the heat required to raise the temperature from 0.0°Cto the final temperature.

f fheat gain by ice = 416 J + 6680 J + × 20.0 g × (T - 0.0°C) = 7.10 × 10 + 83.6 T3

f fheat loss by water = × 100.0 g × (80.0°C - T ) = 3.34 × 10 - 418 T4

Solving for the final temperature:

f f f f7.10 × 10 + 83.6 T = 3.34 × 10 - 418 T , 502 T = 2.63 × 10 , T = 52.4°C3 4 4

2101. 1.00 lb × = 454 g H O; A change of 1.00°F is equal to a change of 5/9°C.

The amount of heat in J in 1 Btu is:

2 vapIt takes 40.7 kJ to vaporize 1 mol H O ()H ). Combining these:


= 258 mol/hr

or: = 4650 g/hr = 4.65 kg/hr

102. The critical temperature is the temperature above which the vapor cannot be liquefied no matter what

2pressure is applied. Since N has a critical temperature below room temperature (~22°C), it cannot

3be liquefied at room temperature. NH , with a critical temperature above room temperature, can beliquefied at room temperature.

Challenge Problems

2 2103. A single hydrogen bond in H O has a strength of 21 kJ/mol. Each H O molecule forms two H bonds.Thus, it should take 42 kJ/mol of energy to break all of the H bonds in water. Consider the phasetransitions:

sub fus vapsolid liquid vapor )H = )H + )H

2 subIt takes a total of 46.7 kJ/mol to convert solid H O to vapor ()H ). This would be the amount ofenergy necessary to disrupt all of the intermolecular forces in ice. Thus, (42 ÷ 46.7) × 100 = 90% ofthe attraction in ice can be attributed to H bonding.

104. Both molecules are capable of H bonding. However, in oil of wintergreen the hydrogen bonding isintramolecular.

In methyl-4-hydroxybenzoate, the H bonding is intermolecular, resulting in stronger intermolecularforces and a higher melting point.

2 2 3105. NaCl, MgCl , NaF, MgF AlF all have very high melting points indicative of strong intermolecular

4 4 2 2 5 6forces. They are all ionic solids. SiCl , SiF , F , Cl , PF and SF are nonpolar covalent molecules.

3 2Only LD forces are present. PCl and SCl are polar molecules. LD forces and dipole forces arepresent. In these 8 molecular substances, the intermolecular forces are weak and the melting points

3low. AlCl doesn't seem to fit in as well. From the melting point, there are much stronger forcespresent than in the nonmetal halides, but they aren't as strong as we would expect for an ionic solid.

3AlCl illustrates a gradual transition from ionic to covalent bonding, from an ionic solid to discretemolecules.

106. a. The NaCl unit cell has a face centered cubic arrangement of the anions with cations in theoctahedral holes. There are 4 NaCl formula units per unit cell and, since there is a 1:1 ratio ofcations to anions in MnO, there would be 4 MnO formula units per unit cell, assuming an NaCltype structure. The CsCl unit cell has a simple cubic structure of anions with the cations in thecubic holes. There is one CsCl formula unit per unit cell, so there would be one MnO formula unitper unit cell if a CsCl structure is observed.


× = 4.00 molecules MnO

From the calculation, MnO crystallizes in the NaCl type structure.

b. From the NaCl structure and assuming the ions touch each other, then R = cube edge length = .

R = 4.47 × 10 cm = = 84 pm-8

107. Out of 100.00 g: 28.31 g O × = 1.769 mol O; 71.69 g Ti × = 1.497 mol Ti

1.182 0.8462 The formula is TiO or Ti O.

0.8462For Ti O, let x = Ti per mol O and y = Ti per mol O . Setting up two equations and solving:2+ 2- 3+ 2-

x + y = 0.8462 (mass balance) and 2x + 3y = 2 (charge balance); 2x + 3(0.8462 - x) = 2

x = 0.539 mol Ti /mol O and y = 0.307 mol Ti /mol O2+ 2- 3+ 2-

× 100 = 63.7% of the titanium ions is Ti and 36.3% is Ti (a 1.75:1 ion ratio).2+ 3+

108. First we need to get the empirical formula of spinel. Assume 100.0 g of spinel.

37.9 g Al × = 1.40 mol Al

The mole ratios are 2:1:4.17.1 g Mg × = 0.703 mol Mg

2 4Empirical Formula = Al MgO

45.0 g O × = 2.81 mol O

2 4 2 4Assume each unit cell contains an integral value (n) of Al MgO formula units. Each Al MgOformula unit has a mass of: 24.31 + 2(26.98) + 4(16.00) = 142.27 g/mol

density = , Solving: n = 8.00

2 4Each unit cell has 8 formula units of Al MgO or 16 Al, 8 Mg and 32 O atoms.

109.


The type of cubic cell formed is not important; only that Cu and Mn crystallize in the same type ofcubic unit cell is important. Each cubic unit cell has a specific relationship between the cube edgelength, l, and the radius, r. In all cases l % r. Therefore, V % l % r . For the mass ratio, we can use3 3

the molar masses of Mn and Cu since each unit cell must contain the same number of Mn and Cuatoms. Solving:

Mn Cudensity = 0.7341 × density = 0.7341 × 8.96 g/cm = 6.58 g/cm3 3

110. a. The arrangement of the layers are:

A total of 20 cannon balls will be needed.

b. The layering alternates abcabc which is cubic closest packing.

c. tetrahedron

111.As P is lowered, we go from a to b on the phase diagram.The water boils. The boiling of water is endothermic andthe water is cooled (b ÷c), forming some ice. If the pumpis left on, the ice will sublime until none is left. This is thebasis of freeze drying.

112. w = -P)V; Assuming a constant P of 1.00 atm.

373V = = 30.6 L for one mol of water vapor

2 2Since the density of H O(l) is 1.00 g/cm , 1.00 mol of H O(l) occupies 18.0 cm or 0.0180 L.3 3

w = -1.00 atm (30.6 L - 0.0180 L) = -30.6 L atm


w = -30.6 L atm × 101.3 J/LCatm = -3.10 × 10 J = -3.10 kJ 3

)E = q + w = 40.7 kJ - 3.10 kJ = 37.6 kJ

× 100 = 92.4% of the energy goes to increase the internal energy of the water.

The remainder of the energy (7.6%) goes to do work against the atmosphere.

CHAPTER TEN LIQUIDS AND SOLIDS · CHAPTER TEN LIQUIDS AND SOLIDS Questions 12. ... 20. Evaporation...

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Transcript of CHAPTER TEN LIQUIDS AND SOLIDS · CHAPTER TEN LIQUIDS AND SOLIDS Questions 12. ... 20. Evaporation...