chapter9-p2_After lecture notssssses.pdf

HKUST chem 1012

1. CHEM 1012:
General Chemistry B
Chapter 9: Liquids and Solids
Professor Haipeng Lu (呂海鵬)
Departmentof Chemistry
The Hong Kong University of Science and Technology
Spring 2025
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Chapter #9 in the Textbook

2. Reviewquestions:
exercise1:Which of the following is the correct order of boiling points for SO
2，
CH
3OH, C
2H
6, Ne?
A) Ne < CH
3OH < C
2H
6< SO
2
B) SO
2< CH
3OH < C
2H
6< Ne
C) Ne < C
2H
6< SO
2< CH
3OH
D) Ne < C
2H
6< CH
3OH < SO
2
E) C
2H
6< Ne < CH
3OH < SO
2
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4. Reviewquestions:
exercise1:Which of the following is the correct order of boiling points for SO
2，
CH
3OH, C
2H
6, Ne?
A) Ne < CH
3OH < C
2H
6< SO
2
B) SO
2< CH
3OH < C
2H
6< Ne
C) Ne < C
2H
6< SO
2< CH
3OH
D) Ne < C
2H
6< CH
3OH < SO
2
E) C
2H
6< Ne < CH
3OH < SO
2
Major force:
Ne < C
2H
6< SO
2 < CH
3OH
London, London, dipole-dipole, H-bonding
Compare Molar Mass
20g/mol30g/mol
bigger

5. CHEM 1012: Chapter 9
CHAPTER OUTLINE
1.Intermolecular Forces
2.Some Properties of Liquid States
3.Change of States and Phase Diagrams
4.An Introduction to Structures and Types of Solids
5.Structure and Bonding in Metals and Alloys
6.Covalent Network Solids
7.Ionic Solids
8.Molecular Solids
9.Non-Crystalline Solids
Reference and Suggested Reading:
“Chemistry, an atoms first approach”, Zumdahl& Zumdahl, 2016: Chapter 9

6. Change of States and Phase Diagrams

7. Equilibrium and interchange between physical
states
General consideration: Equilibrium and inter-change between physical states;
Equilibrium: the state at which two reversible processes occur at the same rate.
Equilibrium between physical states: the state at which two (or more) physical states
coexist at a given T and P, and at which the rates from one physical state to another is
the same to its reverse process, e.g.,
Equilibriumbetweenphysicalstatesismicroscopicallydynamic:atmicroscopic(or
molecularlevel),thetwooppositeprocessesofchangeoccurconstantly,butat
macroscopiclevel,thereisnonetchange.
Theinter-changebetweenphysicalstatesinvolvesthechangeofenthalpy∆H(=
H
f–H
i),inanotherwords,involvestheconsumptionorreleaseofheat(q).
kis reaction rate constant

8. Equilibrium and interchange between physical
states
General consideration : Equilibrium and inter-change between physical states;
The most common types of equilibria and interchanges between physical states:

9. Equilibrium and interchange between physical
states
General consideration : Equilibrium and inter-change between physical states;
The enthalpy of phase change: Signs of ∆H
•H
fus, Heat of Fusion:
Energy required to change
a solid at its melting point
to a liquid.
•H
vap, Heat of
Vaporization:Energy
required to change a
liquid at its boiling
point to a gas.

10. Equilibrium and interchange between physical
states
General consideration : The heating/cooling curve and the change of physical state
ss
+
l
l
l + g
g
vaporization
or boiling
fusion
or melting
Under equilibrium, T.
remains a constant

11. Equilibrium and interchange between physical
states
Gas(vapor) Liquid equilibrium and their interchange: P
vap, T
b and ∆H
vap
Vapor pressure (P
vap): the pressure of the vapor at the vapor-liquid equilibrium at a given T.
Molar enthalpy of vaporization (∆H
vap): the energy (often heat) required to vaporize 1 mole of a
liquid at a pressure of 1 atmand at a given T.
Molar enthalpy of condensation: ∆H
cond= −∆H
vapat the same T and P;
Boiling point, T
b: Temperature at which the P
vapof a liquid is equal to its environment;
Normal boiling point, T
B: Temperature at which the P
vapof a liquid is equal to 1 atm.

12. Equilibrium and interchange between physical
states
Gas(vapor) Liquid equilibrium and their interchange: P
vap, T
b
Vapor pressure (P
vap) depends sensitively on the temperature ( T );
P
vapincreases as the T increases.
T
2> T
1
100 760
At higher T, the proportion of molecules with enough energy to escape liquids to the vapor phase
(shaded area) increases dramatically, causing Pvapto increase.

13. Equilibrium and interchange between physical
states
Gas(vapor) Liquid equilibrium and their interchange: T
b
At a given P
vap, the higher T
bimplies larger intermolecular forces
Similarly, at a given T, the lower P
vap, implies larger intermolecular forces

14. Equilibrium and interchange between physical
states
Gas(vapor) Liquid equilibrium and their interchange: how to get ∆H
vap?
Assuming ∆H
vapis T-independent within a small range of temperature change, the measured P
vapvs. Tin the
figure can be fit by
The derivation of this equation involves Gibbs energy and it is out of scope here

15. Equilibrium and interchange between physical
states
Gas(vapor) Liquid equilibrium and their interchange: how to get ∆H
vap?
To obtain Pvapat different T and to obtain Tb at different P.
Clausius-Clapeyron equation: how to obtain Pvapat T2 if given Pvapat T1?
it is assumed that ∆H
vapis known, and that ∆H
vapis T-independent between T
2and T
1.

16. Phase Diagrams
Phase:astateofmatterthatpossessuniformphysicalandchemicalproperties.For
example,solid,liquid,andgasarethreedifferentphases
Phase diagrams: display the state of a substance at various pressures (P) and
temperatures (T) and the places where equilibria exist between phases.

17. Phase Diagrams
•The ABline is the liquid-vapor interface.
•It starts at the triple point(A), the point at which all three states are in equilibrium.

18. Phase Diagrams
It ends at the critical point(B); above this critical temperature and critical pressure
the liquid and vapor are indistinguishable from each other.
Above the critical
temperature the
sample is quite
uniform and it is
difficult to know
whether to call it
a liquid or a gas.

19. Phase Diagrams
It ends at the critical point(B); above this critical temperature and critical pressure
the liquid and vapor are indistinguishable from each other.
•The Figure illustrates what happens experimentally
in the case of propane. As the temperature nears
the critical value of 97°C, liquid and vapor become
very similar in appearance and the meniscus
between them becomes difficult to distinguish.
•At the critical temperature the meniscus
disappears completely. Above the critical
temperature the sample is quite uniform and it is
difficult to know whether to call it a liquid or a gas.
liquid or gas?
propane

20. Phase Diagrams
•The ABline is the liquid-vapor interface.
Each point along this line is the boiling point of the substance at that pressure.

21. Phase Diagrams
•The ADline is the interface between liquid and solid.
•The melting point at each pressure can be found along this line.

22. Phase Diagrams
•Along the ACline the solid and gas phases are in equilibrium;
the sublimation point at each pressure is along this line.

23. Phase Diagrams
example2:Answer the following questions
(a) What phases ispresent at T = 373 K and P = 0.8 atm?
(b)What is the minimum pressure at which liquid H
2O
can exist?
(c)H
2O (s) initially at 273 Kand 0.5atmis compressed
to 400atm. What might happen?
Phase Diagram of water

24. Phase Diagrams
example2:Answer the following questions
(a) What phases ispresent at T = 373 K and P = 0.8 atm?
gas
(b)What is the minimum pressure at which liquid H
2O
can exist?
0.006 atm
(c)H
2O (s) initially at 273 Kand 0.5atmis compressed
to 400atm. What might happen?
It changes to liquid
Phase Diagram of water

25. Reviewquestions:
exercise1:The phase diagram for mysterious compound Xisshownbelow.
At350 °C, ~50 atm, itcanexistas_____________
A) solid
B) liquid
C) gas
D) all of the above
E) noneoftheabove
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27. Reviewquestions:
exercise2:The phase diagram for mysterious compound Xisshownbelow.
At350 °C, ~50 atm, itcanexistas_____________
A) solid
B) liquid
C) gas
D) all of the above
E) noneoftheabove
Triple point (A):the point at which all three states are in
equilibrium.

28. Structures and Types of Solids
•Amorphous Solids:
Disorder in the structures
Based on the structures, solids can be classified as
Crystalline
•Crystalline Solids:
ordered structures
•glass
•polymers
•gels
•thin films
•nanostructured
materials
Amorphous

29. Structures and Types of Solids
There are threetypes of crystalline solids.
–Atomic solids
•metals,
•non-metals (network
covalent, e.g. diamond),
•Group 8A elements (noble
gases e.g. helium, He; neon,
Ne; argon, Ar)
–Ionic solids (e.g. NaCl)
–Molecular solid (e.g. solid
carbon dioxide,ice,tablesugar)

30. Structure and Bonding in Different Solids
A Summary of Types, Bondingand Properties ofCrystallineSolids

31. Structures and Types of Solids
Properties of Crystalline Solids
Metallic crystals
Crystals of packed molecules
Ionic crystals
Ag, Cu: soft to hard, low to high melting points, good conductors of heat and
electricity
CH
4, cholesterol:soft, low melting, poor conductors
NaCl,CuSO
4: hard, brittle, poor conductors of heat and electricity
Network covalent crystals
Diamond,silicon: hard, high melting, poor electrical conductors, poor to
excellent heat conduction

32. Structures and Types of Solids
Classification of solids: A Summary
•Depending on the criterion used, solids can be classified in different ways; (so, do
not be confused by what appeared to be overlapping classifications).
•The most important factors in discussing a solid are (i) chemical nature of its building
blocks (atoms, molecules, ions), (ii) the dominant bonding or interaction force that
holds the components together, and (iii) its long-range orderness(crystalline or
amorphous).

33. Structures and Types of Solids
Properties of Crystalline Solids
In terms of crystal structures, they can be thought as formed by packing of
atoms, ions or molecules. (how do we describe them?)
How to describe periodic patterns??

34. Can you see the periodic patterns below?
Now, can you imagine if these pieces are replaced with atoms/molecules?

35. How to describe the periodic patterns?
Repeating unit + how they repeat
Unit cell Lattice

36. General properties of crystalline solids
Crystalline solid: a solid whose constituent components or building blocks (atoms,
molecules, or ions) are arranged in an orderedand periodicpattern extending in all
three spatial dimensions.
Common structural features of crystalline solids: lattice and unit cell
Crystalline solids share two structural features: structural lattice and unit cell.
Lattice: a three-dimensional system of pointsdesignating the positions of the
building blocks (atoms, molecules, or ions). --an infinite array of points in space
Unit cell (Bravais lattice): the smallest repeating unit of the lattice.

37. The lattice and unit cell

38. The lattice and unit cell
Now let’s look at a few patterns.. The Snowman Pattern below has only translationalsymmetry. This is
found in many complex molecular crystals
How to identify lattice point and then unit
cell?
•Look for identicalpositionsin the pattern –
the lattice
•join together to form a box –the unit cell
•There are different ways of drawing unit
cells
At lattice points:
•Atoms
•Molecules
•Ions

39. Now, can you draw the lattice point and unit cell?
When Art imitates molecules…

40. Crystals are periodic patterns
Can you identify lattice points and what is in the unit cell ?

41. Crystals are periodic patterns
•Each point represents one Na and one Cl but whether the point is located at Na, at Cl, or in between is
irrelevant.
•The unit cell is constructed by linking the lattice points:
•Bhas lattice points only at the corners is primitive, (P);
•Awhich has additional lattice points is centred(C).
We know how to define unit cells, but how
do describe them?

42. Crystals class and Bravais Lattice
•Crystal Class: Dictates the shape of the unit cell
•2D: 4 types
•3D: 7 types
•Bravais Lattice: Describes the translational symmetry of the lattice. By specifying
the Bravais lattice, you specify the shape of the unit cell (crystal class) and the
centeringconditions.
•2D: 5types
•3D: 14types

43. 2-Dimensional: Latticepoints, Lattice, Unit cell

44. Crystals class in 2D: defines the shape of the
unit cell (4of them)
Cell Edges Cell Angles
Cubic a = b g = 90˚
Rectangular a ≠ b g = 90˚
Hexagonal a = b g= 120˚
Oblique a ≠ b g≠ 90˚

45. Bravais lattice in 2D: crystal class + centering
condition (5of them)
For your information only

46. 3-Dimensional: Latticepoints, Lattice, Unit cell

47. Crystals class in 3D: defines the shape of the
unit cell (7of them)
Class Cell Edges Cell Angles
Cubic a = b = c a = b = g = 90˚
Tetragonal a = b ≠ c a = b = g = 90˚
Orthorhombic a ≠ b ≠ c a = b = g = 90˚
Hexagonal a = b ≠ c a = b = 90˚g= 120˚
Rhombohedral (or trigonal) a = b = c a = b = g < 120˚≠ 90˚
Monoclinic a ≠ b ≠ c a = b = 90˚g≠ 90˚
Triclinic a ≠ b ≠ c a ≠b ≠ g ≠ 90˚
For your information only

48. Bravais lattice in 3D: crystal class + centering
condition (14of them)
Class Centerings
Cubic P, I, F
Tetragonal P, I
Orthorhombic P, I, C, F
Hexagonal P
Rhombohedral P
Monoclinic P, C
Triclinic P
14
For your information only

49. Three Common Cubic Unit Cells
Three Common Unit Cells (these are our primary focus in this course)
Simple cubic
(SC)
Body-centered cubic
(BCC)
Face-centered cubic
(FCC)

50. Three Common Cubic Unit Cells
Please note which balls are in
touchwith each other in the
unit cells.
Another view of the three cubic lattice types

51. Crystalline Solids
Counting Atoms in 3D Cells
•Atoms can be at different positions in a unit cell.
•They may have different contribution to a unit cell,
depending on their positions.
Contribution of atoms to a unit cell
Corner atom Face atom Edge atom Atom withincell

52. Crystalline Solids
A corner atom is shared
by __unit cells.
It contributes ___to a
single unit cell
A face atom is shared
by __unit cells
It contributes ___to a
single unit cell
Corner atoms
8
1/8
2
1/2
Face-centered atoms
Counting Atoms in 3D Cells

53. Crystalline Solids
A edge atom is shared
by __unit cells.
It contributes ___to a
single unit cell
An Atom within the cell is
shared by __unit cell(s)
It contributes ___to a
single unit cell
4
1/4 1
1
Counting Atoms in 3D Cells
An edge atom Atoms within the cell

54. Crystalline Solids
Counting Atoms in 3D Cells
Contribution of atoms to a unit cell:
Corner atom: shared by __ cells___ atom per cell
Edge atom: shared by ___ cells___atom per cell
Face atom: shared by ___ cells__atom per cell
Atom withincell: shared by ___ cell(s)__atom per cell
8
1/8
4 1/4
2 1/2
1 1
Corner atom Face atom Edge atom Atom withincell

55. Crystalline Solids
example1:
example1: Give the following informationfor the simple cubic unit cell
(a)Number of spheres in the unit cell:
8x(1/8) = 1
(b) Relationship between cell size (l) and radius of ball (r):
l = 2r
l
r
r
l = 2r
1 2
34
5 6
78

56. Crystalline Solids
example2:Give the following information for the fccunit cell
(a)Number of spheres in the unit cell:
8x(1/8) + 6x(1/2) = 4
(b) Relationship between cell size (l) and radius of ball (r):
4r = 2
1/2
L, L = 2 (2)
1/2
r
X
r
X=4r
L
4r=2½L
L = 2 (2)
1/2
r
L
r
r
r

57. Crystalline Solids
example3:How about Body-centered cubic (BCC)?
(a)Number of spheres in the unit cell:
(b) Relationship between cell size (l) and radius of ball (r):
Y=4r
L
L
X
2
+ L
2
= Y
2
L
2
+ L
2
= X
2
4r = (3)
1/2
l
2
r
r
r
r

58. Crystalline Solids
exercise1:What are the empirical formulas for these compounds?
Green: chlorine;
Gray: cesium
Yellow: sulfur;
Gray: zinc
Green: calcium;
Gray: fluorine
A:CsCl,Zn
2S
3,CaF
B:CsCl,ZnS,CaF
2
C:CsCl
8,ZnS,CaF
D:CsCl
8,Zn
2S
3,CaF
2
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60. Crystalline Solids
exercise1:What are the empirical formulas for these compounds?
Green: chlorine;
Gray: cesium
Yellow: sulfur;
Gray: zinc
Green: calcium;
Gray: fluorine
A:CsCl,Zn
2S
3,CaF
B:CsCl,ZnS,CaF
2
C:CsCl
8,ZnS,CaF
D:CsCl
8,Zn
2S
3,CaF
2
# Cs = 1
# Cl= 8x(1/8) = 1
CsCl
# Zn = 4
# S = 8x(1/8) + 6x(1/2) = 4
ZnS
# F = 8
# Ca= 8x(1/8) + 6x(1/2) = 4
CaF
2

61. Crystalline Solids
Coord. no. = 8Coord. no. = 6
Coord. no. = coordination number: the number of nearest atoms
Simple cubic
Body-centered cubic
Coord. no. = 12
Face-centered cubic

62. Packing density in crystalline solids
Fraction of Space Occupied by Spheres
Can be easily calculated.
e.g. for FCC,
There are 4 atoms in the unit cell. V
sphere
V
unit cell
= =
4 (4/3) p r
3
l
3
l = 2(2)
1/2
r
= 74.05%
l
V
sphere= (4/3)pr
3
（packing density）
V
sphereforoneatom,
l
2
+l
2
=(4r)
2
x
x
X
l
X=4r
4r=2½l
l= 2 (2)
1/2
r
V
cell= l
3
V
sphereforunit cell,

63. Summary of packing density in cubic cells
Fraction of Space Occupied by Spheres
Name Coord. no.Sphere touchingCell size% Space used
Simple cubic6 Cell edge I = 2r 52%
Body-centered8 Body diagonal 4r = (3)
1/2
l68%
Face-centered12 Face diagonal 4r = (2)
1/2
l74%
l r
Face-centercubic (fcc) has the largest packing density!!

64. Crystalline Solids
Mass of unit cell = Number of atoms in unit cell x Mass of each atom
Mass of unit cell = Mass of each atom =
a
3
is the volume of the unit cell, where ais the edge length of a unit cellZ m m
M
N
= =


ZM
Na
3 a
a
V
cell= a
3
Calculation of Density of Unit CellDensityofUnitCell
MassofunitCell
VolumeofunitCell
=
Z = No of atoms in unit cell
Nis Avogadro’s Number
Mis the Molar mass of the atom

65. Crystalline Solids
Example:Nickelhasaface-centeredcubicunitcell.Thedensityof
nickelis6.84g/cm
3
.Calculateavaluefortheatomicradiusofnickel.DensityofUnitCell
MassofunitCell
VolumeofunitCell
=
A:6.8x10
-7
cm
B:1.36x10
-8
cm
C:2.04x10
-8
cm
D:2.72x10
-8
cm
x
3
=0.057x10
-21
cm
3
x=0.385x10
-7
cm
3

66. Crystalline Solids
Example:Nickelhasaface-centeredcubicunitcell.Thedensityofnickelis
6.84g/cm
3
.Calculateavaluefortheatomicradiusofnickel.
There are four Ni atoms in each unit cell.
For a unit cell:
l
3
=
4x58.69g
6.022x10
23
x6.84g/cm
3
l
3
=0.057x10
-21
cm
3
l=0.385x10
-7
cm
3

67. Structures and Types of Solids
X-Ray Analysis of Solids
•X-ray diffraction is used to determine the structure of crystalline solids
•Diffraction occurs due to:
•Constructive interference when parallel beam waves are in phase
•Destructive interference when waves are out of phase
•Distance traveled by waves depends on the distance between the atoms
•A diffractometer is used to carry out X-ray analysis of crystals
Constructive
interference
Destructive
interference

68. Structures and Types of Solids
X-Ray Analysis of Solids
•Used in the estimation of interatomic spacing
•Where
•nis an integer
•λis the wavelength of the X rays
•dis the distance between atoms
•is the angle of incidence and reflection λ = 2 sin nd θ 
The Bragg Equation
Reflection of X rays of Wavelength λfrom a Pair
of Atoms in two Different Layers of a Crystal

69. Structures and Types of Solids
X-Ray Analysis of Solids
•Used in the estimation of interatomic spacing
•Where
•nis an integer
•λis the wavelength of the X rays
•dis the distance between atoms
•is the angle of incidence and reflection λ = 2 sin nd θ 
The Bragg Equation
Reflection of X rays of Wavelength λfrom a Pair
of Atoms in two Different Layers of a Crystal

70. Structures and Types of Solids
example1:X rays of wavelength 1.54 Åwere used to analyzean aluminumcrystal. A
reflection was produced at = 19.3 degrees. Assuming n =1, calculate the distance d
between the planes of atoms producing this reflection
•Solution
•To determine the distance between the planes, use the Bragg equation where
•n= 1
•λ= 1.54 Å
•= 19.3 degrees 2 sin =λdθn 
 
o
o
1 1.54 A
λ
= = = 2.33A = 233 pm
2 sin 2 0.3305
n
d
θ



•Since
Reflection of X rays of Wavelength λfrom a Pair
of Atoms in two Different Layers of a Crystal

71. SummaryofChapter 9(part 2)
Liquids and Solids
1.Intermolecular Forces
2.Some Properties of Liquid States
3.Change of States and Phase Diagrams
4.An Introduction to Structures and Types of Solids
5.Structure and Bonding in Metals and Alloys
6.Covalent Network Solids
7.Ionic Solids
8.Molecular Solids
9.Non-Crystalline Solids
simplecubicbody-centeredcubic
PhaseChanges
triplepoint
criticalpoint
PhaseDiagram
H
vap, Heat of Vaporization
H
fus, Heat of Fusion
atomicsolids
ionicsolids
molecularsolids
crystallinesolidsamorphoussolids
face-centeredcubic
x-rayBragg Equation
calculation of density of unit cell