Chapter 11 Liquids, Solids, And Intermolecular Forces

Chapter 11Liquids,

Solids, and Intermolecular

Forces

2008, Prentice Hall

Chemistry: A Molecular Approach, 1st Ed.Nivaldo Tro

Roy KennedyMassachusetts Bay Community College

Wellesley Hills, MA

Tro, Chemistry: A Molecular Approach 2

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 densernotable 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



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 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


Properties of the 3 Phases of Matter

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

State Shape Volume Compressible Flow Strength of Intermolecular

Attractions

Solid Fixed Fixed No No very strong

Liquid Indef. Fixed No Yes moderate

Gas Indef. Indef. Yes Yes very weak


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 motiondegrees of freedom = translational, rotational,

vibrational• attractive forces try to keep the molecules together• kinetic energy depends only on the temperature

KE = 1.5 kT


Gas Structure

Gas molecules are rapidly moving in random straight lines and free from sticking to each other.


Explaining the Properties of Solids• the particles in a solid are packed close

together and are fixed in positionthough 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


Solids• some solids have their particles

arranged in an orderly geometric pattern – we call these crystalline solidssalt and diamonds

• other solids have particles that do not show a regular geometric pattern over a long range – we call these amorphous solidsplastic and glass


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


Compressibility


Phase Changes


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


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


Attractive Forces+ - + - + - + -

+++

+

____

+ + + + + + +

- - - - - - -

++ + +

+

--

- --



Dispersion Force


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 forcesaka 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


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 moleculemore surface-to-surface contact = larger

induced dipole = stronger attraction


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.


Relationship between Induced Dipole and Molecular Size

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

1 2 3 4 5 6

Period

Bo

ilin

g P

oin

t, °C

BP, Noble Gas

BP, Halogens

BP, XH4


Name Molar Mass BP, °C MP, °C Density, g/mLMethane 16 -162 -183 0.47Ethane 30 -89 -183 0.57Propane 44 -42 -188 0.5Butane 58 0 -138 0.58Pentane 72 36 -130 0.56Hexane 86 69 -95 0.66Heptane 100 98 -91 0.68Octane 114 126 -57 0.7Nonane 128 151 -54 0.72Decane 142 174 -30 0.74Undecane 156 196 -26 0.75Dodecane 170 216 -10 0.76Tridecane 184 235 -5 0.76Tetradecane 198 254 6 0.77Pentadecane 212 271 10 0.79Hexadecane 226 287 18 0.77

Properties of Straight Chain AlkanesNon-Polar Molecules


Boiling Points of n-Alkanes


n-Alkane Boiling & Melting Points

-300

-200

-100

0

100

200

300

400

500

0 100 200 300 400 500Molar Mass

Tem

per

atu

re, °

C

BP, n-alkane

MP, n-alkane


Effect of Molecular Shapeon Size of Dispersion Force


Alkane Boiling Points

-20

0

20

40

60

80

100

120

140

58 72 86 100 114

Molar Mass

Tem

per

atu

re,

°Cn-alkanes

iso-alkanes

Alkane Boiling Points

• branched chains have lower BPs than straight chains

• the straight chain isomers have more surface-to-surface contact


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

a) CH4 CH3CH2CH2CH3

b) CH3CH2CH=CHCH2CH3 cyclohexane

CC

CC

H

H H

HH

H H

HH

HC

H

HHH

CC

CC

H

H

H

HH

H

CC

H

HH

H

HH

H

H HH

H

HC

CH

H

HC

CH C

H

HC



a) CH4 CH3CH2CH2CH3

b) CH3CH2CH=CHCH2CH3 cyclohexane

both molecules are nonpolarlarger molar mass

both molecules are nonpolarflat molecule larger surface-to-surface contact

CC

CC

H

H H

HH

H H

HH

HC

H

HHH

CC

CC

H

H

H

HH

H

CC

H

HH

H

HH

H

H HH

H

HC

CH

H

HC

CH C

H

HC


Dipole-Dipole Attractions• polar molecules have a permanent dipole

because of bond polarity and shapedipole momentas 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


Effect of Dipole-Dipole Attraction on Boiling and Melting Points

31

Molar Mass

Boiling Point

Dipole Size

CH3CH2CH3 44.09 -42°C 0.08 D

CH3-O-CH3 46.07 -24°C 1.30 D

CH3 - CH=O 44.05 20.2°C 2.69 D

CH3-CN 41.05 81.6°C 3.92 D


or


a) CH2FCH2F CH3CHF2

b)

C C

HH

H HF

F

C C

HH

H FH

F


or


more polar

polar nonpolar

a) CH2FCH2F CH3CHF2

b)

C C

HH

H HF

F

C C

HH

H FH

F


Attractive Forces and Solubility• Solubility depends on the attractive forces of solute

and solvent moleculesLike dissolves Likemiscible liquids will always dissolve in each other

• polar substance dissolve in polar solventshydrophilic 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

hydrophobic parts - solubility becomes competition between parts


Immiscible Liquids


Polar Solvents

Water

Dichloromethane(methylene chloride)

Ethanol(ethyl alcohol)


Nonpolar Solvents

CH3

CH2

CH2

CH2

CH2

CH3

n-hexane

CH

CHCH

CH

CHC

CH3

toluene

C

Cl

ClClCl

carbon tetrachloride


Hydrogen Bonding• When a very electronegative atom is bonded to

hydrogen, it strongly pulls the bonding electrons toward itO-H, N-H, or F-H

• Since hydrogen has no other electrons, when it loses the electrons, the nucleus becomes deshieldedexposing the H proton

• The exposed proton acts as a very strong center of positive charge, attracting all the electron clouds from neighboring molecules


H-Bonding

HF


H-Bonding in Water


-200

-150

-100

-50

0

50

100

150

1 2 3 4 5

Boi

lin P

oint

, °C

Period

Relationship between H-bonding and Intermolecular Attraction BP, HX

BP, H2X

BP, H3X

BP, XH4

CH4

NH3

HF

H2O

SiH4GeH4

SnH4H2S

H2Se

H2Te


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

a) CH3OH CH3CHF2

b) CH3-O-CH2CH3 CH3CH2CH2NH2


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

a) CH3OH CH3CHF2

b) CH3-O-CH2CH3 CH3CH2CH2NH2

can H-bond

can H-bond


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

a) CH3OH CH3CHF2

b) CH3CH2CH2CH3 CH3Cl


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

a) CH3OH CH3CHF2

b) CH3CH2CH2CH3 CH3Cl

can H-bond with H2O

more polar


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


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


Summary (cont’d)• Hydrogen bonds are the strongest of the intermolecular

attractive forcesa pure substance can have

• Hydrogen bonds will be present when a molecule has H directly bonded to either O , N, or F atomsonly 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


Liquids Properties and Structure

• Surface tensionhttp://

www.sciencefriday.com/videos/watch/10210

• Viscosity• Capillary action• Meniscus

50

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 sphericalas 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


Surface Tension• because they have fewer neighbors

to attract them, the surface molecules are less stable than those in the interiorhave a higher potential energy

• the surface tension of a liquid is the energy required to increase the surface area a given amountat room temp, surface tension of H2O

= 72.8 mJ/m2


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 tensionraising the temperature of the liquid increases the

average kinetic energy of the moleculesthe increased molecular motion makes it easier to

stretch the surface


Surface Tension of Water vs. Temperature

50

55

60

65

70

75

80

-20 0 20 40 60 80 100 120

Temperature, °C

Su

rfac

e T

ensi

on, m

J/m

2


Viscosity• viscosity is the resistance of a liquid to flow

1 poise = 1 P = 1 g/cm∙soften given in centipoise, cP

• larger intermolecular attractions = larger viscosity• higher temperature = lower viscosity


Viscosity of Water vs. Temperature

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

Temperature, deg C

Vis

cosi

ty, c

P


Capillary Action• capillary action is the ability of a liquid to

flow up a thin tube against the influence of gravitythe 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 togetheradhesive forces attract the molecules on the edge

to the tube’s surface


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


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 glassmetallic bonds stronger than intermolecular

attractions

59

Heating Curve of Water


Distribution of Thermal Energy• only a small fraction of the molecules in a liquid

have enough energy to escape• the higher the temperature, the faster the rate

of evaporation


Vaporization• molecules in the liquid are

constantly in motion• if these molecules are at the

surface, they may have enough energy to overcome the attractive forcestherefore – the larger the

surface area, the faster the rate of evaporation


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 liquidparticularly on surrounding surfaces

• we call this process condensation


Effect of Intermolecular Attraction on Evaporation and Condensation

• the weaker the attractive forces, the faster the rate of evaporation

• liquids that evaporate easily are said to be volatilee.g., gasoline, fingernail polish removerliquids that do not evaporate easily are called

nonvolatilee.g., motor oil


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 +

· DHcondensation = -DHvaporization


Dynamic Equilibrium


Vapor Pressure• the pressure exerted by the vapor when it is in

dynamic equilibrium with its liquid is called the vapor pressureremember using Dalton’s Law of Partial Pressures to

account for the pressure of the water vapor when collecting gases by water displacement?

• therefore, the weaker the attractive forces, the higher the vapor pressurethe higher the vapor pressure, the more volatile the

liquid


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


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


Vapor Pressure CurvesTemperature vs Vapor Pressure

0

100

200300

400

500

600

700800

900

1000

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150Temperature, °C

Vap

or P

ress

ure

, mm

Hg

w ater

TiCl4

chloroform

ether

ethanol

acetone

760 mmHg

normal BP100°C

BP Ethanol at 500 mmHg68.1°C


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 liquidnot 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


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


Clausius-Clapeyron Equation• the graph of vapor pressure vs. temperature is an

exponential growth curve

RT

H

vap

vap

P

e

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

)(lnT

1

R

H)ln(P

RT

H)(ln)ln(P

ln)(ln)ln(P

ln)ln(P

vapvap

vapvap

RT

H

vap

RT

H

vap

vap

vap

e

e

• the slope of the line x 8.314 J/mol∙K = DHvap

in J/mol


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


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


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 containerat temperatures below the melting point therefore, molecular solids have a vapor pressure

solid gassublimation

deposition


Sublimation


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

78

Heat of Fusion• the amount of heat energy required to melt one mole of

the solid is called the Heat of Fusion, DHfussometimes called the enthalpy of fusion

• always endothermic, therefore DHfus is +· DHcrystallization = -DHfusion

· generally much less than DHvap

· DHsublimation = DHfusion + DHvaporization


Heats of Fusion and Vaporization


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 0°C at 1 atm


Heating Curve of a Liquid• as you heat a liquid, its

temperature increases linearly until it reaches the boiling pointq = 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

82

Heating Curve of Water


ExampleHow much energy is required to heat 18.0 g of ice

(1.00 mole) from -25°C to 125°C?


Segment 1• heating 1.00 mole of ice at -25.0°C up to the melting

point, 0.0°C• q = mass x Cs x DT

mass of 1.00 mole of ice = 18.0 gCs = 2.09 J/mol∙°C

kJ 0.941J 941

C25.0C0.009.2g 0.18Cg

J

q

q


Segment 2• melting 1.00 mole of ice at the melting point, 0.0°C• q = n∙DHfus

n = 1.00 mole of iceDHfus = 6.02 kJ/mol

kJ 6.02

02.6mol 1.00molkJ

q

q


Segment 3• heating 1.00 mole of water at 0.0°C up to the boiling

point, 100.0°C• q = mass x Cs x DT

mass of 1.00 mole of water = 18.0 gCs = 2.09 J/mol∙°C

kJ 52.7J 1052.7

C.00C100.018.4g 0.18

3

CgJ

q

q


Segment 4• boiling 1.00 mole of water at the boiling point, 100.0°C• q = n∙DHvap

n = 1.00 mole of iceDHfus = 40.7 kJ/mol

kJ 7.04

7.40mol 1.00molkJ

q

q


Segment 5• heating 1.00 mole of steam at 100.0°C up to 125.0°C• q = mass x Cs x DT

mass of 1.00 mole of water = 18.0 gCs = 2.01 J/mol∙°C

kJ 904.0J 904

C.0100C125.001.2g 0.18Cg

J

q

q

89

Phase DiagramsP

ress

ure

Temperature

vaporization

condensation

criticalpoint

triplepoint

Solid Liquid

Gas

1 atm

normalmelting pt.

normalboiling pt.

Fusion Curve

Vapor PressureCurve

SublimationCurve

melting

freezing

sublimation

deposition




Morphic Forms of Ice




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

Solidsproperties & structure


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


X-ray Crystallography


Bragg’s Law• when the interference between x-rays is constructive,

the distance between the two paths (a) is an integral multiple of the wavelength

nl=2a• the angle of reflection is therefore related to the

distance (d) between two layers of particlessin q = a/d

• combining equations and rearranging we get an equation called Bragg’s Law

sin2

nd


Crystal Lattice• when allowed to cool slowly, the particles in a

liquid will arrange themselves to give the maximum attractive forcestherefore 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


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

102

7 Unit Cells

Cubica = b = call 90°

ab

c

Tetragonala = c < ball 90°

a

b

c

Orthorhombica ¹ b ¹ call 90°

a

b

c

Monoclinica ¹ b ¹ c

2 faces 90°

a b

c

Hexagonala = c < b

2 faces 90°1 face 120°

c

a

b

Rhombohedrala = b = cno 90°

ab

c

Triclinica ¹ b ¹ cno 90°


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


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

⅛ of each corner particle is within the cube½ of each particle on a face is within the cube¼ of each particle on an edge is within the cube

3

3

π3

4 Sphere a of Volume

length edge Cube a of Volume

r



Simple Cubic


Cubic Unit Cells - Simple Cubic

• 8 particles, one at each corner of a cube

• 1/8th of each particle lies in the unit celleach particle part of 8 cells1 particle in each unit cell

8 corners x 1/8• edge of unit cell = twice the

radius• coordination number of 6

2r


Body-Centered Cubic


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 cell2 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

3

4r


Face-Centered Cubic


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 cell4 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

22r

fcc = 4 atoms/uc, Al = 26.982 g/mol, 1 mol = 6.022 x 1023 atoms

cm 1043.1m 10

cm 1

pm 1

m 10pm 431 8

2-

-12

g 10792.1mol 1

g 982.26

atoms106.022

mol 1Al atoms 4 22

23

Example 11.7 – Calculate the density of Al if it crystallizes in a fcc and has a radius of 143 pm

the accepted density of Al at 20°C is 2.71 g/cm3, so the answer makes sense

face-centered cubic, r = 143 pm

density, g/cm3

Check:

Solution:

Concept Plan:

Relation-ships:

Given:Find:

1 cm = 102 m, 1 pm = 10-12 m

lr Vmassfcc

dm, V

# atoms x mass 1 atom

V = l3, l = 2r√2, d = m/Vd = m/V

l = 2r√2 V = l3

face-centered cubic, r = 1.43 x 10-8 cm, m = 1.792 x 10-22 g

density, g/cm3

cm 10544.0cm)(1.414) 1043.1(222 -88 rl

323

383

cm 10618.6

cm 10045.4

lV

3cm

g

323

22

71.2

cm 10618.6

g 10792.1

V

md


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


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


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

Hexagonal Closest-PackedCubic Closest-PackedFace-Centered Cubic


Hexagonal Closest-Packed Structures


Cubic Closest-Packed Structures


Molecular Solids• the lattice site are occupied by

molecules• the molecules are held together

by intermolecular attractive forcesdispersion forces, dipole

attractions, and H-bonds• because the attractive forces are

weak, they tend to have low melting pointgenerally < 300°C


Ionic Solids

• held together by attractions between opposite chargesnondirectionaltherefore every cation

attracts all anions around it, and vice versa


Nonbonding Atomic Solids• noble gases in solid form• solid held together by weak

dispersion forcesvery low melting

• tend to arrange atoms in closest-packed structureeither hexagonal cp or cubic cpmaximizes attractive forces and

minimizes energy


Metallic Atomic Solids• solid held together by

metallic bondsstrength varies with sizes and

charges of cationscoulombic attractions

• melting point varies• mostly closest packed

arrangements of the lattice pointscations


Metallic Bonding• metal atoms release their

valence electrons• metal cation “islands” fixed

in a “sea” of mobile electrons

e-

e- e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

+ + + + + + + + +

+ + + + + + + + +

+ + + + + + + + +


Crystal Structure of Metals at Room Temperature

= body-centered cubic

= hexagonal closest packed

= other

= cubic cp, face-centered

= diamond


Network Covalent Solids• carbon

diamondgraphite

• silicatesquartzmica


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 pointsgenerally > 1000°C

• dimensionality of the network affects other physical properties


The Diamond Structure:a 3-Dimensional Network

• the carbon atoms in a diamond each have 4 covalent bonds to surrounding atomssp3

tetrahedral geometry• this effectively makes each

crystal one giant molecule held together by covalent bondsyou can follow a path of covalent

bonds from any atom to every other atom


The Graphite Structure:a 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


Quartz

• 3-dimensional array of Si covalently bonded to 4 O tetrahedral

• melts at ~1600°C• very hard


Micas• minerals that are mainly

2-dimensional arrays of Si bonded to Ohexagonal arrangement of

atoms• sheets• chemically stable• thermal and electrical

insulator


Conductors, Semiconductors and Insulators

• the structures of metals and covalent network solids result in every atom’s 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


Molecular Orbitals of Polylithium


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


Types of Band Gaps andConductivity


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 gapthe larger the band gap, the fewer electrons there are

with enough energy to make the jump


Doping Semiconductors• doping is adding impurities to the semiconductor’s

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


Ionic Crystals

CsClcoordination number = 8

Cs+ = 167 pmCl─ = 181 pm

NaClcoordination number = 6

Na+ = 97 pmCl─ = 181 pm


Coordination Number

• 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 anionsgenerally, 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


Lattice Holes

Simple CubicHole

OctahedralHole

TetrahedralHole


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


Cesium Chloride Structures

• coordination number = 8• ⅛ of each Cl─ (184 pm) inside

the unit cell• whole Cs+ (167 pm) inside the

unit cellcubic hole = hole in simple cubic

arrangement of Cl─ ions• Cs:Cl = 1: (8 x ⅛), therefore the

formula is CsCl


Rock Salt Structures(Sodium Chloride)

• coordination number = 6• Cl─ ions (181 pm) in a face-centered

cubic arrangement ⅛ 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

• Na:Cl = (¼ x 12) + 1: (⅛ x 8) + (½ x 6) = 4:4 = 1:1,

• therefore the formula is NaCl


Zinc Blende Structures

• coordination number = 4• S2─ ions (184 pm) in a face-centered

cubic arrangement ⅛ 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

• Zn:S = (4 x 1) : (⅛ x 8) + (½ x 6) = 4:4 = 1:1,

• therefore the formula is ZnS


Wurtzite Structures• coordination number = 4• Zn2+ ions in a hexagonal arrangement• each S2─ in holes between Zn2+

tetrahedral holes 1 whole in all the holes

• Zn:S = (1/3 x 2) + (1/6 x 2) + (1) : (1/6 x 4) + (1/12 x 4) + (1) = 2:2 = 1:1,

• therefore the formula is ZnS wurtzite structure common for 1:1 ratio



Documents

Chapter 11 Liquids, Solids, And Intermolecular Forces