Chemistry: A Molecular Approach, 2nd Ed.
Nivaldo Tro
Chapter 11
Liquids,
Solids, and
Intermolecu
lar Forces
April Senger
MALMSTROM Park University
Great Falls Montana
Properties of the
three Phases of Matter
of r
th la
n g cu
re le
St o
rm ns
te o
In ti
ac
?
ttr
ow
A
Fl
it
e?
ill
bl
si
W
es
pr
om
C
State Shape Volume
Solid
fixed
fixed
Liquid indefinite fixed
Gas indefinite indefinite
Density
high
high
low
No No
No Yes
Yes Yes
very strong
intermediate
weak
• Fixed = keeps shape when placed in a container
• Indefinite = takes the shape of the container
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Three Phases of Water
Notice that the densities
of ice and liquid water
are much larger than the
density of steam
Notice that the densities
and molar volumes of ice
and liquid water are
much closer to each
other than to steam
Notice that the densities of
ice is larger than the
density of liquid water.
This is not the norm, but is
vital to the development of
life as we know it.
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Degrees of Freedom
• Particles may have one or several types of
freedom of motion
– and various degrees of each type
• Translational freedom is the ability to move
from one position in space to another
• Rotational freedom is the ability to reorient
the particles direction in space
• Vibrational freedom is the ability to oscillate
about a particular point in space
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Solids
• The particles in a solid are packed
close together and are fixed in
position
– though they may vibrate
• The close packing of the particles
results in solids being
incompressible
• The inability of the particles to move
around results in solids retaining
their shape and volume when
placed in a new container, and
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Solids
• Some solids have their particles
arranged in an orderly
geometric pattern – we call
these crystalline solids
– salt and diamonds
• Other solids have particles that
do not show a regular
geometric pattern over a long
range – we call these
amorphous solids
– plastic and glass
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Liquids
• The particles in a liquid are
closely packed, but they have
some ability to move around
• The close packing results in
liquids being incompressible
• But the ability of the particles to
move allows liquids to take the
shape of their container and to
flow – however, they don’t have
enough freedom to escape or
expand to fill the container
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Gases
• In the gas state, the particles
have complete freedom of motion
and are not held together
• The particles are constantly flying
around, bumping into each other
and the container
• There is a large amount of
space between the particles
– compared to the size of the
particles
– therefore the molar volume of the
gas state of a material is much
larger than the molar volume of
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the
solidApproach,
or liquid
states
Gases
• Because there is a lot of
empty space, the particles
can be squeezed closer
together – therefore gases
are compressible
• Because the particles are not
held in close contact and are
moving freely, gases expand
to fill and take the shape of
their container, and will flow
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Compressibility
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Kinetic – Molecular Theory
• What state a material is in depends
largely on two major factors
1. the amount of kinetic energy the particles
possess
2. the strength of attraction between the
particles
• These two factors are in competition with
each other
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States and Degrees of Freedom
• The molecules in a gas have complete
freedom of motion
– their kinetic energy overcomes the attractive forces
between the molecules
• The molecules in a solid are locked in place,
they cannot move around
– though they do vibrate, they don’t have enough
kinetic energy to overcome the attractive forces
• The molecules in a liquid have limited freedom
– they can move around a little within the
structure of the liquid
– they have enough kinetic energy to overcome
some of the attractive forces, but not enough to
escape each other
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Kinetic Energy
• Increasing kinetic energy increases the
motion energy of the particles
• The more motion energy the molecules
have, the more freedom they can have
• The average kinetic energy is directly
proportional to the temperature
– KEavg = 1.5 kT
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Attractive Forces
• The particles are attracted to each other by
electrostatic forces
• The strength of the attractive forces varies,
some are small and some are large
• The strength of the attractive forces
depends on the kind(s) of particles
• The stronger the attractive forces between
the particles, the more they resist moving
– though no material completely lacks particle
motion
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Kinetic–Molecular Theory
of Gases
• When the kinetic energy is so large it
overcomes the attractions between particles,
the material will be a gas
• In an ideal gas, the particles have complete
freedom of motion – especially translational
• This allows gas particles to expand to fill their
container
– gases flow
• It also leads to there being large spaces
between the particles
– therefore low density 15and compressibility
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Gas Structure
Gas molecules are rapidly
moving in random straight
lines, and are free from
sticking to each other.
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Kinetic–Molecular Theory
of Solids
• When the attractive forces are strong
enough so the kinetic energy cannot
overcome it at all, the material will be a
solid
• In a solid, the particles
are packed together
without any translational
or rotational motion
– the only freedom
they have is
vibrational
motion
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Kinetic–Molecular Theory
of Liquids
• When the attractive forces are strong
enough so the kinetic energy can only
partially overcome them, the material will be
a liquid
• In a liquid, the particles
are packed together
with only very limited
translational or
rotational freedom
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Explaining the Properties
of Liquids
• Liquids have higher densities than gases and
are incompressible because the particles are in
contact
• They have an indefinite shape because the
limited translational freedom of the particles
allows them to move around enough to get to
the container walls
• It also allows them to flow
• But they have a definite volume because the
limit on their freedom keeps the particles from
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Phase Changes
• Because the attractive forces between the molecules
are fixed, changing the material’s state requires
changing the amount of kinetic energy the particles
have, or limiting their freedom
• Solids melt when heated because the particles gain
enough kinetic energy to partially overcome the
attactive forces
• Liquids boil when heated because the particles gain
enough kinetic energy to completely overcome the
attractive forces
– the stronger the attractive forces, the higher you will need to
raise the temperature
• Gases can be condensed by decreasing the
temperature and/or increasing the pressure
– pressure can be increased by decreasing the gas volume
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Phase Changes
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Intermolecular Attractions
• The strength of the attractions between
the particles of a substance determines its
state
• At room temperature, moderate to strong
attractive forces result in materials being
solids or liquids
• The stronger the attractive forces are, the
higher will be the boiling point of the liquid
and the melting point of the solid
– other factors also influence
the melting point
22
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Why Are Molecules Attracted to
Each
Other?
Intermolecular attractions are due to
attractive forces between opposite
charges
– + ion to − ion
– + end of polar molecule to − end of polar
molecule
• H-bonding especially strong
– even nonpolar molecules will have
temporary charges
• Larger charge = stronger attraction
• Longer distance = weaker attraction
• However, these attractive forces are
small relative to the bonding forces
between atoms
– generally smaller charges
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Trends in the Strength of
Intermolecular Attraction
• The stronger the attractions between the atoms
or molecules, the more energy it will take to
separate them
• Boiling a liquid requires we add enough energy
to overcome all the attractions between the
particles
– However, not breaking the covalent bonds
• The higher the normal boiling point of the
liquid, the stronger the intermolecular
attractive
forces
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Kinds of Attractive Forces
• Temporary polarity in the molecules due to
unequal electron distribution leads to
attractions called dispersion forces
• Permanent polarity in the molecules due to
their structure leads to attractive forces
called dipole–dipole attractions
• An especially strong dipole–dipole attraction
results when H is attached to an extremely
electronegative atom. These are called
hydrogen bonds.
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Dispersion Forces
• Fluctuations in the electron distribution in
atoms and molecules result in a temporary
dipole
– region with excess electron density has partial (─)
charge
– region with depleted electron density has partial (+)
charge
• The attractive forces caused by these
temporary dipoles are called dispersion
forces
– aka London Forces
• All molecules and atoms will have them
As aA Molecular
temporary
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26 is established in one
Effect of Molecular Size
on Size of Dispersion Force
As
molar
mass
Thethe
Noble
gases
increases,
the number
are all nonpolar
of
electrons
increases.
atomic
elements
Therefore the strength
of the dispersion
forces increases.
The stronger the
attractive forces
between the
molecules, the higher
the boiling point will be.
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Boiling Points of n-Alkanes
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Alkane Boiling Points
• Branched
chains have
lower BPs
than straight
chains
• The straight
chain isomers
have more
surface-tosurface
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contact
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Practice – Choose the Substance
in Each Pair with the Higher Boiling
Point
a) CH4
C4H10
b) C6H12
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C6H12
30
Practice – Choose the Substance
in Each Pair with the Higher Boiling
Point
a) CH4
CH3CH2CH2CH3
b) CH3CH2CH=CHCH2CH3
Both molecules
are nonpolar
larger molar
mass
cyclohexane
Both molecules
are nonpolar, but
the flatter ring
molecule has
larger surface-tosurface contact
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Dipole–Dipole Attractions
• Polar molecules have a permanent dipole
– because of bond polarity and shape
– dipole moment
– as well as the always present induced dipole
• The permanent dipole adds to the attractive
forces between the molecules
– raising the boiling and melting points relative to
nonpolar molecules of similar size and shape
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Example 11.1b: Determine if dipole–
dipole attractions occur between
CH
Cl
molecules
2
2
CH Cl , EN C = 2.5, H = 2.1, Cl = 3.0
Given:
2 2
Find: If there are dipole–dipole attractions
Conceptual
Plan:
Formula
Lewis
Structure
Bond
Polarity
EN Difference
Relationships:
Solution:
Molecule
Polarity
Shape
molecules that have dipole–dipole attractions must be polar
Cl—C
3.0−2.5areas
= 0.5
4 bonding
polarpairs =
no lone
tetrahedral
C—H shape
2.5−2.1 = 0.4
nonpolar
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polar bonds and
tetrahedral shape
= polar molecule
polar molecule;
therefore dipole–
dipole attractions
Practice – Choose the substance
in each pair with the higher
boiling point
a)
CH2FCH2F
CH3CHF2
b)
or
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Practice – Choose the substance
in each pair with the higher boiling
point
a)
CH2FCH2F
CH3CHF2
b)
or
polar
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nonpolar
35
more polar
Hydrogen Bonding
• When a very electronegative atom is
bonded to hydrogen, it strongly pulls the
bonding electrons toward it
– O─H, N─H, or F─H
• Because hydrogen has no other electrons,
when its electron is pulled away, the nucleus
becomes deshielded
– exposing the H proton
• The exposed proton acts as a very strong
center of positive charge, attracting all the
electron
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H-Bonding
HF
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H-Bonding in Water
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H-Bonds
• Hydrogen bonds are very strong
intermolecular attractive forces
– stronger than dipole–dipole or dispersion forces
• Substances that can hydrogen bond will
have higher boiling points and melting points
than similar substances that cannot
• But hydrogen bonds are not nearly as strong
as chemical bonds
– 2 to 5% the strength of covalent bonds
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Attractive Forces and Solubility
• Solubility depends, in part, on the attractive
forces of the solute and solvent molecules
– like dissolves like
– miscible liquids will always dissolve in each
other
• Polar substances dissolve in polar solvents
– hydrophilic groups = OH, CHO, C=O, COOH, NH2,
Cl
• Nonpolar molecules dissolve in nonpolar
solvents
– hydrophobic groups = C-H, C-C
• Many molecules have both hydrophilic and
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hydrophobic
parts
– solubility
in water
Immiscible Liquids
Pentane, C5H12 is a
nonpolar molecule.
Water is a polar
molecule.
The attractive
forces between the
water molecules is
much stronger than
their attractions for
the pentane
molecules. The
result is the liquids
are immiscible.
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Ion–Dipole Attraction
• In a mixture, ions from an ionic compound
are attracted to the dipole of polar
molecules
• The strength of the ion–dipole attraction is
one of the main factors that determines the
solubility of ionic compounds in water
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Summary
• Dispersion forces are the weakest of the
intermolecular attractions
• Dispersion forces are present in all
molecules and atoms
• The magnitude of the dispersion forces
increases with molar mass
• Polar molecules also have dipole–dipole
attractive forces
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Summary (cont’d)
• Hydrogen bonds are the strongest of the
intermolecular attractive forces
– a pure substance can have
• Hydrogen bonds will be present when a
molecule has H directly bonded to either O , N,
or F atoms
– only example of H bonded to F is HF
• Ion–dipole attractions are present in mixtures
of ionic compounds with polar molecules.
• Ion–dipole attractions are the strongest
intermolecular attraction
Ion–dipole
attractions
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Liquids
Properties &
Structure
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Surface Tension
• Surface tension is a property of liquids that
results from the tendency of liquids to
minimize their surface area
• To minimize their surface
area, liquids form drops
that are spherical
– as long as there
is no gravity
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Surface Tension
• The layer of molecules on the surface
behave differently than the interior
– because the cohesive forces on the surface
molecules have a net pull into the liquid interior
• The surface layer acts like an elastic skin
– allowing you to “float” a paper clip even though
steel is denser than water
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Surface Tension
• Because they have fewer
neighbors to attract them, the
surface molecules are less
stable than those in the interior
– have a higher potential energy
• The surface tension of a liquid is
the energy required to increase
the surface area a given amount
– surface tension of H2O = 72.8
mJ/m2
• at room temperature
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Factors Affecting
Surface Tension
• The stronger the intermolecular attractive
forces, the higher the surface tension will
be
• Raising the temperature of a liquid
reduces its surface tension
– raising the temperature of the liquid increases
the average kinetic energy of the molecules
– the increased molecular motion makes it
easier to stretch the surface
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Viscosity
• Viscosity is the resistance of a liquid to flow
– 1 poise = 1 P = 1 g/cm∙s
– often given in centipoise, cP
• H2O = 1 cP at room temperature
• Larger intermolecular attractions = larger
viscosity
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Factors Affecting
Viscosity
• The stronger the intermolecular attractive forces,
the higher the liquid’s viscosity will be
• The more spherical the molecular shape, the lower
the viscosity will be
– molecules roll more easily
– less surface-to-surface contact lowers attractions
• Raising the temperature of a liquid reduces its
viscosity
– raising the temperature of the liquid increases the
average kinetic energy of the molecules
– the increased molecular motion makes it easier to
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Capillary Action
• Capillary action is the ability of a liquid to
flow up a thin tube against the influence of
gravity
– the narrower the tube, the higher the liquid rises
• Capillary action is the result of two forces
working in conjunction, the cohesive and
adhesive forces
– cohesive forces hold the liquid molecules
together
– adhesive forces attract the outer liquid
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molecules
to 2/e
the tube’s
surface
Capillary Action
• The adhesive forces pull the surface liquid up
the side of the tube, and the cohesive forces
pull the interior liquid with it
• The liquid rises up the tube until the force of
gravity counteracts the capillary action forces
• The narrower the tube diameter, the higher the
liquid will rise up the tube
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Meniscus
• The curving of the liquid surface in a
thin tube is due to the competition
between adhesive and cohesive
forces
• The meniscus of water is concave in
a glass tube because its adhesion to
the glass is stronger than its
cohesion for itself
• The meniscus of mercury is convex
in a glass tube because its cohesion
for itself is stronger than its
adhesion for the glass
– metallic bonds are stronger
than
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The Molecular Dance
• Molecules in the liquid are constantly in
motion
– vibrational, and limited rotational and
translational
• The average kinetic energy is
proportional to the temperature
• However, some molecules have more
kinetic energy than the average, and
others have less
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Vaporization
• If these high energy molecules
are at the surface, they may
have enough energy to
overcome the attractive forces
– therefore – the larger the
surface area, the faster the
rate of evaporation
• This will allow them to escape
the liquid and become a vapor
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Condensation
• Some molecules of the vapor will lose
energy through molecular collisions
• The result will be that some of the
molecules will get captured back into the
liquid when they collide with it
• Also some may stick and gather together to
form droplets of liquid
– particularly on surrounding surfaces
• We call this process condensation
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Evaporation vs. Condensation
• Vaporization and condensation are opposite
processes
• In an open container, the vapor molecules generally
spread out faster than they can condense
• The net result is that the rate of vaporization is
greater than the rate of condensation, and there is a
net loss of liquid
• However, in a closed container, the vapor is not
allowed to spread out indefinitely
• The net result in a closed container is that at some
time
the
rates
of
vaporization
and
condensation
will
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Effect of Intermolecular Attraction
on Evaporation and
Condensation
• The weaker the
attractive forces between
molecules, the less energy they will need to
vaporize
• Also, weaker attractive forces means that more
energy will need to be removed from the vapor
molecules before they can condense
• The net result will be more molecules in the vapor
phase, and a liquid that evaporates faster – the
weaker the attractive forces, the faster the rate
of evaporation
• Liquids that evaporate easily are said to be
volatile
60 polish remover
– e.g., gasoline, fingernail
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Energetics of Vaporization
• When the high energy molecules are lost
from the liquid, it lowers the average kinetic
energy
• If energy is not drawn back into the liquid,
its temperature will decrease – therefore,
vaporization is an endothermic process
– and condensation is an exothermic process
• Vaporization requires input of energy to
overcome the attractions between
molecules
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Heat of Vaporization
• The amount of heat energy required to
vaporize one mole of the liquid is called the
heat of vaporization, DHvap
– sometimes called the enthalpy of vaporization
• Always endothermic, therefore DHvap is +
• Somewhat temperature dependent
 DHcondensation = −DHvaporization
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Example 11.3: Calculate the mass of
water that can be vaporized with 155
kJ
of
heat
at
100
°C
Given:
155 kJ
Find:
Conceptual
Plan:
g H2O
kJ
mol H2O
g H2O
Relationships: 1 mol H2O = 40.7 kJ, 1 mol = 18.02 g
Solution:
Check: because the given amount of heat is almost 4x
the DHvap, the amount of water makes sense
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Practice – Calculate the amount of heat needed to
vaporize 90.0 g of C3H7OH at its boiling point
Given:
Find:
Conceptual
Plan:
90.0 g
kJ
g
mol
kJ
Relationships: 1 mol C3H7OH = 39.9 kJ, 1 mol = 60.09 g
Solution:
Check:
because the given amount of C3H7OH is more
than 1 mole the amount of heat makes sense
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Dynamic Equilibrium
• In a closed container, once the rates of
vaporization and condensation are equal, the
total amount of vapor and liquid will not change
• Evaporation and condensation are still
occurring, but because they are opposite
processes, there is no net gain or loss of either
vapor or liquid
• When two opposite processes reach the same
rate so that there is no gain or loss of material,
we call it a dynamic equilibrium
– this does not mean there are equal amounts of
vapor
and
liquid
that they are changing
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Dynamic Equilibrium
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Vapor Pressure
• The pressure exerted by the vapor when it is in
dynamic equilibrium with its liquid is called the
vapor pressure
– remember using Dalton’s Law of Partial Pressures
to account for the pressure of the water vapor when
collecting gases by water displacement?
• The weaker the attractive forces between the
molecules, the more molecules will be in the
vapor
• Therefore, the weaker the attractive forces,
the higher the vapor pressure
– the higher the vapor pressure,
the more volatile the
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Vapor–Liquid Dynamic
Equilibrium
If the volume of the
chamber is increased, it will
decrease the pressure of the vapor inside the
chamber
– at that point, there are fewer vapor molecules in a given
volume, causing the rate of condensation to slow
• Therefore, for a period of time, the rate of
vaporization will be faster than the rate of
condensation, and the amount of vapor will increase
• Eventually enough vapor accumulates so that the
rate of the condensation increases to the point
where it is once again as fast as evaporation
– equilibrium is reestablished
• At this point, the vapor 68
pressure will be the same as
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Changing the Container’s Volume
Disturbs the Equilibrium
Initially, the rate of
vaporization and
condensation are equal
and the system is in
dynamic equilibrium
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When the volume is
increased, the rate of
vaporization becomes
faster than the rate of
condensation
69
When the volume is
decreased, the rate of
vaporization becomes
slower than the rate of
condensation
Dynamic Equilibrium
• A system in dynamic equilibrium can
respond to changes in the conditions
• When conditions change, the system
shifts its position to relieve or reduce
the effects of the change
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Vapor Pressure vs. Temperature
• Increasing the temperature increases the
number of molecules able to escape the
liquid
• The net result is that as the temperature
increases, the vapor pressure
increases
• Small changes in temperature can make
big changes in vapor pressure
– the rate of growth depends on strength of the
intermolecular
forces
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Practice – Which of the following
is the most volatile?
a)
b)
c)
d)
e)
water
TiCl4
ether
ethanol
acetone
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Practice – Which of the following
has the strongest Intermolecular
attractions?
a)
b)
c)
d)
e)
water
TiCl4
ether
ethanol
acetone
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Boiling Point
• When the temperature of a liquid reaches a
point where its vapor pressure is the same
as the external pressure, vapor bubbles can
form anywhere in the liquid
– not just on the surface
• This phenomenon is what is called boiling
and the temperature at which the vapor
pressure = external pressure is the boiling
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point
Boiling Point
• The normal boiling point is the temperature
at which the vapor pressure of the liquid =
1 atm
• The lower the external pressure, the lower the
boiling point of the liquid
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Practice – Which of the following
has the highest normal boiling
point?
a)
b)
c)
d)
e)
water
TiCl4
ether
ethanol
acetone
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Heating Curve of a Liquid
• As you heat a liquid, its
temperature increases
linearly until it reaches
the boiling point
– q = mass x Cs x DT
• Once the temperature
reaches the boiling
point, all the added heat
goes into boiling the
liquid – the temperature
stays constant
• Once all the liquid has
been turned into gas,
the temperature can
againA Molecular
startApproach,
to rise
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Sublimation and Deposition
• Molecules in the solid have thermal energy
that allows them to vibrate
• Surface molecules with sufficient energy may
break free from the surface and become a gas
– this process is called sublimation
• The capturing of vapor molecules into a solid is
called deposition
• The solid and vapor phases exist in dynamic
equilibrium in a closed container
– at temperatures below the melting point
– therefore, molecular solids have a vapor
sublimation
pressure
solid
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gas
Sublimation
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Melting = Fusion
• As a solid is heated, its temperature rises
and the molecules vibrate more vigorously
• Once the temperature reaches the melting
point, the molecules have sufficient energy
to overcome some of the attractions that
hold them in position and the solid melts
(or fuses)
• The opposite of melting is freezing
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Heating Curve of a Solid
• As you heat a solid, its
temperature increases
linearly until it reaches the
melting point
– q = mass x Cs x DT
• Once the temperature
reaches the melting point, all
the added heat goes into
melting the solid – the
temperature stays constant
• Once all the solid has been
turned into liquid, the
temperature can again start to
rise
– ice/water will always have 81
a
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Energetics of Melting
• When the high energy molecules are lost
from the solid, it lowers the average kinetic
energy
• If energy is not drawn back into the solid its
temperature will decrease – therefore,
melting is an endothermic process
– and freezing is an exothermic process
• Melting requires input of energy to
overcome the attractions between
molecules
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Phase Diagrams
• Phase diagrams describe the different states
and state changes that occur at various
temperature/pressure conditions
• Regions represent states
• Lines represent state changes
– liquid/gas line is vapor pressure curve
– both states exist simultaneously
– critical point is the furthest point on the vapor
pressure curve
• Triple point is the temperature/pressure
condition where all three states exist
simultaneously
•
For
most
substances,
freezing
point
increases
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Pressure
Phase Diagram of Water
1 atm
critical
point
374.1 °C
217.7 atm
Ice
Water
normal
melting pt.
0 °C
normal
boiling pt.
100 °C
triple
point
0.01 °C
0.006 atm
Steam
Temperature
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•
Water – An Extraordinary
Substance
Water is a liquid at
room temperature
– most molecular substances with similar molar masses are
gases at room temperature
• e.g. NH3, CH4
– due to H-bonding between molecules
• Water is an excellent solvent – dissolving many ionic and
polar molecular substances
– because of its large dipole moment
– even many small nonpolar molecules have some solubility in
water
• e.g. O2, CO2
• Water has a very high specific heat for a molecular
substance
– moderating effect on coastal climates
• Water expands when it freezes
• at a pressure of 1 atm
– about 9%
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Solids
Properties &
Structure
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Crystal Lattice
• When allowed to cool slowly, the particles in
a liquid will arrange themselves to give the
maximum attractive forces
– therefore minimize the energy
• The result will generally be a crystalline
solid
• The arrangement of the particles in a
crystalline solid is called the crystal lattice
• The smallest unit that shows the pattern of
arrangement for all the particles is called
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Unit Cells
• Unit cells are 3-dimensional
– usually containing 2 or 3 layers of particles
• Unit cells are repeated over and over to give the
macroscopic crystal structure of the solid
• Starting anywhere within the crystal results in the
same unit cell
• Each particle in the unit cell is called a lattice point
• Lattice planes are planes connecting equivalent
points in unit cells throughout the lattice
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7 Unit Cells
c
c
c
b
b
b
a
Cubic
a=b=c
all 90°
a
Tetragonal
a=c<b
all 90°
a
Orthorhombic
abc
all 90°
c
c
b
a
Hexagonal
a=c<b
2 faces 90°
1 face 120°
c
a b
Monoclinic
abc
2 faces 90°
c
b
b
a
Rhombohedral
a=b=c
no 90°
90
a
Triclinic
abc
no 90°
Molecular Solids
• The lattice sites are occupied by molecules
– CO2, H2O, C12H22O11
• The molecules are held together by
intermolecular attractive forces
– dispersion forces, dipole–dipole attractions,
and H-bonds
• Because the attractive forces are weak,
they tend to have low melting points
– generally < 300 °C
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Ionic Solids
• Lattice sites occupied by ions
• Held together by attractions between oppositely charged
ions
– nondirectional
– therefore every cation attracts all anions around it, and viceversa
• The coordination number represents the number of close
cation–anion interactions in the crystal
• The higher the coordination number, the more stable the
solid
– lowers the potential energy of the solid
• The coordination number depends on the relative sizes
of the cations and anions that maintains charge balance
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Ionic Crystals
CsCl
coordination number = 8
Cs+ = 167 pm
Cl─ = 181 pm
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NaCl
coordination number = 6
Na+ = 97 pm
Cl─ = 181 pm
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