Chapter 16 Liquids and Solids
Red beryl
Be3Al2Si6O18
16.1
Intermolecular Forces
16.2
The Liquid State
16.3
Structures and Types of Solids
16.4
Structure and Bonding in Metals
16.5
Carbon and Silicon: Network Atomic Solids
16.6
Molecular Solids
16.7
Ionic Solids
16.8
Structures of Actual Ionic Solids
16.9
Lattice Defects
H2O(s)
H2O(l)
∆Hofus = 6.02 kJ/mol
H2O(l)
H2O(g)
∆Hovap = 40.7 kJ/mol
The liquid and solid states show many similarities and are
strikingly different from the gaseous state.
16.1 Intermolecular Forces
The forces cause the aggregation of the components
of a substance to form a liquid or a solid
 Ionic bonding
 Covalent bonding
 intermolecular forces
Dipole-Dipole Forces
London Dispersion Forces
Dipole-Dipole Forces
 Molecules with dipole moments can attract each
other
electrostatically by lining up so that the
positive and negative ends are close to each other.
 In a condensed state such
as a liquid, the dipoles find
the best comprise between
attraction and repulsion.
 Dipole-dipole forces are
typically only ~1% as strong
as covalent or ionic bonds,
and
they
weaker
as
between
increases.
rapidly
the
the
become
distance
dipoles
 Strong dipole-dipole forces are seen among molecules
in which hydrogen is bound to a highly electronegative
atom, such as N, O, or F.
 The strengths of these interactions are affected by the
great polarity of the bond and the close approach of the
dipoles, allowed by the very small size of the H atom.
 Because dipole-dipole attractions of this type are so
unusually strong, they are given a special name –
hydrogen bonding.
Why?
Group 4A: nonpolar hybrides
b.p. increase with molar mass
 The relatively large electronegativity values
for the lightest elements in each group, which
leads to especially polar X-H bonds.
 The small size of the first element of each
groups allows for the close approach of the
dipoles,
further
intermolecular forces.
strengthening
the
London Dispersion Forces
 The weak forces that exist among noble gas
atoms and nonpolar molecules are called London
dispersion forces.
 Atoms can develop a momentary nonsymmetrical
electron distribution that produces a temporary dipolar
arrangement of charge.
 This instantaneous dipole
can then induce a similar
dipole in a neighboring atom.
 This phenomenon leads to
an interatomic attraction that is
both weak and short-lived.
 For these interactions to
become strong enough to
produce a solid, the motions of
the atoms must be greatly
reduced.
 This explains why the noble
gas elements have such low
freezing points.
 As the mass increases, the number of electrons increases,
so there is an increased chance of the occurrence of
momentary dipoles.
London dispersion forces greatly
increases as atomic size increases.
London dispersion forces between H2 molecules
Nonpolar molecules
such as H2, CH4,
CCl4 and CO2
16.2 The Liquid State
 When a liquid is poured onto a solid surface, it
tends to bead as droplets, a phenomenon that
depends on the intermolecular forces.
 The effect of this uneven
pull
on
the
surface
molecules tends to draw
them into the body of the
liquid and causes a droplet
of liquid.
Capillary action
 Polar liquids exhibit capillary action, the
spontaneous rising of a liquid in a narrow tube.
 Two different types of forces responsible for
this property: cohesive forces and adhesive forces.
The property of like molecules (of the same
substance) to stick to each other due to mutual
attraction
Adhesion is the property of different molecules or
surfaces to cling to each other.
Water
has
both
(intermolecular)
strong
forces
cohesive
and
strong
adhesive forces to glass, it “pulls itself”
up a glass capillary tube to a height
where the weight of the column of
water
just
balances
the
water’s
tendency to be attracted to the glass
surface.
The concave shape of the meniscus shows that water’s
adhesive forces toward the glass are stronger than its
cohesive forces.
A
nonpolar
liquid
such
as
mercury Hg shows a convex
meniscus in a glass tube. This
behavior is characteristic of a
liquid in which the cohesive
forces are stronger than the
adhesive forces toward the glass.
Viscosity
 Liquids with large intermolecular forces tend
to be highly viscous.
 Glycerol has an unusually high viscosity,
mainly because of its high capacity to form
hydrogen bonds.
 Molecular complexity also leads to higher
viscosity because very large molecules can
become entangled with each other.
 Nonviscous gasoline contains molecules of
the type CH3-(CH2)n-CH3, where n varies from
about 3 to 8.
 However, grease, which is very viscous,
contains much larger molecules in which n
varies from 20 to 50.
16.3 An introduction to Structures and Types of Solids
Quartz
Fluorite
ZnS
ZnS
Unit Cell
 The smallest repeating unit of the lattice is
called the unit cell.
 A particular lattice can be generated by
repeating (translating) the unit cell in three
dimensions to form the extended structure.
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Primitive Cubic
Unit cell
can be atoms, ions or molecules
Lattice
Body-Centered Cubic
Unit cell
Lattice
Space-filling
unit cell
Face-Centered Cubic
Unit cell
X-Ray Analysis of Solids
 The structures of crystalline solids are most
commonly determined by X-ray diffraction.
 Diffraction occurs when beams of light are
scattered from a regular array of points or lines
where the spacing between the components are
comparable to the wavelength of lights
Constructive interference
the parallel beams are in phase
d1 the difference in the distance traveled by the two
ways is a integer number of wavelengths
Destructive interference
the parallel beams are out of phase
d2 the difference in the distance traveled by the two
ways is odd number of 1/2 wavelengths
The distance traveled after reflection depends on the
distance between the atoms, so the diffraction pattern can
be used to determine the interatomic spacings.
dsin
xy + yz = 2dsin
xy + yz = n
xy + yz = 2dsin
Bragg equation
2dsin = n
William Henry Bragg (1862-1942)
William Lawrence Bragg (1890-1972)
They shared the Nobel Prize in Physics in 1915 for their
pioneering work in X-ray crystallography.
16.4 Structure and Bonding in Metals
 Metals are characterized by high thermal and
electrical conductivity, malleability and ductility,
which properties can be traced to the nondirectional
covalent bonding found in metallic crystals.
 We can model a metallic structure by pacing
uniform, hard spheres in a manner that most
efficiently uses the available space.
 Such an arrangement is called closest packing.
abab… close packing
abcabc…. close packing
Hexagonal closed packed (hcp) structure
abab close packing
Hexagonal unit cell
Cubic closed packed (ccp) structure
abcabc close packing
Face-centred unit cell
A characteristic of both hcp and ccp structures is that
each sphere has 12 equivalent nearest neighbots
The net number of spheres in a unit cell
corner: 1/8
face: 1/2
net number of spheres in a fcc unit cell
(1/8 x 8) + (1/2 x 6)
=4
Example 16.1 Silver (Ag) crystallizes in a cubic closest
packed structure. The radius of a silver atom is 1.44 Å.
Calculate the density of solid silver.
d
8r 
8  1.44
d = 4.07 Å = 4.07 x 10-8 cm
density
= mass of four Ag atoms / unit cell volume
= (4 atoms)(107.9 g/mol)(1mol/6.022 x 1023 atoms) / 6.74 x 10-23 cm3
= 10.6 g/cm3
The efficiency of close packing
fv = volume occupied by spheres in the unit cell /
volume of unit cell
4 3
4  r
3
fv 
 0.740
3
( 8r )
d  8r
In a cubic closest packed solid 74% of the space is
occupied by spheres.
Body-Centered Cubic Packing
Each sphere has 8 nearest atoms (12 atoms in closest
packed structures)
The spheres are touched along the body diagonal
net number of spheres in a fcc unit cell : (1/8)x8 + 1 = 2
f2 = 2e2
b2 = (4r)2 = e2 + f2
4r
e
3
4
2  r 3
3
fv 
 0.680
4r 3
(
)
3
Bonding in Metals
 The electron sea model for
metals postulates a regular
array of cations in a “sea” of
valence electrons.
 The
mobile
electrons
conduct heat and electricity
and the cations are easily
moved around as the metal is
hammered into a sheet or
pulled into a wire.
 A related model that gives a more detailed
view of the electron energies and motions is
the band model, or the molecular orbital (MO)
model for metals.
 In this model the electrons are assumed to
travel around the metal crystal in MOs formed
from the valence atomic orbitals of the metal
atoms.
The molecular orbital energy levels produced when various
number of atomic orbitals interact
As many metal atoms
interact in a metal
crystal,
the
large
number of resulting
MOs become closely
spaced,
forming
a
virtual continuous of
levels, call bands.
The energy levels (bands) in a Mg crystal
The electrons in the 3s and 3p valence
orbitals overlap and mix to form MOs.
The electrons in the 1s, 2s and 2p orbitals are close
to the nuclei and thus are localized on each Mg atom.
16.5 Carbon and Silicon: Network Atomic Solids
 Many atomic solids contain strong directional
covalent bonds. These substances are called
network solids.
 In contrast to metals, these materials are
typically brittle and do not efficiently conduct heat
or electricity.
Diamond C
Each
carbon
surrounded
by
is
a
tetrahedral arrangement
of other carbon atoms.
The structure of diamond is stabilized by covalent
bonds, which are formed by the overlap of sp3
hybrid atomic orbitals on each carbon atom.
Graphite C
The
structure
of
graphite is based on
layers of carbon atoms
arranged in fused sixmembered rings.
The three sp2 orbitals on each carbon are used to
form s bonds to three other carbon atoms.
Graphite is slippery, black, and a conductor
 One 2p orbital remains unhybridized on each carbon
and is perpendicular to the plane of carbon atoms.
 These orbitals combine to form a group of closely
spaced  MOs.
Closely spaced  MOs in graphite
 They contribute significantly
to the stability of the graphite
layer because of the  bonding.
 The

MOs
with
their
delocalized electrons account
for the electrical conductivity of
graphite.
These closely spaced orbitals are exactly analogue to
the conduction bands found in metal crystals.
Diamond is hard, colorless and an insulator
The MO energy
Diamond
Metal
Semiconductors Si
 In silicon the energy gap is smaller
and a few electrons can cross the gap
oC,
at
25
making
silicon
a
semiconductor.
 At higher temperature, more energy
is available to excite electrons into the
conduction bands, the conductivity of
silicon increases.
 In
metals,
the
conductivity
decreases with increasing temperature.
Doped silicon ~ n-type
When a small fraction of Si atoms is replaced by As
atoms, each having one more valence electron than
silicon, extra electrons become available for conduction.
Energy level of n-type semiconductor
These extra electrons from
As
atoms
lie
close
in
energy to the conduction
bands and can easily be
excited into these levers
for conducting an electric
current.
Doped silicon ~ p type
When a small fraction
of
Si
atoms
is
replaced by B atoms,
each having one less
valence electron than
silicon.
hole (electron vacancy)
Energy level of p-type semiconductor
There is only one unpaired
electron in some of the
MOs, and these unpaired
electrons can function as
conducting electrons.
p-n junction
 A small number of electrons migrate from ntype region to p-type region.
 The effect of this migration is to place a negative charge
on the p-type region and a positive charge on the n-type
region. This charge buildup, called contact potential or
junction potential, prevents further migration of electrons.
Reverse bias
opposite to the natural
flow of electrons
The junction resists the imposed current flow
through the system.
Forward bias
The movement of electrons is in the favored
direction. The junction has low resistance, and a
current flows easily.
16.6 Molecular Solids
Sulfur crystals contains S8
White phosphorous contains
molecules
P4 molecules
16.7 Ionic Solids
 The structures of most binary compounds,
such as NaCl can be explained by the closest
packing of spheres.
 The large ions, which are usually anions, are
packed
in
one
of
the
closest
packing
arrangements (hcp or ccp), while the smaller
cations fit into holes among the closest packed
anions.
Three types of holes in closest packed structures
(b)
(a)
(c)
The hole increase in size as follows:
Trigonal < Tetrahedral < Octahedral
Whether the tetrahedral or octahedral holes in
a given binary ionic solid are occupied
depends mainly on the relative sizes of the
anions and cation.
Octahedral Holes
e = 2R
R is radius of the packed spheres
r is the radius of octahedral hole
The radius ratio for an octahedral hole
d2 = (2R)2 + (2R)2
d  8R  2( R  r )
r  2R  R  0.414R
Tetrahedral Holes
f  2R
e  2R
R is radius of the packed spheres
r is the radius of octahedral hole
The radius ratio for a tetrahedral hole
b  f  e  (2R)  ( 2R)
2
2
b  6R
2
2
2
b
6
3
r R  
R R
2 2
2
r
3
R  R  0.225R
2
Cubic Holes
f 2  (2R)2  (2R)2
f  2 2R
b 2  f 2  (2R)2  12R 2
b  2 3R  2R  2r
r  3R  R  0.732R
The radius ratio for a cubic hole
Guidelines for Filling Octahedral and Tetrahedral Holes
for Ionic Solid MX
rTet = 0.225 R
rOct = 0.414 R
rCubic = 0.732 R
16.8 Structures of Actual Ionic Solids
The location of tetrahedral hole in face-centered
cubic unit cell
Z = 4 for close packed spheres
Z = 8 for tetrahedral holes
The structure of zinc sulfide ZnS
rZn2+ ≈ 0.35 RS2-
only half tetrahedral
sites are occupied
by Zn2+ ions
The location of octahedral hole in face-centered
cubic unit cell
Z = 4 for close packed spheres
Z = 4 for octahedral holes
The structure of NaCl
rNa+ ≈ 0.66 RCl-
all the octahedral sites are occupied by Na+ ions
The structure of fluorite CaF2
Face-centered cubic
array of Ca2+ with
the F- ions in all the
tetrahedral holes
16.9 Lattice Defects
All real crystals have imperfections called lattice defects
Schottky defects
Crystals with missing particles
For every missing Ca2+ ion in
CaF2, there must be two
missing F‒ ions.
Frenkel defects
Crystals with particles migrated
to nonstandard positions
AgCl, AgBr, AgI
The anions form close packing;
the Ag+ ions are distributed
randomly in the various holes
and can easily travel within the
solid structure.
16.11 Phase Diagrams
The phase diagram for H2O as a function of T and P
Critical point
Tc = 374 ºC
Pc = 218 atm
Triple point
T3 = 0.0098 ºC
P3 = 4.588 torr
The phase diagram for CO2 as a function of T and P
Solid CO2 is more
dense than liquid CO2
fire
extinguisher
dry
ice