Chapter 11 Liquids, Solids, and Intermolecular Forces

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Chapter 11Liquids, Solids, and Intermolecular
Forces
Chemistry A Molecular Approach, 1st Ed.Nivaldo
Tro
Roy Kennedy Massachusetts Bay Community
College Wellesley Hills, MA
2008, Prentice Hall
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Comparisons of the States of Matter

• the solid and liquid states have a much higher
  density than the gas state
• therefore the molar volume of the solid and
  liquid states is much smaller than the gas state
• the solid and liquid states have similar
  densities
• generally the solid state is a little denser
• notable exception ice is less dense than liquid
  water
• the molecules in the solid and liquid state are
  in close contact with each other, while the
  molecules in a gas are far apart

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Freedom of Motion

• 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 dont 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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Properties of the 3 Phases of Matter

• Fixed keeps shape when placed in a container
• Indefinite takes the shape of the container

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Kinetic - Molecular Theory

• the properties of solids, liquids, and gases can
  be explained based on the kinetic energy of the
  molecules and the attractive forces between
  molecules
• kinetic energy tries to give molecules freedom of
  motion
• degrees of freedom translational, rotational,
  vibrational
• attractive forces try to keep the molecules
  together
• kinetic energy depends only on the temperature
• KE 1.5 kT

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Gas Structure
Gas molecules are rapidly moving in random
straight lines and free from sticking to each
other.
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Explaining the Properties of 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
  prevents the particles from flowing

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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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Explaining the Properties of Liquids

• they have higher densities than gases because the
  molecules are in close contact
• they have an indefinite shape because the limited
  freedom of the molecules allows them to move
  around enough to get to the container walls
• but they have a definite volume because the limit
  on their freedom keeps them from escaping the
  rest of the molecules

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Compressibility
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Phase Changes
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Phase Changes animation
Phase Changes and Temp animation
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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 the charge stronger attraction
• longer the distance weaker attraction
• however, these attractive forces are small
  relative to the bonding forces between atoms
• generally smaller charges
• generally over much larger distances

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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 the attractions between the molecules or
  atoms
• the higher the normal boiling point of the
  liquid, the stronger the intermolecular
  attractive forces

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Attractive Forces
-
-
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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 a temporary dipole is established in one
  molecule, it induces a dipole in all the
  surrounding molecules

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Dispersion Force
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Size of the Induced Dipole

• the magnitude of the induced dipole depends on
  several factors
• polarizability of the electrons
• volume of the electron cloud
• larger molar mass more electrons larger
  electron cloud increased polarizability
  stronger attractions
• shape of the molecule
• more surface-to-surface contact larger induced
  dipole stronger attraction

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Effect of Molecular Sizeon Size of Dispersion
Force
Noble Gases are all nonpolar atomic elements.
As the molar mass increases, the number of
electrons increase. 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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Properties of Straight Chain AlkanesNon-Polar
Molecules
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Boiling Points of n-Alkanes
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Effect of Molecular Shapeon Size of Dispersion
Force
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Alkane Boiling Points

• branched chains have lower BPs than straight
  chains
• the straight chain isomers have more
  surface-to-surface contact

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Practice Choose the Substance in Each Pair with
the Highest Boiling Point

1. CH4 CH3CH2CH2CH3
2. CH3CH2CHCHCH2CH3 cyclohexane

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Practice Choose the Substance in Each Pair with
the Highest Boiling Point
both molecules are nonpolar larger molar mass

1. CH4 CH3CH2CH2CH3
2. CH3CH2CHCHCH2CH3 cyclohexane

both molecules are nonpolar flat molecule larger
surface-to-surface 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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Effect of Dipole-Dipole Attraction on Boiling and
Melting Points
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Practice Choose the Substance in Each Pair with
the Highest Boiling Point

1. CH2FCH2F CH3CHF2

b)
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Practice Choose the Substance in Each Pair with
the Highest Boiling Point

1. CH2FCH2F CH3CHF2

more polar
b)
polar
nonpolar
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Attractive Forces and Solubility

• Solubility depends on the attractive forces of
  solute and solvent molecules
• Like dissolves Like
• miscible liquids will always dissolve in each
  other
• polar substance dissolve in polar solvents
• hydrophilic groups OH, CHO, CO, COOH, NH2, Cl
• nonpolar molecules dissolve in nonpolar solvents
• hydrophobic groups C-H, C-C
• Many molecules have both hydrophilic and
  hydrophobic parts - solubility becomes
  competition between parts

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Immiscible Liquids
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Polar Solvents
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KMnO4 animation
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Nonpolar Solvents
n-hexane
toluene
carbon tetrachloride
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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
• Since hydrogen has no other electrons, when it
  loses the electrons, the nucleus becomes
  deshielded
• exposing the H proton
• The exposed proton acts as a very strong center
  of positive charge, attracting all the electron
  clouds from neighboring molecules

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H-Bonding
HF
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H-Bonding in Water
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H-Bonding animation
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Practice Choose the substance in each pair that
is a liquid at room temperature (the other is a
gas)

1. CH3OH CH3CHF2
2. CH3-O-CH2CH3 CH3CH2CH2NH2

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Practice Choose the substance in each pair that
is a liquid at room temperature (the other is a
gas)

1. CH3OH CH3CHF2
2. CH3-O-CH2CH3 CH3CH2CH2NH2

can H-bond
can H-bond
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Practice Choose the substance in each pair that
is more soluble in water

1. CH3OH CH3CHF2
2. CH3CH2CH2CH3 CH3Cl

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Practice Choose the substance in each pair that
is more soluble in water

1. CH3OH CH3CHF2
2. CH3CH2CH2CH3 CH3Cl

can H-bond with H2O
more polar
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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 (contd)

• 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 are especially important
  in aqueous solutions of ionic compounds

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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
• in order to minimize their surface area, liquids
  form drops that are spherical
• as long as there is no gravity
• 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

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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
• at room temp, surface tension of H2O 72.8 mJ/m2

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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/cms
• often given in centipoise, cP
• larger intermolecular attractions larger
  viscosity
• higher temperature lower viscosity

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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 the two forces
  working in conjunction, the cohesive and adhesive
  forces
• cohesive forces attract the molecules together
• adhesive forces attract the molecules on the edge
  to the tubes surface

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Capillary Action

• the adhesive forces pull the surface liquid up
  the side of the tube, while 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

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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 stronger than intermolecular
  attractions

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Vaporization

• molecules in the liquid are constantly in motion
• the average kinetic energy is proportional to the
  temperature
• however, some molecules have more kinetic energy
  than the average
• if these 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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Distribution of Thermal Energy

• only a small fraction of the molecules in a
  liquid have enough energy to escape
• but, as the temperature increases, the fraction
  of the molecules with escape energy increases
• the higher the temperature, the faster the rate
  of evaporation

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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 be equal

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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
• e.g., gasoline, fingernail polish remover
• liquids that do not evaporate easily are called
  nonvolatile
• e.g., motor oil

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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 100C
155 kJ g H2O
Given Find
1 mol H2O 40.7 kJ, 1 mol 18.02 g
Concept Plan Relationships
Solution
since the given amount of heat is almost 4x the
DHvap, the amount of water makes sense
Check
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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 or 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 it means that they are
  changing by equal amounts

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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 Daltons 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 liquid

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Vapor-Liquid Dynamic Equilibrium

• if the volume of the chamber is increased, that
  will decrease the pressure of the vapor inside
• at that point, there are fewer vapor molecules in
  a given volume, causing the rate of condensation
  to slow
• eventually enough liquid evaporates so that the
  rates of the condensation increases to the point
  where it is once again as fast as evaporation
• equilibrium is reestablished
• at this point, the vapor pressure will be the
  same as it was before

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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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Vapor Pressure Curves
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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 required to have the vapor pressure
  external pressure is the boiling point

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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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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 again start to rise

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Clausius-Clapeyron Equation

• the graph of vapor pressure vs. temperature is an
  exponential growth curve

• the logarithm of the vapor pressure vs.
• inverse absolute temperature is a linear
  function

• the slope of the line x 8.314 J/molK DHvap
• in J/mol

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Example 11.4 Determine the DHvap of
dichloromethane given the vapor pressure vs.
temperature data

• enter the data into a spreadsheet and calculate
  the inverse of the absolute temperature and
  natural log of the vapor pressure

Temperature, K Vapor Pressure, torr Inverse Temperature, K-1 ln(Vapor Pressure)
200 0.8 0.00500 -0.2
220 4.5 0.00455 1.5
240 21 0.00417 3.0
260 71 0.00385 4.3
280 197 0.00357 5.3
300 391 0.00333 6.0
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Example 11.4 Determine the DHvap of
dichloromethane given the vapor pressure vs.
temperature data

• graph the inverse of the absolute temperature vs.
  the natural log of the vapor pressure

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Example 11.4 Determine the DHvap of
dichloromethane given the vapor pressure vs.
temperature data

• add a trendline, making sure the display equation
  on chart option is checked off

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Example 11.4 Determine the DHvap of
dichloromethane given the vapor pressure vs.
temperature data

• determine the slope of the line
• -3776.7 3800 K

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Example 11.4 Determine the DHvap of
dichloromethane given the vapor pressure vs.
temperature data

• use the slope of the line to determine the heat
  of vaporization
• -3776.7 3800 K

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Clausius-Clapeyron Equation2-Point Form

• the equation below can be used with just two
  measurements of vapor pressure and temperature
• however, it generally gives less accurate results
• fewer data points will not give as accurate an
  average because there is less averaging out of
  the errors
• as with any other sets of measurements
• can also be used to predict the vapor pressure if
  you know the heat of vaporization and the normal
  boiling point
• remember the vapor pressure at the normal
  boiling point is 760 torr

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Example 11.5 Calculate the vapor pressure of
methanol at 12.0C
T1 BP 64.6C, P1 760 torr, DHvap 35.2
kJ/mol, T2 12.0C P2, torr
Given Find
T1 BP 337.8 K, P1 760 torr, DHvap 35.2
kJ/mol, T2 285.2 K P2, torr
Concept Plan Relationships
T(K) T(C) 273.15
Solution
Check
the units are correct, the size makes sense since
the vapor pressure is lower at lower temperatures
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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 pressure

sublimation
solid gas
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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 a temperature of 0C
• at 1 atm

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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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Heat of Fusion

• the amount of heat energy required to melt one
  mole of the solid is called the Heat of Fusion,
  DHfus
• sometimes called the enthalpy of fusion
• always endothermic, therefore DHfus is
• somewhat temperature dependent
• DHcrystallization -DHfusion
• generally much less than DHvap
• DHsublimation DHfusion DHvaporization

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Heats of Fusion and Vaporization
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Heating Curve of Water
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Segment 1

• heating 1.00 mole of ice at -25.0C up to the
  melting point, 0.0C
• q mass x Cs x DT
• mass of 1.00 mole of ice 18.0 g
• Cs 2.09 J/gC

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Segment 2

• melting 1.00 mole of ice at the melting point,
  0.0C
• q nDHfus
• n 1.00 mole of ice
• DHfus 6.02 kJ/mol

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Segment 3

• heating 1.00 mole of water at 0.0C up to the
  boiling point, 100.0C
• q mass x Cs x DT
• mass of 1.00 mole of water 18.0 g
• Cs 2.09 J/gC

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Segment 4

• boiling 1.00 mole of water at the boiling point,
  100.0C
• q nDHvap
• n 1.00 mole of ice
• DHvapor 40.7 kJ/mol

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Segment 5

• heating 1.00 mole of steam at 100.0C up to
  125.0C
• q mass x Cs x DT
• mass of 1.00 mole of water 18.0 g
• Cs 2.01 J/gC

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Phase Diagrams

• describe the different states and state changes
  that occur at various temperature - pressure
  conditions
• areas 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 as
  pressure increases

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Normal Boiling/Freezing point is at 1 atm
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Phase Diagrams
Liquid
Solid
Pressure
normal boiling pt.
normal melting pt.
Gas
Temperature
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The Critical Point

• the temperature required to produce a
  supercritical fluid is called the critical
  temperature
• the pressure at the critical temperature is
  called the critical pressure
• at the critical temperature or higher
  temperatures, the gas cannot be condensed to a
  liquid, no matter how high the pressure gets

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Supercritical Fluid

• as a liquid is heated in a sealed container, more
  vapor collects causing the pressure inside the
  container to rise
• and the density of the vapor to increase
• and the density of the liquid to decrease
• at some temperature, the meniscus between the
  liquid and vapor disappears and the states
  commingle to form a supercritical fluid
• supercritical fluid have properties of both gas
  and liquid states

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Phase Diagram of Water
109
Phase Diagram of CO2
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Phase diagram CO2 animation
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Water An Extraordinary Substance

• water is a liquid at room temperature
• most molecular substances with small molar masses
  are gases at room temperature
• 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
  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
• making ice less dense than liquid water

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Solids

• properties
• structure

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Determining Crystal Structure

• crystalline solids have a very regular geometric
  arrangement of their particles
• the arrangement of the particles and distances
  between them is determined by x-ray diffraction
• in this technique, a crystal is struck by beams
  of x-rays, which then are reflected
• the wavelength is adjusted to result in an
  interference pattern at which point the
  wavelength is an integral multiple of the
  distances between the particles

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X-ray Crystallography
117
Braggs Law

• when the interference between x-rays is
  constructive, the distance between the two paths
  (a) is an integral multiple of the wavelength
• nl2a
• the angle of reflection is therefore related to
  the distance (d) between two layers of particles
• sinq a/d
• combining equations and rearranging we get an
  equation called Braggs Law

118
Example 11.6 An x-ray beam at l154 pm striking
an iron crystal results in the angle of
reflection q 32.6. Assuming n 1, calculate
the distance between layers
n 1, q 32.6, l 154 pm d, pm
Given Find
Concept Plan Relationships
Solution
Check
the units are correct, the size makes sense since
the iron atom has an atomic radius of 140 pm
119
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 the
  unit cell

120
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

121
7 Unit Cells
c
b
a
Rhombohedral a b c no 90
122
Unit Cells

• the number of other particles each particle is in
  contact with is called its coordination number
• for ions, it is the number of oppositely charged
  ions an ion is in contact with
• higher coordination number means more
  interaction, therefore stronger attractive forces
  holding the crystal together
• the packing efficiency is the percentage of
  volume in the unit cell occupied by particles
• the higher the coordination number, the more
  efficiently the particles are packing together

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Cubic Unit Cells

• all 90 angles between corners of the unit cell
• the length of all the edges are equal
• if the unit cell is made of spherical particles
• ? of each corner particle is within the cube
• ½ of each particle on a face is within the cube
• ¼ of each particle on an edge is within the cube

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Simple Cubic
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Cubic Unit Cells - Simple Cubic

• 8 particles, one at each corner of a cube
• 1/8th of each particle lies in the unit cell
• each particle part of 8 cells
• 1 particle in each unit cell
• 8 corners x 1/8
• edge of unit cell twice the radius
• coordination number of 6

2r
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Body-Centered Cubic
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Definitions
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BCC cell Body Diagonal
WHY??
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Cubic Unit Cells - Body-Centered Cubic

• 9 particles, one at each corner of a cube one
  in center
• 1/8th of each corner particle lies in the unit
  cell
• 2 particles in each unit cell
• 8 corners x 1/8 1 center
• edge of unit cell (4/Ö 3) times the radius of
  the particle
• coordination number of 8

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Face-Centered Cubic
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Crystal animation
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Cubic Unit Cells - Face-Centered Cubic

• 14 particles, one at each corner of a cube one
  in center of each face
• 1/8th of each corner particle 1/2 of face
  particle lies in the unit cell
• 4 particles in each unit cell
• 8 corners x 1/8 6 faces x 1/2
• edge of unit cell 2Ö 2 times the radius of the
  particle
• coordination number of 12

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Example 11.7 Calculate the density of Al if it
crystallizes in a fcc and has a radius of 143 pm
face-centered cubic, r 143 pm density, g/cm3
Given Find
face-centered cubic, r 1.43 x 10-8 cm, m
1.792 x 10-22 g density, g/cm3
Concept Plan Relation-ships
atoms x mass 1 atom
l 2rv2
V l3
d m/V
1 cm 102 m, 1 pm 10-12 m
V l3, l 2rv2, d m/V
fcc 4 atoms/uc, Al 26.982 g/mol, 1 mol
6.022 x 1023 atoms
Solution
the accepted density of Al at 20C is 2.71 g/cm3,
so the answer makes sense
Check
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Closest-Packed StructuresFirst Layer

• with spheres, it is more efficient to offset each
  row in the gaps of the previous row than to
  line-up rows and columns

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Closest-Packed StructuresSecond Layer

• the second layer atoms can sit directly over the
  atoms in the first called an AA pattern

or the second layer can sit over the holes in
the first called an AB pattern
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Closest-Packed StructuresThird Layer with
Offset 2nd Layer

• the third layer atoms can align directly over the
  atoms in the first called an ABA pattern

or the third layer can sit over the uncovered
holes in the first called an ABC pattern
Cubic Closest-Packed Face-Centered Cubic
Hexagonal Closest-Packed
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Hexagonal Closest-Packed Structures
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Cubic Closest-Packed Structures
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FCC Closest Packing
Cannon balls
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HCP
CCP/FCC
You can see another sphere
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Packing animation
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The face centered cubic and hexagonal close
packed structures both have a packing factor of
0.74, consist of closely packed planes of atoms,
and have a coordination number of 12. The
difference between the fcc and hcp is the
stacking sequence. Cubic lattice structures allow
slippage to occur more easily than non-cubic
lattices, so hcp metals are not as ductile as the
fcc metals. Coordination number 12.
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CCPFCC
HCP
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Classifying Crystalline Solids

• classified by the kinds of units found
• sub-classified by the kinds of attractive forces
  holding the units together
• molecular solids are solids whose composite units
  are molecules
• ionic solids are solids whose composite units are
  ions
• atomic solids are solids whose composite units
  are atoms
• nonbonding atomic solids are held together by
  dispersion forces
• metallic atomic solids are held together by
  metallic bonds
• network covalent atomic solids are held together
  by covalent bonds

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Molecular Solids

• the lattice site are occupied by molecules
• the molecules are held together by intermolecular
  attractive forces
• dispersion forces, dipole attractions, and
  H-bonds
• because the attractive forces are weak, they tend
  to have low melting point
• generally lt 300C

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Ionic SolidsAttractive Forces

• held together by attractions between opposite
  charges
• nondirectional
• therefore every cation attracts all anions around
  it, and vice versa
• 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
• generally, anions are larger than cations
• the number of anions that can surround the cation
  limited by the size of the cation
• the closer in size the ions are, the higher the
  coordination number is

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Ionic Crystals
CsCl coordination number 8 Cs 167 pm Cl-
181 pm
NaCl coordination number 6 Na 97 pm Cl-
181 pm
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Lattice Holes
Tetrahedral Hole
Octahedral Hole
Simple Cubic Hole
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Lattice Holes

• in hexagonal closest packed or cubic closest
  packed lattices there are 8 tetrahedral holes and
  4 octahedral holes per unit cell
• in simple cubic there is 1 hole per unit cell
• number and type of holes occupied determines
  formula (empirical) of salt

Octahedral
Tetrahedral
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Cesium Chloride Structures

• coordination number 8
• ? of each Cl- (184 pm) inside the unit cell
• whole Cs (167 pm) inside the unit cell
• cubic hole hole in simple cubic arrangement of
  Cl- ions
• CsCl 1 (8 x ?), therefore the formula is CsCl

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Rock Salt Structures

• coordination number 6
• Cl- ions (181 pm) in a face-centered cubic
  arrangement
• ? of each corner Cl- inside the unit cell
• ½ of each face Cl- inside the unit cell
• each Na (97 pm) in holes between Cl-
• octahedral holes
• 1 in center of unit cell
• ¼ of each edge Na inside the unit cell
• NaCl (¼ x 12) 1 (? x 8) (½ x 6) 44
  11,
• therefore the formula is NaCl

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Zinc Blende Structures

• coordination number 4
• S2- ions (184 pm) in a face-centered cubic
  arrangement
• ? of each corner S2- inside the unit cell
• ½ of each face S2- inside the unit cell
• each Zn2 (74 pm) in holes between S2-
• tetrahedral holes
• 1 whole in ½ the holes
• ZnS (4 x 1) (? x 8) (½ x 6) 44 11,
  
• therefore the formula is ZnS

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Fluorite Structures

• coordination number 4
• Ca2 ions (99 pm) in a face-centered cubic
  arrangement
• ? of each corner Ca2 inside the unit cell
• ½ of each face Ca2 inside the unit cell
• each F- (133 pm) in holes between Ca2
• tetrahedral holes
• 1 whole in all the holes
• CaF (? x 8) (½ x 6) (8 x 1) 48 12,
• therefore the formula is CaF2
• fluorite structure common for 12 ratio
• usually get the antifluorite structure when the
  cationanion ratio is 21
• the anions occupy the lattice sites and the
  cations occupy the tetrahedral holes

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Nonbonding Atomic Solids

• noble gases in solid form
• solid held together by weak dispersion forces
• very low melting
• tend to arrange atoms in closest-packed structure
• either hexagonal cp or cubic cp
• maximizes attractive forces and minimizes energy

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Metallic Atomic Solids

• solid held together by metallic bonds
• strength varies with sizes and charges of cations
• coulombic attractions
• melting point varies
• mostly closest packed arrangements of the lattice
  points
• cations

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Metallic Structure
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Metallic Bonding

• metal atoms release their valence electrons
• metal cation islands fixed in a sea of mobile
  electrons

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Crystal Structure of Metals at Room Temperature
other
body-centered cubic
cubic cp, face-centered
hexagonal closest packed
diamond
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Network Covalent Solids

• atoms attached to its nearest neighbors by
  covalent bonds
• because of the directionality of the covalent
  bonds, these do not tend to form closest-packed
  arrangements in the crystal
• because of the strength of the covalent bonds,
  these have very high melting points
• generally gt 1000C
• dimensionality of the network affects other
  physical properties

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The Diamond Structurea 3-Dimensional Network

• the carbon atoms in a diamond each have 4
  covalent bonds to surrounding atoms
• sp3
• tetrahedral geometry
• this effectively makes each crystal one giant
  molecule held together by covalent bonds
• you can follow a path of covalent bonds from any
  atom to every other atom

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Properties of Diamond

• very high melting, 3800C
• need to overcome some covalent bonds
• very rigid
• due to the directionality of the covalent bonds
• very hard
• due to the strong covalent bonds holding the
  atoms in position
• used as abrasives
• electrical insulator
• thermal conductor
• best known
• chemically very nonreactive

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The Graphite Structurea 2-Dimensional Network

• in graphite, the carbon atoms in a sheet are
  covalently bonded together
• forming 6-member flat rings fused together
• similar to benzene
• bond length 142 pm
• sp2
• each C has 3 sigma and 1 pi bond
• trigonal-planar geometry
• each sheet a giant molecule
• the sheets are then stacked and held together by
  dispersion forces
• sheets are 341 pm apart

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Properties of Graphite

• hexagonal crystals
• high melting, 3800C
• need to overcome some covalent bonding
• slippery feel
• because there are only dispersion forces holding
  the sheets together, they can slide past each
  other
• glide planes
• lubricants
• electrical conductor
• parallel to sheets
• thermal insulator
• chemically very nonreactive

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Silicates

• 90 of earths crust
• extended arrays of Si?O
• sometimes with Al substituted for Si
  aluminosilicates
• glass is the amorphous form

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Quartz

• 3-dimensional array of Si covalently bonded to 4
  O
• tetrahedral
• melts at 1600C
• very hard

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Micas

• minerals that are mainly 2-dimensional arrays of
  Si bonded to O
• hexagonal arrangement of atoms
• sheets
• chemically stable
• thermal and electrical insulator

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Band Theory

• the structures of metals and covalent network
  solids result in every atoms orbitals being
  shared by the entire structure
• for large numbers of atoms, this results in a
  large number of molecular orbitals that have
  approximately the same energy, we call this an
  energy band

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Band Theory

• when 2 atomic orbitals combine they produce both
  a bonding and an antibonding molecular orbital
• when many atomic orbitals combine they produce a
  band of bonding molecular orbitals and a band of
  antibonding molecular orbitals
• the band of bonding molecular orbitals is called
  the valence band
• the band of antibonding molecular orbitals is
  called the conduction band

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Molecular orbitals of polylithium
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Band Gap

• at absolute zero, all the electrons will occupy
  the valence band
• as the temperature rises, some of the electrons
  may acquire enough energy to jump to the
  conduction band
• the difference in energy between the valence band
  and conduction band is called the band gap
• the larger the band gap, the fewer electrons
  there are with enough energy to make the jump

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Types of Band Gaps andConductivity
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Band Gap and Conductivity

• the more electrons at any one time that a
  substance has in the conduction band, the better
  conductor of electricity it is
• if the band gap is 0, then the electrons will be
  almost as likely to be in the conduction band as
  the valence band and the material will be a
  conductor
• metals
• the conductivity of a metal decreases with
  temperature
• if the band gap is small, then a significant
  number of the electrons will be in the conduction
  band at normal temperatures and the material will
  be a semiconductor
• graphite
• the conductivity of a semiconductor increases
  with temperature
• if the band gap is large, then effectively no
  electrons will be in the conduction band at
  normal temperatures and the material will be an
  insulator

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Doping Semiconductors

• doping is adding impurities to the
  semiconductors crystal to increase its
  conductivity
• goal is to increase the number of electrons in
  the conduction band
• n-type semiconductors do not have enough
  electrons themselves to add to the conduction
  band, so they are doped by adding electron rich
  impurities
• p-type semiconductors are doped with an electron
  deficient impurity, resulting in electron holes
  in the valence band. Electrons can jump between
  these holes in the valence band, allowing
  conduction of electricity

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PV Cells
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Diodes

• when a p-type semiconductor adjoins an n-type
  semiconductor, the result is an p-n junction
• electricity can flow across the p-n junction in
  only one direction this is called a diode
• this also allows the accumulation of electrical
  energy called an amplifier