Chapter 12: Intermolecular Attractions
and the Properties of Liquids and Solids
Chemistry: The Molecular Nature of Matter, 6E
Jespersen/Brady/Hyslop
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
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Intermolecular Forces Important differences between
gases, solids, and liquids: Gases
Expand to fill their container Liquids
Retain volume, but not shape Solids
Retain volume and shape
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Intermolecular Forces Physical state of molecule depends
on Average kinetic energy of particles
Recall KE Tave
Intermolecular Forces Energy of Inter-particle attraction
Physical properties of gases, liquids and solids determined by How tightly molecules are packed together Strength of attractions between
molecules
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Converting gas liquid or solid Molecules must get closer together
Cool or compress
Converting liquid or solid gas Requires molecules to move farther
apart Heat or reduce pressure
As T decreases, kinetic energy of molecules decreases At certain T, molecules don’t have
enough energy to break away from one another’s attraction
Intermolecular Attractions
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Inter vs. Intra-Molecular Forces Intramolecular forces
Covalent bonds within molecule Strong Hbond (HCl) = 431 kJ/mol
Intermolecular forces Attraction forces between molecules Weak Hvaporization (HCl) = 16 kJ/mol
Cl H Cl H
Covalent Bond (strong) Intermolecular attraction (weak)
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
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Electronegativity ReviewElectronegativity: Measure of
attractive force that one atom in a covalent bond has for electrons of the bond
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Bond Dipoles Two atoms with different
electronegativity values share electrons unequally
Electron density is uneven Higher charge concentration around more
electronegative atom Bond dipoles
Indicated with delta (δ) notation Indicates partial charge has arisen
H F
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Net Dipoles Symmetrical molecules
Even if they have polar bonds Are non-polar because bond dipoles cancel
Asymmetrical molecules Are polar because bond dipoles do not
cancel These molecules have permanent, net
dipoles Molecular dipoles
Cause molecules to interact Decreased distance between molecules
increases amount of interaction
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Intermolecular Forces When substance melts or boils
Intermolecular forces are broken Not covalent bonds
Responsible for non-ideal behavior of gases
Responsible for existence of condensed states of matter
Responsible for bulk properties of matter
Boiling points and melting points Reflect strength of intermolecular forces
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Three Important Types of Intermolecular Forces
1. London dispersion forces2. Dipole-dipole forces
Hydrogen bonds
3. Ion-dipole forces Ion-induced dipole forces
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London Forces When atoms near one
another, their valence electrons interact
Repulsion causes electron clouds in each to distort and polarize
Instantaneous dipoles result from this distortion Effect enhanced with increased
volume of electron cloud size Effect diminished by increased
distance between particles and compact arrangement of atoms
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London Forces Instantaneous dipole-induced dipole
attractions London Forces Dispersion forces
Operate between all molecules Neutral or net charged Nonpolar or polar
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
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London Dispersion Forces
Ease with which dipole moments can be induced and thus London Forces depend on
1. Polarizability of electron cloud2. Points of attraction
Number atoms Molecular shape (compact or
elongated)
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Polarizability
Ease with which the electron cloud can be distorted
Larger molecules often more polarizable Larger number of less tightly
held electrons Magnitude of resulting partial
charge is larger Larger electron cloud
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Table 12.1 Boiling Points of Halogens and Noble Gases
Larger molecules have stronger London forces and thus higher boiling points.
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Number of Atoms in Molecule London forces depend on number atoms in molecule Boiling point of hydrocarbons demonstrates this trend
Formula BP at 1 atm, C Formula BP at 1 atm, CCH4 –161.5 C5H12 36.1
C2H6 –88.6 C6H14 68.7
C3H8 –42.1 : :
C4H10 –0.5 C22H46 327
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Hexane, C6H14
BP 68.7 °C More sites (marked with *) along its chain where attraction to other molecules can occur
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How Intermolecular Forces Determine Physical Properties
Propane, C3H8
BP –42.1 °C
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Molecular Shape Increased surface area available for contact
= increased London forces London dispersion forces between spherical
molecules are lower than chain-like molecules More compact molecules
Hydrogen atoms not as free to interact with hydrogen atoms on other molecules
Less compact molecules Hydrogen atoms have more chance to
interact with hydrogen atoms on other molecules
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Physical Origin of Shape Effect Small area for
interaction Larger area
for interaction
More compact – lower BP Less compact – higher BP
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Dipole-Dipole Attractions Occur only between
polar molecules Possess dipole moments
Molecules need to be close together
Polar molecules tend to align their partial charges Positive to negative
As dipole moment increases, intermolecular force increases
+ +
+ +
+ +
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Dipole-Dipole Attractions Tumbling molecules
Mixture of attractive and repulsive dipole-dipole forces
Attractions (- -) are maintained longer than repulsions(- -)
Get net attraction ~1–4% of covalent
bond
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Dipole-Dipole Attractions
Interactions between net dipoles in polar molecules
About 1–4% as strong as a covalent bond Decrease as molecular distance
increases Dipole-dipole forces increase with
increasing polarity
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Hydrogen Bonds Special type of dipole-dipole Interaction
Very strong dipole-dipole attraction ~10% of a covalent bond
Occurs between H and highly electronegative atom (O, N, or F) H—F, H—O, and H—N bonds very polar
Electrons are drawn away from H, so high partial charges
H only has one electron, so +H presents almost bare
proton –
X almost full –1 charge Element’s small size, means high charge density Positive end of one can get very close to negative end
of another
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Examples of Hydrogen Bonding
H O
H
H O
H
H O
H
H N
H
H
H F H O
H
H F H N
H
H
H N
H
H
H N
H
H
H N
H
H
H O
H
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Hydrogen Bonding in Water
Responsible for expansion of water as it freezes Hydrogen bonding produces strong attractions in
liquid Hydrogen bonding (dotted lines) between
water molecules in ice form tetrahedral configuration
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Your Turn!List all intermolecular forces for
CH3CH2OH.
A. Hydrogen-bondsB. Hydrogen-bonds, dipole-dipole
attractions, London dispersion forcesC. Dipole-dipole attractionsD. London dispersion forcesE. London dispersion forces, dipole-dipole
attractions
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Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Your Turn!In the liquid state, which species has the strongest intermolecular forces, CH4, Cl2, O2 or HF?
A. CH4
B. Cl2C. O2
D. HF
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Ion-Dipole Attractions Attractions between ion and charged
end of polar molecules Attractions can be quite strong as ions
have full charges
(a) Negative ends of water dipoles surround cation (b) Positive ends of water dipoles surround anion
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Ex. Ion-Dipole Attractions: AlCl3·6H2O
Positive charge of Al3+ ion attracts partial negative charges – on O of water molecules
Ion-dipole attractions hold water molecules to metal ion in hydrate Water molecules are found
at vertices of octahedron around aluminum ion
Attractions between ion and polar molecules
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Ion-Induced Dipole Attractions
Attractions between ion and dipole it induces on neighboring molecules Depends on
Ion charge and Polarizability of its neighbor
Attractions can be quite strong as ion charge is constant, unlike instantaneous dipoles of ordinary London forces
E.g., I– and Benzene
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Summary of Intermolecular Attractions
Dipole-dipole Occur between neutral molecules with
permanent dipoles About 1–4% of covalent bond Mid range in terms of intermolecular forcesHydrogen bonding
Special type of dipole-dipole interaction Occur when molecules contain N—H,
H—F and O—H bonds About 10% of a covalent bond
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Summary of Intermolecular Attractions
London dispersion Present in all substances Weakest intermolecular force Weak, but can add up to large net attractions
Ion-dipole Occur when ions interact with polar molecules Strongest intermolecular attraction
Ion-induced dipole Occur when ion induces dipole on neighboring
particle Depend on ion charge and polarizability of its
neighbor
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Using Intermolecular Forces Often can predict physical properties (like
BP, MP and many others) by comparing strengths of intermolecular attractions Ion-Dipole Hydrogen Bonding Dipole-Dipole London Forces
Larger, longer, and therefore heavier molecules often have stronger intermolecular forces
Smaller, more compact, lighter molecules have generally weaker intermolecular forces
Weakest
Strongest
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Physical Properties that Depend on How Tightly Molecules Pack
Compressibility Measure of ability of substance to be forced
into smaller volume Determined by strength of intermolecular
forces Gases highly compressible
Molecules far apart Weak intermolecular forces
Solids and liquids nearly incompressible Molecules very close together Stronger intermolecular forces
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Intermolecular Forces Determine Strength of Many Physical
Properties Retention of volume and shape Solids retain both volume and shape
Strongest intermolecular attractions Molecules closest
Liquids retain volume, but not shape Attractions intermediate
Gases, expand to fill their containers Weakest intermolecular attractions Molecules farthest apart
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Intermolecular Forces and Temperature
Decrease with increasing temperature Increasing kinetic energy overcomes
attractive forces If allowed to expand, increasing
temperature increases distance between gas particles and decreases attractive forces
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Diffusion Movement that
spreads one gas though another gas to occupy space uniformly
Spontaneous intermingling of molecules of one gas with molecules of another gas
Occurs more rapidly in gases than in liquids
Hardly at all in solids
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Diffusion In Gases
Molecules travel long distances between collisions
Diffusion rapid In Liquids
Molecules closer Encounter more
collisions Takes a long time to
move from place to place
In Solids Diffusion close to zero
at room temperature Will increase at high
temperature
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Surface Tension
Inside body of liquid Intermolecular forces are
the same in all directions Molecules at surface
Potential energy increases when removing neighbors
Molecules move together to reduce surface area and potential energy
Why does H2O bead up on a freshly waxed car instead of forming a layer?
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Surface Tension Causes a liquid to
take the shape (a sphere) that minimizes its surface area Molecules at
surface have higher potential energy than those in bulk of liquid and move to reduce the potential energy
Wax = nonpolar H2O = polar Water beads in order
to reduce potential energy by reducing surface area
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Surface Tension Liquids containing
molecules with strong intermolecular forces have high surface tension Allows us to fill glass
above rim Gives surface rounded
appearance Surface acts as “skin” that
lets water pile up Surface resists expansion
and pushes back
Surface tension increases as intermolecular forces increase
Surface tension decreases as temperature increases
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Wetting Ability of liquid to
spread across surface to form thin film
Greater similarity in attractive forces between liquid and surface, yields greater wetting effect
Occurs only if intermolecular attractive force between surface and liquid about as strong as within liquid itself
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WettingEx. H2O wets clean glass surface as it
forms H–bonds to SiO2 surface
Does not wet greasy glass, because grease is nonpolar and water is very polar Only London forces Forms beads instead
Surfactants Added to detergents to lower surface tension
of H2O Now water can spread out on greasy glass
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Surfactants (Detergents) Substances that have both polar and non-polar
characteristics Long chain hydrocarbons with polar tail
OS
O
O Na+
O
O
O Na+
Nonpolar end dissolves in nonpolar grease Polar end dissolves in polar H2O Thus increasing solubility of grease in water
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Viscosity Resistance to flow Measure of fluid’s
resistance to flow or changing form
Related to intermolecular attractive forces
Also called internal friction Depends on intermolecular attractions
www.chemistryexplained.com
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Viscosity Viscosity decreases when temperature
increases Most people associate liquids with
viscosity Syrup more viscous than water
Gases have viscosity Respond almost instantly to form-changing
forces Solids, such as rocks and glass have
viscosity Normally respond very slowly to forces
acting to change their shape
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Effect of Intermolecular Forces on Viscosity
Acetone Polar molecule
Dipole-dipole and London forces
Ethylene glycol Polar molecule
Hydrogen-bonding Dipole-dipole and London forces
Which is more viscous?
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Your Turn!For each pair given, which is has more
viscosity?CH3CH2CH2CH2OH, CH3CH2CH2CHO
C6H14, C12H26
NH3(l ), PH3(l )
A. CH3CH2CH2CH2OH C6H14 NH3(l )
B. CH3CH2CH2CH2OH C12H26 NH3(l )
C. CH3CH2CH2CHO C6H14 PH3(l )
D. CH3CH2CH2CHO C12H26 NH3(l )
E. CH3CH2CH2CH2OH C12H26 PH3(l )48
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Solubility “Like dissolves like”
To dissolve polar substance, use polar solvent
To dissolve nonpolar substance, use nonpolar solvent
Compare relative polarity Similar polarity means greater ability to
dissolve in each other Differing polarity means that they don’t
dissolve, they are insoluble Surfactants
Both polar and non-polar characteristics Used to increase solubility
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Your Turn!Which of the following are not expected to be soluble in water?A. HFB. CH4
C. CH3OH
D. All are soluble
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Phase Changes
Changes of physical state Deal with motion of molecules
As temperature changes Matter will undergo phase changes
Liquid Gas Evaporation, vaporization As heat is added, H2O, forms steam or
water vapor Requires energy or source of heat
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Phase Changes Solid Gas
Sublimation Ice cubes in freezer, leave in long enough
disappear Endothermic
Gas Liquid Condensation Dew is H2O vapor condensing onto cooler
ground Exothermic Often limits lower night time temperature
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Rate of Evaporation Depends on
Temperature Surface area Strength of
intermolecular attractions
Molecules that escape from liquid have larger than minimum escape KE
When they leave Average KE of
remaining molecules is less and so T lower
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Effect of Temperature on Evaporation Rate
For given liquid Rate of evaporation
per unit surface area increases as T increases
Why? At higher T, total
fraction of molecules with KE large enough to escape is larger
Result: rate of evaporation is larger
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Kinetic Energy Distribution in Two Different Liquids
Smaller intermolecular forces
Lower KE required to escape liquid
A evaporates faster
Larger intermolecular forces
Higher KE required to escape liquid
B evaporates slower
A B
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Changes Of State Involve Equilibria Fraction of molecules in condensed
state is higher when intermolecular attractions are higher
Intermolecular attractions must be overcome to separate the particles, while separated particles are simultaneously attracted to one anothercondensedphase
separatedphase
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Before System Reaches Equilibrium
Liquid is placed in empty, closed, container Begins to evaporate
Once in gas phase Molecules can
condense by Striking surface of liquid
and giving up some kinetic energy
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System At Equilibrium
Rate of evaporation = rate of condensation
Occurs in closed systems where molecules cannot escape
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Similar Equilibria Reached in Melting
Melting Point (mp) Solid begins to change
into liquid as heat added
Dynamic equilibria exists between solid and liquid states Melting (red arrows) and
freezing (black arrows) occur at same rate
As long as no heat added or removed from equilibrium mixture
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Equilibria Reached in Sublimation
At equilibrium Molecules sublime
from solid at same rate as molecules condense from vapor
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Phase ChangesEn
erg
y o
f S
yst
em
Gas
Solid
Liquid
Meltingor Fusion
Vaporization Condensation
Freezing
SublimationDeposition
Exothermic, releases heat Endothermic, absorbs heat
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Energy Changes Accompanying Phase Changes
All phase changes are possible under the right conditions
Following sequence is endothermic
heat solid melt heat liquid boil heat gas
Following sequence is exothermic
cool gas condense cool liquid freeze cool solid
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Enthalpy Of Phase ChangesEndothermic Phase Changes
1. Must add heat2. Energy entering system (+)
Sublimation: Hsub > 0
Vaporization: Hvap > 0
Melting or Fusion: Hfus > 0
Exothermic Phase Changes1. Must give off heat2. Energy leaving system (–)
Deposition: H < 0 = –Hsub
Condensation: H < 0 = –Hvap
Freezing: H < 0 = –Hfus
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Phase Changes
As T changes, matter undergoes phase changes
Phase Change Transformation from one phase to
another Liquid-Vapor Equilibrium
Molecules in liquid Not in rigid lattice In constant motion Denser than gas, so more collisions Some have enough kinetic energy to
escape, some don’t
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Liquid-Vapor Equilibrium At any given T,
Average kinetic energy of molecules is constant
But particles have a distribution of kinetic energies
Certain number of molecules have enough KE to escape surface
As T increases, average KE increases and number molecules with enough KE to escape increases
Kinetic EnergyF
ract
ion
of m
olec
ules
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Vapor Pressure Pressure molecules exert when they
evaporate or escape into gas (vapor) phase Pressure of gas when liquid or solid is at
equilibrium with its gas phase Increasing temperature increases vapor
pressure because vaporization is endothermic liquid + heat of vaporization ↔ gas
Equilibrium Vapor Pressure VP once dynamic equilibrium reached Usually referred to as simply vapor pressure
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Measuring Vapor Pressure
To measure pressures inside vessels, a manometer is used.
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Vapor Pressure Diagram
RT = 25 C
Variation of vapor pressure with T
Ether Volatile High vapor
pressure near RT
Propylene glycol Non-volatile Low vapor
pressure near RT
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Effect of Volume on VPA.Initial V
Liquid – vapor equilibrium exists
B. Increase V Pressure
decreases Rate of
condensation decreases
C. More liquid evaporates
New equilibrium established
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Measuring Hvap
Clausius-Clapeyron equation Measure pressure at various temperatures,
then plot
Two point form of Clausius-Clapeyron equation
Measure pressure at two temperatures and solve equation
CTR
HP vap
1ln
122
1 11ln
TTR
H
PP vap
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Learning Check The vapor pressure of diethyl ether is 401 mm Hg at 18 °C, and its molar heat of vaporization is 26 kJ/mol. Calculate its vapor pressure at 32 °C.
122
1 11ln
TTR
H
PP vap
6109.04928.0
2
1 ePP
21
6109.0P
P
T1 = 273.15 + 18 = 291.15 KT2 = 273.15 + 32 = 305.15 K
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Your Turn!Determine the enthalpy of vaporization, in kJ/mol, for benzene, using the following vapor pressure data.
T = 60.6 °C; P = 400 torrT = 80.1 °C; P = 760 torr
A. 32.2 kJ/molB. 14.0 kJ/molC. –32.4 kJ/molD. 0.32 kJ/molE. –14.0 kJ/mol
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Your Turn! - Solution
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Do Solids Have Vapor Pressures? Yes At given temperature
Some solid particles have enough KE to escape into vapor phase
When vapor particles collide with surface They can be captured
Equilibrium vapor pressure of solid Pressure of vapor in equilibrium with solid
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Boiling Point (bp)
T at which vapor pressure of liquid = atmospheric pressure.
Bp increases as strength of intermolecular forces increase
Normal Boiling Point T at which vapor pressure of liquid = 1
atm
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Effects of Hydrogen Bonding
Boiling points of hydrogen compounds of elements of Groups 4A, 5A, 6A, and 7A.
Boiling points of molecules with hydrogen bonding are much higher than expected
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Your Turn!Which of the following will affect the boiling point of a substance?A.PolarizabilityB.Intermolecular attractionsC.The external pressure on the materialD.All of theseE.None of these
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Heating Curve Heat added at constant rate
Diagonal lines Heating of solid, liquid or gas
Horizontal linesPhase changesMelting pointBoiling point
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Cooling Curve Heat removed at constant rate
Diagonal lines Cooling of solid,
liquid or gas
Horizontal linesPhase changesMelting pointBoiling point
Supercooling Temperature of liquid dips below its freezing point
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Your Turn!How much heat, in J, is required to convert 10.00 g of ice at -10.00 °C to water at 50.00 °C?Specific heat (J/g K): ice, 2.108, water, 4.184Enthalpy of fusion = 6.010 kJ/molA. 5483 JB. 5643 JC. 2304 JD. 2364 JE. 62,400 J
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Energies of Phase Changes Expressed per mole Molar heat of fusion (Hfus)
Heat absorbed by one mole of solid when it melts to give liquid at constantT and P
Molar heat of vaporization (Hvap ) Heat absorbed when one mole of liquid is changed
to one mole of vapor at constant T and P Molar heat of sublimation (Hsub )
Heat absorbed by one mole of solid when it sublimes to give one mole of vapor at constant T and P
All of these quantities tend to increase with increasing intermolecular forces
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Le Chatelier’s Principle Equilibria are often disturbed or upset When dynamic equilibrium of system is
upset by a disturbance System responds in direction that tends to
counteract disturbance and, if possible, restore equilibrium
Position of equilibrium Used to refer to relative amounts of
substance on each side of double (equilibrium) arrows
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Liquid Vapor Equilibrium Liquid + Heat Vapor
Increasing T Increases amount of vapor Decreases amount of liquid
Equilibrium has shifted Shifted to the right More vapor is produced at expense of liquid
Temperature-pressure relationships can be represented using a phase diagram
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Phase Diagrams Show the effects of both pressure and
temperature on phase changes Boundaries between phases indicate
equilibrium Triple point:
The temperature and pressure at which s, l, and g are all at equilibrium
Critical point: The temperature and pressure at which a gas can
no longer be condensed TC
= temperature at critical point
PC = pressure at critical point
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Phase Diagram
X axis – temperature
Y axis – pressure As P increases
(T constant), solid most likely More compact
As T increases (P constant), gas most likely Higher energy
Each point = T and P B = E = F =
E
0.01 °C, 4.58 torr
100 °C, 760 torr
–10 °C, 2.15 torr
F
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Phase Diagram of Water AB = vapor pressure
curve for ice BD = vapor pressure
curve for liquid water BC = melting point line B = triple point: T and
P where all three phases are in equilibrium
D = critical point T and P above which
liquid does not exist
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Case Study: An Ice Necklace
A cube of ice may be suspended on a string simply by pressing the string into the ice cube. As the string is pressed onto the surface, it becomes embedded into the ice.
Why does this happen?
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Phase Diagram – CO2
Now line between solid and liquid slants to right
More typical Where is triple
point? Where is
critical point?
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Supercritical Fluid Substance with temperature above its
critical temperature (TC) and density near its liquid density
Have unique properties that make them excellent solvents
Values of TC tend to increase with increased intermolecular attractions between particles
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Your Turn!
At 89 °C and 760 mmHg, what physical state is present?A.SolidB.LiquidC.GasD.Supercritical fluidE.Not enough information is given
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Types of Solids Crystalline Solids
Solids with highly regular arrangements of components
Amorphous Solids Solids with considerable disorder in their
structures
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Crystalline Solids
Unit Cell Smallest
segment that repeats regularly
Smallest repeating unit of lattice
Two-dimensional unit cells
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Crystal Structures Have Regular Patterns
Lattice Many repeats of unit
cell Regular, highly
symmetrical system Three (3) dimensional
system of points designating positions of components
Atoms Ions Molecules
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Three Types Of 3-D Unit Cells Simple cubic
Has one host atom at each corner Edge length a = 2r Where r is radius of atom or ion
Body-centered cubic (BCC) Has one atom at each corner and one
in center Edge length
Face-centered cubic (FCC) Has one atom centered in each face,
and one at each corner Edge length
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Most efficient arrangement of spheres in two dimensions
Each sphere has 6 nearest neighbors Second layer with atoms in holes on the first
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Close Packing of Spheres
1st layer 2nd layer
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Two Ways to Put on Third Layer
1. Directly above spheres in first layer
2. Above holes in first layer
Remaining holes not covered by second layer
Cubic lattice: 3-dimensional arrays
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3-D Simple Cubic Lattice
Portion of lattice—open view
Unit Cell
Space filling model
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Other Cubic Lattices
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Face Centered
Cubic
Body Centered
Cubic
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Ionic Solids Lattices of alternating charges Want cations next to anions
Maximizes electrostatic attractive forces Minimizes electrostatic repulsions
Based on one of three basic lattices: Simple cubic Face centered cubic Body centered cubic
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Common Ionic SolidsRock salt or NaCl Face centered cubic lattice of Cl– ions (green) Na+ ions (blue) in all octahedral holes
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Other Common Ionic Solids
Cesium Chloride,
CsCl
Zinc Sulfide,
ZnS
Calcium Fluoride,
CaF2
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Spaces In Ionic Solids Are Filled With Counter Ions
In NaCl Cl– ions form face-
centered cubic unit cell
Smaller Na+ ions fill spaces between Cl–ions
Count atoms in unit cell Have 6 of each or
1:1 Na+:Cl– ratio
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Counting Atoms per Unit Cell Four types of sites in unit cell
Central or body position – atom is completely contained in one unit cell
Face site – atom on face shared by two unit cells Edge site – atom on edge shared by four unit cells Corner site – atom on corner shared by eight unit
cells
Site Counts as Shared by X unit cells
Body 1 1
Face 1/2 2
Edge 1/4 4
Corner 1/8 8
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Example: NaCl
Site # of Na+ # of Cl–
Body 1 0
Face 0
Edge 0
Corner 0
Total 4 4
36 21
312 41
18 81
FaceEdge Corner
Center
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Learning Check:
1:1CsCl
Determine the number of each type of ion in the unit cell.
4:4ZnS
4:8CaF2
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Some Factors Affecting Crystalline Structure
Size of atoms or ions involved Stoichiometry of salt Materials involved
Some substances do not form crystalline solids
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Amorphous Solids (Glass) Have little order, thus referred to as “super
cooled liquids” Edges are not clean, but ragged due to the lack
of order
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X-Ray Crystallography
X rays are passed through crystalline solid
Some x rays are absorbed, most re-emitted in all directions
Some emissions by atoms are in phase, others out of phase
Emission is recorded on film
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X-ray Diffraction
Experimental Setup Diffraction Pattern
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Interpreting Diffraction Data As x rays hit
atoms in lattice they are deflected
Angles of deflections related to lattice spacing
So we can estimate atomic and ionic radii from distance data
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Interpreting Diffraction DataBragg Equation nλ=2d sinθ n = integer (1, 2,
…) = wavelength of
X rays d = interplane
spacing in crystal = angle of
incidence and angle of reflectance of X rays to various crystal planes
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Example: Diffraction DataThe diffraction pattern of copper metal was measured with X-ray radiation of wavelength of 131.5 pm. The first order (n = 1) Bragg diffraction peak was found at an angle θ of 50.5°. Calculate the spacing between the diffracting planes in the copper metal.
1(131.5 pm) = 2 × d × sin(50.5)
n = 2d sin
d = 283 pm
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Example: Using Diffraction DataX-ray diffraction measurements reveal that
copper crystallizes with a face-centered cubic lattice in which the unit cell length is 362 pm. What is the radius of a copper atom expressed in picometers?
This is basically a geometry problem.
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Ex. Using Diffraction Data (cont.)
diagonal = 4 rCu = 512 pm
rCu = 128 pm
Pythagorean theorem: a2 + b2 = c2
Where a = b = 362 pm sides and c = diagonal
2a2 = c2 and aac 22 2
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Learning CheckSilver packs together in a faced center cubic fashion. The interplanar distance, d, corresponds to the length of a side of the unit cell, and is 407 pm. What is the radius of a silver atom?
ra 22
r = 53.6 pm
a
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Ionic Crystals (e.g. NaCl, NaNO3) Have cations and anions at lattice
sites Are relatively hard Have high melting points Are brittle Have strong attractive forces between
ions Do not conduct electricity in their solid
states Conduct electricity well when molten
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Sample Homework Problem Potassium chloride crystallizes with the rock salt structure. When bathed in X rays, the layers of atoms corresponding to the surfaces of the unit cell produce a diffracted beam of X rays (λ=154 pm) at an angle of 6.97°. From this, calculate the density of potassium chloride in g/cm3.
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Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Your Turn!Yitterbium crystallizes with a face centered cubic lattice. The atomic radius of yitterbium is 175 pm. Determine the unit cell length.A. 495 pmB. 700 pmC. 350 pmD. 990 pmE. 247 pm
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Your Turn! - Solution
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diagonal of cube = 4 where = atomic radius
diagonal of cube = 2 a where a = side of cube
4 4 x 175 pm a = 495 pm
2 2
r r
r
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Covalent Crystals Lattice positions occupied by atoms
that are covalently bonded to other atoms at neighboring lattice sites
Also called network solids Interlocking network of covalent bonds
extending all directions Covalent crystals tend to
Be very hard Have very high melting points Have strong attractions between covalently
bonded atoms
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Ex. Covalent (Network) Solid
Diamond (all C) Shown
SiO2 silicon oxide Alternating Si and O Basis of glass and quartz
Silicon carbide (SiC)
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Metallic Crystals Simplest models
Lattice positions of metallic crystal occupied by positive ions
Cations surrounded by “cloud” of electrons Formed by valence electrons Extends throughout entire
solid
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Metallic Crystals Conduct heat and electricity
By their movement, electrons transmit kinetic energy rapidly through solid
Have the luster characteristically associated with metals When light shines on metal Loosely held electrons vibrate easily Re-emit light with essentially same
frequency and intensity
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Learning Check:
Substance ionic
molecular
covalent
metallic
X: Pulverizes when struck; non-conductive of heat and electricity
Y: White crystalline solid that conducts electrical current when molten or dissolved
Z: Shiny, conductive, malleable with high melting temperature
Classify the following in terms of most likely type of solid.
Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E
Your Turn!Molecular crystals can contain all of the listed attraction forces except:A. Dipole-dipole attractionsB. Electrostatic forcesC. London forcesD. Hydrogen bonding
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