chapter 10 liquids and solids

Chapter 10 Chapter 10 Liquids and SolidsLiquids and Solids

TopicsTopics Intermolecular forcesIntermolecular forces

– Dipole-dipole forcesDipole-dipole forces Hydrogen bondingHydrogen bonding

– London ForcesLondon Forces The liquid stateThe liquid state

– Surface tensionSurface tension– Capillary actionCapillary action– ViscosityViscosity

An introduction to structures and types of solidsAn introduction to structures and types of solids– X-ray analysis of solidsX-ray analysis of solids– Types of crystalline solidsTypes of crystalline solids

Structure and bonding in metalsStructure and bonding in metals– Bonding metals for metals Bonding metals for metals – Meta alloysMeta alloys

Molecular solidsMolecular solids Ionic solidsIonic solids Vapor pressure and changes of stateVapor pressure and changes of state Phase diagramsPhase diagrams

10.510.5 Section is self studySection is self study

Intra- vs. Inter-molecular forcesIntra- vs. Inter-molecular forces

intramolecular forcesintramolecular forces– inside molecules (bonding)inside molecules (bonding)– hold atoms together into moleculehold atoms together into molecule

intermolecular forcesintermolecular forces– These are what hold the molecules together in the

condensed states.– Forces between moleculesForces between molecules– They get weaker as phase changes from S – L – GThey get weaker as phase changes from S – L – G

When a substance changes state, molecule stays together When a substance changes state, molecule stays together but intermolecular forces are but intermolecular forces are weakenedweakened

10.1 Intermolecular Forces10.1 Intermolecular Forces

Intermolecular ForcesIntermolecular Forces

GasesGases – fill container, random rapid motion, never coming to rest or clumping together• Motion is mainly translational

LiquidsLiquids – fixed volume, flow and assume shape of container, only slightly compressible, stronger forces hold molecules together• Motion is mainly translationalMotion is mainly translational

Solids – fixed volume, definite shape, generally less compressible than liquids, forces hold particles in a fixed shape

• Motion is mainly vibrational

Intermolecular Forces

Intermolecular forces are attractive forces between molecules

Intramolecular forces hold atoms together in a molecule.

Intermolecular vs Intramolecular

• 41 kJ to vaporize 1 mole of water (inter)

• 930 kJ to break all O-H bonds in 1 mole of water (intra)

Generally, intermolecular forces are much weaker than intramolecular forces.

“Measure” of intermolecular force

boiling point

melting point

Hvap

Hfus

Hsub

Dipole – Dipole Foces

Molecules that line up in the presence of a electric field are dipoles.

The opposite ends of the dipole can attract each other so the molecules stay close together.

1% as strong as covalent bonds Weaker the covalent bonds with greater distance. Small role in gases. Molecules with these forces possess higher

melting points and boiling points than nonpolar molecules of comparable molar mass

The strengths of intermolecular forcesintermolecular forces are generally weaker than either ionic or covalent bonds.

16 kJ/mol (to separate molecules)

431 kJ/mol (to break bond)

++-

-

Polar molecules have dipole-dipole attractions for one another.

Types of intermolecular forces (between neutral moleculesthat posses dipole moment):

Dipole-dipole forces: (polar molecules)

SO O.. ::

....

:

+

--

..:

..

--

SO O:

..:

+

dipole-dipole attraction

What effect does this attraction have on the boiling point?

Nonpolar PolarMolecule MM BP Molecule MM BP

N2 28 -196 CO 28 -192

SiH4 32 -112 PH3 34 -88

GeH4 77 -90 AsH3 78 -62

Br2 160 69 ICl 162 97

Effect of polarity on boiling points

• Effect of polarity is usually small enough to be obscured by differences in molar mass

HCl -85BP (oC)

HBr -60

HI -30

BP increase although polarity decreases

Hydrogen BondsHydrogen Bonds

• A hydrogen bond is an intermolecular force in which a hydrogen atom covalently bonded to a nonmetal atom in one molecule is simultaneously attracted to a nonmetalnonmetal atom of a neighboring molecule

• The strongest hydrogen bonds are formed if the nonmetal

atoms are smallsmall and highly electronegativehighly electronegative – e.g., N, O, F

very strong type of dipole-dipole attractionvery strong type of dipole-dipole attraction–because bond is so polarbecause bond is so polar–because atoms are so smallbecause atoms are so small

Hydrogen bondHydrogen bond

Cl(HCl)Cl(HCl) and and S(HS(H22S)S) do not form hydrogen do not form hydrogen

bonding although they have bonding although they have electronegativity similar to N, why? electronegativity similar to N, why? – They are of bigger size to approach the They are of bigger size to approach the

hydrogen atomhydrogen atom

Hydrogen bond is 5-10% as strong as the Hydrogen bond is 5-10% as strong as the covalent bondcovalent bond

Hydrogen bonding is a weak to moderate attractive force that exists between a hydrogen atom covalently bonded to a very small and highly electronegative atom

and a lone pair of electrons on another small, electronegative atom (F, O, or N).

Hydrogen bonding: It is very strong dipole-dipole interaction (bonds involving H-F, H-O, and H-N are most important cases).

+H-F- --- +H-F-

Hydrogen bonding

Hydrogen bonding between water molecules

WaterWater

+

-

+

Hydrogen BondingHydrogen Bonding

• Bonding between hydrogen and more electronegative neighboring atoms such as oxygen and nitrogen

Hydrogen bonding between ammonia and water

Examples of hydrogen bond

The hydrogen bond is a special dipole-dipole interaction between the hydrogen atom in a polar N-H, O-H, or F-H bond and an electronegative O, N, or F atom. IT IS NOT A BOND.

A H…B A H…Aor

A & B are N, O, or F

Hydrogen Bonding EffectsHydrogen Bonding Effects

• Solid water is less dense than liquid water due to hydrogen bonding

• Hydrogen bonding is also the reason for the unusually high boiling point of water

The larger the molecule the larger the Van der Waals attraction due to more electrons in the molecule.

The stronger the attraction, the higher the boiling point.

Boiling Points for Some Non Polar MoleculesBoiling Points for Some Non Polar Molecules

CH4

SiH4

GeH4SnH4

PH3

NH3 SbH3

AsH3

H2O

H2SH2Se

H2Te

HF

HI

HBrHCl

Boilin

g Poin

ts

0ºC

100

-100

200Molar massMolar mass

Hydrogen Bonding in other moleculesHydrogen Bonding in other molecules

Many organic acids can form dimers due to hydrogen bonding

Certain organic molecules can also form an intramolecular hydrogen bond

Ethanol shows hydrogen bonding

O

H

CH3 C O H

H

H CH2 CH3

Do these compounds show hydrogen bonding?

A. NH

H

N

H

H (Hydrazine)

B. CH3 C CH3

O

(Acetone)

C. CH3 O CH3 (dimethyl ether)

Do these compounds show hydrogen bonding?

Hydrogen bonding and solubilityHydrogen bonding and solubility

Some compounds containing O, N & F show Some compounds containing O, N & F show

high solubilities in certain hydrogen high solubilities in certain hydrogen containing solvents.containing solvents.

NHNH33 & CH & CH33OH dissolves in HOH dissolves in H22O through the O through the

formation of H-bondsformation of H-bonds

N

H

H

H

OH

H

CH

H

H

O

H

OH

H

London Dispersion ForcesLondon Dispersion Forces

Non - polar molecules also exert forces on Non - polar molecules also exert forces on each other.each other.

Otherwise, no solids or liquids.Otherwise, no solids or liquids. Electrons are not evenly distributed at Electrons are not evenly distributed at

every instant in time.every instant in time. Have an instantaneous dipole.Have an instantaneous dipole. Induces a dipole in the atom next to it.Induces a dipole in the atom next to it. Induced dipole- induced dipole interaction.Induced dipole- induced dipole interaction.

London Dispersion ForcesLondon Dispersion Forces

The temporary separations of The temporary separations of charge that lead to the London charge that lead to the London force attractions are what attract force attractions are what attract one one nonpolar nonpolar molecule to its molecule to its neighbors.neighbors.

Fritz London Fritz London 1900-19541900-1954

London forces increase with London forces increase with the size of the molecules.the size of the molecules.

London Dispersion ForcesLondon Dispersion Forces

They exist in every molecular They exist in every molecular compoundcompound

They are significant only for nonpolar They are significant only for nonpolar molecules and noble gas atomsmolecules and noble gas atoms

They are weak, short-livedThey are weak, short-lived Caused by formation of temporary Caused by formation of temporary

dipole moments dipole moments

Instantaneous polarization causes instantaneous dipole

“Electrons are shifted to overload one side of an atom or molecule”.

+ +- -

attraction

London Dispersion ForcesLondon Dispersion Forces

- Relatively weakRelatively weak forces that exist among forces that exist among noble gas atoms and nonpolar moleculesnoble gas atoms and nonpolar molecules. . ((Ar, CAr, C88HH1818))

- Caused by Caused by instantaneous dipoleinstantaneous dipole, in which , in which electron distribution becomes asymmetricalelectron distribution becomes asymmetrical..

- The ease with which electron “cloud” of an The ease with which electron “cloud” of an atom can be distorted is called atom can be distorted is called polarizabilitypolarizability..

Polarizability: the ease with which an atom or molecule can be distorted to have an instantaneous dipole. “squashiness”

In general big moleculesare more easily polarized

than little ones.

Intermolecular Forces

Polarizability

Polarizability is the ease with which the electron distribution in the atom or molecule can be distorted.

Polarizability increases with:

• greater number of electrons

• more diffuse electron cloud

Dispersion forces usually increase with molar mass.

London Dispersion ForcesLondon Dispersion Forces

Weak, short lived.Weak, short lived. Lasts longer at low temperature.Lasts longer at low temperature. Eventually long enough to make liquids.Eventually long enough to make liquids. More electrons, more polarizable.More electrons, more polarizable. Bigger molecules, higher melting and Bigger molecules, higher melting and

boiling points.boiling points. Much, much weaker than other forces.Much, much weaker than other forces. Also called Also called Van der Waal’s forces..

RelativeRelative Magnitudes of ForcesMagnitudes of Forces

The types of bonding forces vary in their The types of bonding forces vary in their strength as measured by average bond strength as measured by average bond energy. energy.

Covalent bonds (400 kcal/mol)

Hydrogen bonding (12-16 kcal/mol )

Dipole-dipole interactions (2-0.5 kcal/mol)

London forces (less than 1 kcal/mol)

Strongest Weakest

Halogen Boiling Pt (K)

Noble Gas Boiling Pt (K)

F2 85.1 He 4.6

Cl2 238.6 Ne 27.3

Br2 332.0 Ar 87.5

I2 457.6 Kr 120.9

Which one(s) of the above are most polarizable?Hint: look at the relative sizes.

London Forces in HydrocarbonsLondon Forces in Hydrocarbons

PracticePractice

which has highest boiling pt?which has highest boiling pt?– HF, HCl, or HBr?HF, HCl, or HBr?

Identify the most important Identify the most important intermolecular forces :intermolecular forces :– BaSOBaSO44

– HH22SS

– XeXe

– CC22HH66

– PP44

– HH22OO

– CsICsI

ionic

dipole-dipole

H-bonding

London Dispersion

Which has stronger intermolecuar forcesWhich has stronger intermolecuar forces??

COCO22 or OCS or OCS

– COCO22: nonpolar so : nonpolar so

only LDonly LD– OCS: polar so OCS: polar so

dipole-dipoledipole-dipole

PFPF33 or PF or PF55

– PFPF33: polar so : polar so

dipole-dipoledipole-dipole

– PFPF55: nonpolar so : nonpolar so

only LDonly LD

SFSF22 or SF or SF66

– SFSF22: polar so : polar so

dipole-dipoledipole-dipole

– SFSF66: nonpolar so : nonpolar so

only LDonly LD

SOSO33 or SO or SO22

– SOSO33: nonpolar so : nonpolar so

LD onlyLD only

– SOSO22: polar so : polar so

dipol-dipoledipol-dipole

SO

O

What type(s) of intermolecular forces exist between each of the following molecules?

HBrHBr is a polar molecule: dipole-dipole forces. There are also dispersion forces between HBr molecules.

CH4

CH4 is nonpolar: dispersion forces.

SO2

SO2 is a polar molecule: dipole-dipole forces. There are also dispersion forces between SO2 molecules.

11.2

10.210.2 The Liquid stateThe Liquid state

Properties of LiquidsProperties of LiquidsLow compressibilityLow compressibilityLack of rigidityLack of rigidityHigh density compared to gasesHigh density compared to gasesBeading (beads up as droplets) Beading (beads up as droplets) Surface tensionSurface tensionCapillary actionCapillary actionViscosityViscosity

Stronger intermolecular forces cause Stronger intermolecular forces cause each of these to increase.each of these to increase.

Surface tensionSurface tension

The resistance to an The resistance to an increase in its surface increase in its surface areaarea

Polar molecules and Polar molecules and liquid metalsliquid metals

show high surfaceshow high surface

tensiontension

Surface tensionSurface tension

Molecules in Molecules in the middle are the middle are attracted in all attracted in all directions.directions.

Molecules at the the top are only pulled inside.

Minimizes surface area.

Surface TensionSurface Tension

One water molecule One water molecule can hydrogen bond can hydrogen bond to another because to another because of this electrostatic of this electrostatic attraction.attraction.

Also, hydrogen Also, hydrogen bonding occurs with bonding occurs with other molecules other molecules surrounding them on surrounding them on all sides.all sides.

H HO

+

+

-

H HO

+

-

+

Surface TensionSurface Tension

A water A water molecule in molecule in the the middlemiddle of a of a solution is solution is pulled in all pulled in all directions.directions.

Surface TensionSurface Tension This is This is NotNot true for true for

molecules at the molecules at the surfacesurface.. Molecules at the surface Molecules at the surface

are only pulled down and are only pulled down and to each side.to each side.

This holds the molecules This holds the molecules at the surface together at the surface together tightly.tightly.

This causes surface This causes surface tensiontension..

Surface tensionSurface tension

AllAll liquids have surface tension liquids have surface tension– water is just higher than most otherswater is just higher than most others

How can we decrease surface How can we decrease surface tension?tension?– Use a Use a surfactantsurfactant - - sursurface face actactive ive aagegentnt– Also called a wetting agent, like Also called a wetting agent, like

detergent or soapdetergent or soap– Interferes with hydrogen bondingInterferes with hydrogen bonding

BeadingBeading Water drops are Water drops are

roundedrounded, , because all because all molecules on the molecules on the edge are pulled edge are pulled to the middle- to the middle- not outward to not outward to the air!the air!

Adhesive forcesAdhesive forces are intermolecular forces between unlike molecules

Cohesive forcesCohesive forces are intermolecular forces between like molecules

BeadingBeading

If a polar substance is If a polar substance is placed on a non-polar placed on a non-polar surface. surface. – There are cohesive,There are cohesive,– But no adhesive forces.But no adhesive forces.

And Visa VersaAnd Visa Versa

Meniscus is the interface between a liquid and the air above it

Adhesion

attracted to glass

Cohesionattracted to each other

Capillary ActionCapillary Action

Capillary action results from

intermolecular interactions Liquids spontaneously rise in a narrow Liquids spontaneously rise in a narrow

tube.tube. Glass is polar.Glass is polar. It attracts water molecules (adhesive It attracts water molecules (adhesive

forces)forces)

Glass has polar Glass has polar molecules.molecules.

Glass can also Glass can also hydrogen bond.hydrogen bond.

This attracts the This attracts the water molecules.water molecules.

Some of the pull is Some of the pull is up a cylinderup a cylinder..

Water curves up along Water curves up along the side of glass.the side of glass.

This makes the This makes the meniscusmeniscus, as in a , as in a graduated cylindergraduated cylinder

Plastics are non-Plastics are non-wetting; no attractionwetting; no attraction

MeniscusMeniscus

In Glass In Plastic

ViscosityViscosity

Viscosity is a measure of a liquid’s resistance to flow

–strong inter molecular strong inter molecular forces forces highly viscous highly viscous–large, complex molecules large, complex molecules highly viscous highly viscous–Cyclohexane has a lower Cyclohexane has a lower viscosity than hexane.viscosity than hexane.–Because it is a circle- Because it is a circle- more compact.more compact.

ModelModel

Can’t see molecules so picture them as-Can’t see molecules so picture them as- In motion but attracted to each otherIn motion but attracted to each other With regions arranged like solids butWith regions arranged like solids but

– with higher disorder.with higher disorder.– with fewer holes than a gas.with fewer holes than a gas.– Highly dynamic, regions changing between Highly dynamic, regions changing between

types.types.

10.3 An introduction to structures 10.3 An introduction to structures and types of solidsand types of solids

Types of SolidsTypes of Solids

Crystalline SolidsCrystalline Solids: : highly regular three dimensional highly regular three dimensional arrangement of their components arrangement of their components [[table salt table salt ((NaClNaCl))]]

Amorphous solidsAmorphous solids: : considerable disorder in their considerable disorder in their structures structures ((glass: components are frozen in place glass: components are frozen in place before solidifying and achieving an ordered before solidifying and achieving an ordered arrangementarrangement))

The positions of components in a crystalline solid are The positions of components in a crystalline solid are usually represented by a lattice usually represented by a lattice

Crystalline solidsAmorphous solids

An amorphous solid does not possess a well-defined arrangement and long-range molecular order.

A glass is an optically transparent fusion product of inorganic materials that has cooled to a rigid state without crystallizing

Crystallinequartz (SiO2)

Non-crystallinequartz glass

Representation of Components Representation of Components in a Crystalline Solidin a Crystalline Solid

LatticeLattice: : A 3-dimensional system that describes the locations of components A 3-dimensional system that describes the locations of components ((atoms, ions, or moleculesatoms, ions, or molecules) ) that make up the unit cells of a substancethat make up the unit cells of a substance..Unit CellUnit Cell: The smallest repeating unit in the lattice: The smallest repeating unit in the lattice..There are ThreeThree common types of unit cells:

– simple cubicsimple cubic– bodybody--centered cubiccentered cubic– faceface--centered cubiccentered cubic

Crystal Structures - Crystal Structures - CubicCubic

a

aa

SimpleSimple Face-CenteredFace-Centered Body-CenteredBody-Centered

Unit CellsUnit Cells

The simple cubic cell is the simplest unit cell and has structural particles centered only at its corners

The body-centered cubic (bcc) structure has an additional structural particle at the center of the cube

TheThe face-centered face-centered cubic (fcc)cubic (fcc) structure structure has an additional has an additional structural particle at structural particle at the center of each the center of each faceface

Cubic

Unit cells in 3 dimensions

At lattice points:

•Atoms

•Molecules

•Ions

lattice points

The simple cubic cell is the simplest unit cell and has structural particles centered only at its corners

Body-Centered Cubic

Unit cells in 3 dimensions

The body-centered cubic

(bcc) structure has an additional structural particle at the center of the cube

Face-Centered CubicThe face-centered cubic (fcc) structure has an additional structural particle at the center of each face

• Sample is powdered• X-rays of single wavelength is used• Distance between planes of atoms in the crystal are calculated from the angles at which the rays are diffracted using Bragg equation

X-Ray analysis of solids

Spots from diffracted X-rays

Spot from incident beam

X-Ray analysis of solids

X-Ray diffraction

Extra distance traveled by lower ray = BC + CD = n = 2d sin

Reflection of X-rays from two layers of atoms

1st layer of atoms

2nd layer of atoms

n = 2d sin

Bragg Equation

n 2 = d sin

d = distance between atoms n = an integer = wavelength of the x-rays

X rays of wavelength 0.154 nm are diffracted from a crystal at an angle of 14.170. Assuming that n = 1, what is the distance (in pm) between layers in the crystal?

n = 2d sin n = 1 = 14.170

= 0.154 nm = 154 pm

d =n

2sin=

1 x 154 pm

2 x sin14.17= ____________

When silver crystallizes, it forms face-centered cubic cells. The unit cell edge length is 408.7 pm. Calculate the density of silver.

d = mV

V = a3 = (408.7 pm)3 = 6.78X107 pm3

___ atoms/unit cell in a face-centered cubic cell

m = 4 Ag atoms107.9 gmole Ag

x1 mole Ag

6.022 x 1023 atomsx = 1.79X10-22 g

d = mV

7.17 x 10-22 g6.83 x 10-23 cm3

= = 1.79X10-22 g / 6.78X107 pm3

= 2.6X10-30 g/pm3

Types of crystalline Solids Ionic solids (ionic compounds)

• Ions (held by electrostatic attraction) at point in lattice

• They conduct electric current when dissolved in water

Molecular solids (molecular compounds)• Molecules (held by: dispersion and/or dipole-dipole forces)

at each point in lattice. Ice is a molecular solid H2O atomic solids (metals, nonmetals, noble gases)

• Elements (C, B, Si) that are composed of atoms at lattice points. Three types:

• Metallic– metallic bond• Network – strong covalent bonding• Group 8A –London Dispersion Forces

atomic- network ionic molecular

Name type of solid Force(s) Melting Pt.(oC)

Boiling Pt.(oC)

Ne molecular -249 -246

H2S molecular -86 -61

H2O molecular 0 100

Mercury metallic -39 357

W metallic 3410 5660

CsCl ionic 645 1290

MgO ionic 2800 3600

Quartz (SiO2) covalent network 1610 2230

Diamond (C) covalent network 3550 4827

Types of Crystals

Ionic Crystals – Ion-Ion interactions are the strongest Lattice points occupied by cations and anions

• Held together by electrostatic attraction• Hard, brittle, high melting point• Poor conductor of heat and electricity

CsCl ZnS CaF2

Types of Crystals

Molecular Crystals• Lattice points occupied by molecules• Held together by intermolecular forces (dipole-dipole, and/or London dispersion forces• Soft, low melting point• Poor conductor of heat and electricity

Types of Crystals

Atomic solids/Network – Stronger than IM forces but generally weaker than ion-ion

• Lattice points occupied by atoms• Held together by covalent bonds• Hard, high melting point• Poor conductor of heat and electricity

diamond graphite

carbonatoms

Types of Crystals

Metallic Crystals – Typically weaker than covalent, but can be in the low end of covalent

• Lattice points occupied by metal atoms• Held together by metallic bonds• Soft to hard, low to high melting point• Good conductors of heat and electricity

11.6

Cross Section of a Metallic Crystal

nucleus &inner shell e-

mobile “sea”of e-

Types of Crystals

11.6

10.410.4 Structure and Bonding of MetalsStructure and Bonding of Metals Physical properties of metals Ionization energy E is small (outer electrons

move relatively free); this results in• High electrical conductivity• High thermal conductivity• They are

– Ductile: can be drawn oust into wires– Malleable: can be hammered into thin sheets

Electrons act like a glue holding atomic nuclei Crystals of nonmetals break into small pieces if it

is hammered (brittle) They have luster (reflect light) They form alloys

Metallic Crystals

Can be viewed as containing atoms (spheres) packed together in the closest arrangement possible

The spheres are packed in layers

Closest packing- when each sphere has 12 neighbors

• 6 on the same plane

• 3 in the plane above

• 3 in the plane below

Packing in Crystals

“Open” packing has larger voids in between particles compared to close-packed crystals

Closest packing in MetalsClosest packing in Metals

Closest packed structures

It has (aba) arrangements that occur when the spheres of the third layer occupy positions so that each sphere in the third layer lies directly over a sphere in the first layer

Hexagonal closest-packed (hcp) structure

Closest packed structures

It has (abc) arrangement that occurs when the spheres of the third layer occupy positions that NO sphere lies over one in the first layer

Cubic closest-packed (ccp) structure

An atom in every fourth layerlies over an atom in the First layer

Net number of spheres (atoms) in a unit cell, length of the edge of the cell, density of the closest packed solid

Face centered cubic cell Atoms occupy corners and centers of the faces Atoms at the corners do not touch each other Atoms contact is made at the face diagonal 74% of the space is occupied Ca, Sr, transition metals An atom at the center of the face of cube is

shared by another cube that touches that face. Only atom is assigned to a given cell An atom at the center of the cube is a part of 8-different cubes touching that point. Only cornenr atom belongs to the cell

2

1

8

1

Density of closest packed solid

# of spheres (atoms) per unit cell =

Density of closes packed solid

4)2

16(

8

18 XX

itcellvolumeofun

atomsmassofDensity

unitcellfatomsNetnumbero

deunitcellVolumeofth

rd

dr

)4(

4/

8

24

3

Body centered cubic cell Atoms contact along a body diagonal Atoms occupy the corners and one

at the center In a unit cell, 8 atoms occupy the

corners plus one in the center 68% of the space is occupied Available in Group I elements + Ba

Number of atoms assigned to each type of cell Simple cube

Body centered cube

Face centered cube

eatompercubsXcorneratom 18

18

atomsatomcenteratomsXcorner 2 18

1 8

atomscorner 42

1atomsX face6

8

1atomsX 8

1 atom/unit cell

(8 x 1/8 = 1)

2 atoms/unit cell

(8 x 1/8 + 1 = 2)

4 atoms/unit cell

(8 x 1/8 + 6 x 1/2 = 4)

Relationship between the atomic the radius and the edge length in different unit cells

When silver crystallizes, it forms face-centered cubic cells. The unit cell edge length is 408.7 pm. Calculate the density of silver.

d = mV

V = a3 = (408.7 pm)3 = __________________

___ atoms/unit cell in a face-centered cubic cell

m = 4 Ag atoms107.9 gmole Ag

x1 mole Ag

6.022 x 1023 atomsx = ___________

d = mV

7.17 x 10-22 g6.83 x 10-23 cm3

= = ___________________

12.4Compare Ex 12.3, p.384

Bonding models for Metals

Shape of pure metals con be changed but most metals have high melting points

Thus, bonding in most metals is strong and non-directional (although difficult to separate metal atoms, it is easy to move them provided they stay in contact of each other

The highest energy level for most metal atoms does not contain many electronsThese vacant overlapping orbitals allow outer electrons to move freely around the entire metalMetallic crystal is an array of positive ions (cations) in a sea of roaming valence electrons

Electron Sea Model

Metallic Bonding: “sea of e-’s”

Bonding models for Metals These roaming electrons

form a sea of electrons

around the metal atoms Malleability and ductility

• bonding is the same in

every direction• one layer of atoms can slide past

another without friction Conductivity of heat and electricity

• from the freedom of electrons (mobile electrons) to move around the atoms

Metallic bonding: Molecular orbital model for metals (Band model)

Electrons are assumed to travel around the metal crystal in molecular orbitals formed from the valence atomic orbitals of metal atoms

When many metal atoms interact in a crystal a large number of resulting molecular orbitals become more closely spaced and form a continuum of levels called bands

Metallic bonding: Molecular orbital model for metals (Band model)

1s

2s2p

3s

3pFilled Molecular Orbitals

Empty Molecular Orbitals

Magnesium Atoms

Filled Molecular OrbitalsEmpty Molecular Orbitals

The 1s, 2s, and 2p electrons are close to nucleus, so they are not able to move around (localized).

1s

2s2p

3s

3p

Magnesium Atoms

Filled Molecular OrbitalsEmpty Molecular Orbitals

1s

2s2p

3s

3p

Magnesium Atoms

The 3s and 3p orbitals overlap and form molecular orbitals.

Filled Molecular OrbitalsEmpty Molecular Orbitals

1s

2s2p

3s

3p

Magnesium Atoms

Electrons in these energy level can travel freely throughout the crystal.

Filled Molecular OrbitalsEmpty Molecular Orbitals

1s

2s2p

3s

3p

Magnesium Atoms

This makes metals conductors

Malleable because the bonds are flexible.

Metal Alloys An alloy is a mixture of elements and has metallic

properties substitutional alloy

• host metal atoms are replaced by other metal atoms

• happens when they have similar sizes interstitial alloy

• metal atoms occupy spaces created between host metal atoms

• happens when metal atoms have large difference in size

Examples

Brass

• substitutional

• 1/3 of Cu atoms replaced by Zn

Steel

• interstitial

• Fe with C atoms in between

• makes harder and less malleable

Metal AlloysMetal Alloys Substitutional AlloySubstitutional Alloy: :

some metal atoms some metal atoms replaced by others of replaced by others of similar size. similar size.

• brass = Cu/Zn brass = Cu/Zn •

Metal AlloysMetal Alloys(continued)(continued)

Interstitial AlloyInterstitial Alloy: : Interstices (holes) in Interstices (holes) in closest packed metal closest packed metal structure are occupied structure are occupied by small atoms. by small atoms.

• steel = iron + carbon steel = iron + carbon

10.6 Molecular solids. Molecules occupy the corners of the

lattices. Common examples: ice, dry CO2, S8, P4, I2

Different molecules have different forces between them (H-bonds, or dipole-dipole or London forces, or a combination of all these forces)

These forces depend on the size of the molecule.

They also depend on the strength and nature of dipole moments.

Molecular solids with nonpolar molecules (without dipoles): H2, CCl4

Most are gases at 25ºC. The only forces are London Dispersion

Forces. These depend on size of atom. Large molecules (such as I2 ) can be

solids even without dipoles.

Molecular solids with polar molecules (with dipoles): HCl, NH3

Dipole-dipole forces are generally stronger than L.D.F.

Hydrogen bonding is stronger than Dipole-dipole forces.

No matter how strong the intermolecular force, it is always much, much weaker than the forces in bonds.

Stronger forces lead to higher melting and freezing points.

Water is special Each molecule has two polar

O-H bonds. Each molecule has two lone

pair on its oxygen. Each oxygen can interact with

4 hydrogen atoms.

HO

H

Water is special

HO

H

HO

H

HO

H

This gives water an especially high melting and boiling point.

Examples of molecular solids

10.7 Ionic Solids They comprise the extremes in dipole dipole forces-

(ionic forces) Atoms are actually held together by electrostatic

attractions of opposite charges. They possess huge melting and boiling points. Atoms are locked in lattice so they are hard and

brittle. Every electron is accounted for so they are poor

conductors-good insulators.

In most of binary ionic compounds, larger ions are arranged in closest packing arrangement, hexagonal (hcp) or cubic (ccp) closest packing smaller ions fit in the holes created by the larger ions

Closest Closest Packing Packing

HolesHoles

The hole is formedby 3 spheres in the Same layer

The hole formed when a sphere occupies a dimple formed by three spheres in an adjacent layer

The holes formedbetween two sets of three spheres in adjoining layers of closest packed structure

Closest packing holesTetrahedral holes: are located above a sphere in the bottom layer

Octahedral holes: are located above a void in the bottom layer

Examples Trigonal holes are so small that they are never

occupied in binary ionic compounds The type of the hole whether tetrahedral or

octahedral depends mainly on• Relative sizes of cations and anions

In ZnS S2-, ions are arranged in ccp with the smaller Zn2+ ions in the tetrahedral holes

In NaCl, ions are arranged in ccp with Na+ ions in the octahedral holes.

Two Examples

Ionic Crystal Structures

Smaller cations can fill the voids between the larger anions

Tetrahedral hole filling occurs when the radii ratio is:

0.225 < rc/ra < 0.414Octahedral hole filling occurs when the radii ratio is:

0.414 < rc/ra < 0.732

The arrangement is cubic if rc/ra > 0.732

10 .7 Vapor Pressure and changes of state

vapor- gas phase above a substance gas phase above a substance that exists as solid or liquid at 25°C that exists as solid or liquid at 25°C and 1 atm.and 1 atm.

Vaporization or Evaporation - change from liquid to gas at or below change from liquid to gas at or below the boiling point . (Endothermic the boiling point . (Endothermic process)process)

Condensation is the change of a gas to a liquid (Exothermic process)

Heat or enthalpy of vaporization, ∆HHeat or enthalpy of vaporization, ∆Hvap vap ::

Energy required to vaporize 1 mole of a liquid at 1 atm

water has a large ∆Hvap (40.7 kJ/mol), (because of hydrogen bonding)

Molar Heats of Vaporization for Selected Liquids

Vapor pressure Initially, liquid in a closed container decreases as

molecules enter gaseous phase When equilibrium is reached, no more net change

occurs Rate of condensation and rate of vaporization

become equal Molecules still are changing phase but no

net change (Dynamic equilibrium)

• Gas liquid

Vapor pressure is independent of volumeindependent of volume of container as long as some liquid is present (liquid-vapor equilibrium)

Evaporation and condensation

H2O (l) H2O (g)

Rate ofcondensation

Rate ofevaporation=

Dynamic Equilibrium

Equilibrium vapor pressure or vapor pressure

It is the pressure exerted by the vapor when it is in dynamic equilibrium with a liquid at a constant temperature.

Vapor Pressure’s measurement

Liquid can be injected under inverted tube

part of the liquid evaporates to the top of tube

Pvap can be determined

by height of Hg

Patm = Pvap + PHg

The pressure of the vapor phase at equilibrium: Pvap

can be measured when using a simple barometer

Dish of Hg

Vacuum

Patm=

760 torr

A barometer will hold a column of

mercury 760 mm high at one atm

Dish of Hg

Vacuum

Patm= 760 torr

A barometer will hold a column ofmercury 760 mm high at one atm.

If we inject a volatile liquid in thebarometer it will rise to the top ofthe mercury.

Dish of Hg Patm= 760 torr

A barometer will hold a column of

mercury 760 mm high at one atm.

If we inject a volatile liquid in the

barometer it will rise to the top of

the mercury.

There it will vaporize and push the

column of mercury down.

Water

Dish of Hg

736 mm Hg

Water Vapor

The mercury is pushed down by the vapor pressure.

Patm = PHg + Pvap

Patm - PHg = Pvap

760 - 736 = 24 torr

Vapor pressure and nature of liquidsnature of liquids

Vapor pressure depends upon the nature nature of the liquidof the liquid

Liquids with high vapor P (volatile liquids)• liquids with a high vapor pressure• evaporate quickly• weak intermolecular forces

Liquids with low vapor P• Strong IMFs, London dispersion forces (large molar masses) or dipole-dipole

forces

Vapor pressure and temperature Vapor pressure increases with T More molecules have enough KE to

overcome IMFs

VAPOR PRESSURE CURVES

A liquid boils when its vapor pressure =‘s the external pressure.

Temperature Effect

Kinetic energy

# of

mol

ecu

les T1

Energy needed to overcome intermolecular forces in iquid

Kinetic energy

# of

mol

ecu

les T1T1

T2

At higher temperature more molecules have enough energy - higher vapor pressure.

Energy needed to overcome intermolecular forces in liquid

Molar heat of vaporization (Hvap) is the energy required to vaporize 1 mole of a liquid.

ln P = -Hvap

RT+ C

Clausius-Clapeyron Equation P = (equilibrium) vapor pressure

T = temperature (K)

R = gas constant (8.314 J/K•mol)

Vapor pressure and Temperature

Mathematical relationship

ln is the natural logarithm• ln = Log base e• e = Euler’s number an irrational number like

Hvap is the heat of vaporization in J/mol

12

vap

2T vap,

1Tvap,

T

1-

T

1

R

H =

P

Pln

R = 8.3145 J/K mol.

Mathematical relationship

12

vap

Tvap,

1Tvap,

T

1-

T

1

R

H =

P

Pln

2

Vapor Pressure for solids

Solids also have vapor pressure

Sublimination• solid gas directly

• Example: dry ice: CO2

heat of fusion (∆Hfus)

• enthalpy of fusion• enthalpy change at

melting point

Heating Curve

as energy is added, it is used to increase the T

when it reaches melting point, the energy added is used to change molecules from (s) to (l)

plot of T vs. time where plot of T vs. time where energy is added at constant energy is added at constant raterate

Changes of state

What happens when a solid is heated? The graph of temperature versus heat

applied is called a heating curve. The temperature a solid turns to a liquid is

the melting point. The energy required to accomplish this

change is called the Heat (or Enthalpy) of Fusion Hfus

-40

-20

0

20

40

60

80

100

120

140

0 40 120 220 760 800

Heating Curve for Water

IceWater and Ice

Water

Water and Steam Steam

mp

bp

Tem

p

Time (Heat added)

-40

-20

0

20

40

60

80

100

120

140

0 40 120 220 760 800

Heating Curve for Water

Heat of fusion

Heat of vaporization

Slope is Heat Capacity

Time (Heat added)

Tem

p

Hvap=2260 J/g

Hfus=334 J/g

Heating curve for 1 gram of water

Heating curve for 1 gram of water

Hfus=334 J/g

Specific Heat of ice = 2.09 J/g•K

Specific Heat of water = 4.184 J/g•K

Hvap=2260 J/g

Specific Ht. Steam = 1.84 J/g•K

Calculate the enthalpy change upon converting 1 mole of water from ice at -12oC to steam at 115oC.

solid-12oC

solid0oC

liquid0oC

liquid100oC

gas100oC

gas115oC

H1 + H2 + H3 + H4 + H5 = Htotal

Sp. Ht. + Hfusion + Sp. Ht. + HVaporization + Sp. Ht. = Htotal

Specific Heat of ice = 2.09 J/g•K

Hfus=334 J/g

Specific Heat of water = 4.184 J/g•K

Specific Ht. Steam = 1.84 J/g•K

Hvap=2260 J/g

Calculate the enthalpy change upon converting 1 mole of water from ice at -12oC to steam at 115oC.

solid-12oC

solid0oC

liquid0oC

liquid100oC

gas100oc

gas115oc

H1 + H2 + H3 + H4 + H5 = Htotal

Sp. Ht. + Hfusion + Sp. Ht. + HVaporization + Sp. Ht. = Htotal

Specific Heat of ice = 2.09 J/g•K

Hfus=334 J/g

Specific Heat of water = 4.184 J/g•K

Specific Ht. Steam = 1.84 J/g•K

Normal melting Point

Melting point is determined by the vapor pressure of the solid and the liquid.

Melting point is the temp at which

the vapor pressure of the solid = vapor pressure of the

liquid

where the total pressure is 1 atm.

Solid Water

Liquid Water

Water Vapor Vapor

Apparatus that allows solid and liquid water to interact only through the vapor state

Solid Water

Liquid Water

Water Vapor Vapor

A temp at which the vapor pressure of the solid is higher than that of the liquid the solid will release

molecules to achieve equilibrium.

Solid Water

Liquid Water

Water Vapor Vapor

While the molecules of water condense to a liquid to achieve equilibrium.

This can only happen if the temperature is above the melting point since solid is turning to liquid.

Solid Water

Liquid Water

Water Vapor Vapor

A temperature at which the vapor pressure of the solid is less than that of the liquid, the liquid will release

molecules to achieve equilibrium.

Solid Water

Liquid Water

Water Vapor Vapor

Solid Water

Liquid Water

Water Vapor Vapor

While the molecules of water condense to a solid.

The temperature must be below the melting point since the liquid is turning to a solid.

Solid Water

Liquid Water

Water Vapor Vapor

Temperature at which the vapor pressure of the solid and liquid are equal, the solid and liquid are vaporizing and condensing at the same rate. This is the Melting (freezing) point (Temp at which solid and vapor can coexist)

Solid Water

Liquid Water

Water Vapor Vapor

Normal Boiling Point Temp when vapor

pressure inside the bubbles equals 1 atm

If Pvap < 1 atm, no bubbles can form, there is too much pressure on surface

Normal Boiling Point Boiling occurs when the vapor pressure of

liquid becomes equal to the external pressure.

Normal boiling point is the temperature at which the vapor pressure of a liquid is exactly 1 atm pressure.

Super heating - Heating above the boiling point.

Supercooling - Cooling below the freezing point.

Exceptions

supercooling• Material can stay liquid

below melting point because doesn’t achieve level of organization needed to make solid

superheating• when heated too quickly,

liquid can be raised above boiling point

• causes “bumping”

• Changes of state do not always occur exactly at bp or bp

10.9 Phase Diagrams

A plot Representing phases of a substance in a closed system (no material escapes into the surroundings and no air is present) as a function of temperature and pressure.

Phase changesPhase changes

Gas and liquid areindistinguishable.

Critical temperatureand critical pressure

(all 3 phases exists here)

Phase Diagrams

fusion curve

triple point

critical point

vapor pressure curve

sublimation curve

Critical PointCritical Point

where if the T is increased, vapor where if the T is increased, vapor can’t be can’t be liquefied no matter what P is liquefied no matter what P is appliedapplied

at the end of liquid/gas lineat the end of liquid/gas line after this point, only after this point, only one fluid phaseone fluid phase

exists that is neither gas nor liquidexists that is neither gas nor liquid called called supercritical fluidsupercritical fluid

Critical temperatureCritical temperature

Temperature above which the vapor can Temperature above which the vapor can

not be liquefied. not be liquefied. Critical pressure Critical pressure

pressure required to liquefy gas pressure required to liquefy gas ATAT the the

critical temperature. critical temperature. Critical point Critical point

critical temperature and pressure (for critical temperature and pressure (for

water, water, TTcc = 374°C and 218 atm). = 374°C and 218 atm).

Phase diagram Phase diagram for Waterfor Water

Normal mp

No

rmal b

p

Critical tem

pWaterExpands uponfreezing

-ve slope of S/L boundaryline means that mp of icedecreases as the externalP increases

Phase Diagram for H2O

Most Most substances substances have a positive have a positive slope of slope of solid/liquid line solid/liquid line

because because solid is usually solid is usually more dense more dense than liquidthan liquidwater has a water has a negative slopenegative slope

Temperature

SolidLiquid

Gas

1 Atm

AA

BB

CCD

D D

Pre

ssur

e

D

SolidLiquid

Gas

Triple Point

Critical Point

Temperature

Pre

ssur

e

SolidLiquid

Gas

This is the phase diagram for water. The density of liquid water is higer than solid

water.

Temperature

Pre

ssur

e

Solid Liquid

Gas

1 Atm

This is the phase diagram for CO2

The solid is more dense than the liquid The solid sublimes at 1 atm.

Temperature

Pre

ssur

e