Intermolecular Attractions & the Properties of Liquids & Solids CHAPTER 12

transcript

Intermolecular Attractions & the Properties of Liquids & Solids

CHAPTER 12 Chemistry: The Molecular Nature of Matter, 6th edition

By Jesperson, Brady, & Hyslop

CHAPTER 12 Intermolecular Attractions & the Properties of Liquids & Solids

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Understand, describe, and rank in order of strength the types of

intermolecular forces.

Difference between bonds and intermolecular forces

Changes of state: heat of vaporization, fusion, & sublimation

Clausius-Clapyron equation

Heating and cooling curves: ΔH, phase transition temperatures

Phase diagrams

Solids: Unit cell, stoichiometry, packing patterns, XRD, common

types and their properties

Lecture Road Map:

① Properties of gas, liquids, solids

② Intermolecular forces

③ Changes of state

④ Dynamic Equilibrium

⑤ Structure & Characterization of a solid

Properties of gases, liquids, &

solids

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E 5

Intermolecular ForcesImportant differences between gases, solids, and liquids:oGases

oExpand to fill their container oLiquids

oRetain volume, but not shapeoSolids

o Retain volume and shape

Intermolecular Forceso Physical state of molecule depends on

o Average kinetic energy of particlesoRecall KE Tave

o Intermolecular Forces oEnergy of Inter-particle attraction

o Physical properties of gases, liquids and solids determined by oHow tightly molecules are packed togethero Strength of attractions between

molecules

o Converting gas liquid or solidoMolecules must get closer together

oCool or compress

o Converting liquid or solid gasoRequires molecules to move farther apart

oHeat or reduce pressure

o As T decreases, kinetic energy of molecules decreaseso At certain T, molecules don’t have

enough energy to break away from one another’s attraction

Intermolecular Attractions

Inter vs. Intra-Molecular Forceso Intramolecular forces

o Covalent bonds within molecule o Strong o Hbond (HCl) = 431 kJ/mol

o Intermolecular forces o Attraction forces between moleculeso Weako Hvaporization (HCl) = 16 kJ/mol

Cl H Cl H

Covalent Bond (strong) Intermolecular attraction (weak)

Electronegativity Review

Electronegativity: Measure of attractive force that one atom in a covalent bond has for electrons of the bond

Bond Dipoleso Two atoms with different electronegativity

values share electrons unequallyo Electron density is uneven

oHigher charge concentration around more electronegative atom

o Bond dipoles o Indicated with delta (δ) notationo Indicates partial charge has arisen

o Net Dipoleso Symmetrical molecules

o Even if they have polar bondso Are non-polar because bond dipoles cancel

o Asymmetrical molecules o Are polar because bond dipoles do not cancelo These molecules have permanent, net dipoles

o Molecular dipoles oCause molecules to interactoDecreased distance between molecules increases

amount of interaction

COVALENTBOND

IONICBOND

POLARCOVALENT

GroupProblem

Identify the overall dipole moment for CHCl3

GroupProblem

Identify the overall dipole moment for these molecules:

Solubility

LIKE DISSOLVES LIKEpolar molecules dissolve in polar solvents

nonpolar molecules dissolve in nonpolar solvents

Polar SolventsWater: H2OMethanol: CH3OHEthanol: CH3CH2OHAcetone: (CH3)2COAcetic Acid: CH3CO2HAmmonia: NH3

Acetonitrile: CH3CN

Nonpolar SolventsPentane: C5H12

Hexane: C6H14

Cyclohexane: C6H12

Benzene: C6H6

Toluene: CH3C6H5 Chloroform: CHCl3Diethylether: (CH3CH2)2O

Which molecule will dissolve in water?

Vitamin A

Vitamin B12

GroupProblem

IntermolecularForces

Intermolecular Forces The forces of attraction or repulsion between neighboring particles (atoms or molecules).

+ / - charges attract one another - / - or + / + forces repel each other

Intermolecular Forces o When substance melts or boils

o Intermolecular forces are broken, not covalent bonds

o Responsible for non-ideal behavior of gaseso Responsible for existence of condensed

states of mattero Responsible for bulk properties of matter

o Boiling points and melting points reflect strength of intermolecular forces

Types of Intermolecular Forces

① London dispersion forces② Dipole-dipole forces③ Hydrogen bonds④ Ion-dipole forces

o Ion-induced dipole forces

London-Dispersion Forceso When atoms near one another,

their valence electrons interacto Repulsion causes electron clouds

in each to distort and polarizeo Instantaneous dipoles result from

this distortiono Effect enhanced with increased

volume of electron cloud sizeo Effect diminished by increased

distance between particles and compact arrangement of atoms

London Dispersion ForcesAffects ALL molecules, both polar & nonpolar

Boiling Point (BP) is an indication of relative intermolecular force strength.

Ease with which dipole moments can be induced and thus London Forces depend on

① Distance between particles② Polarizability of electron cloud③ Points of attraction

oNumber atomsoMolecular shape (compact or elongated)

Polarizability = Ease with which the electron cloud can be distorted

Larger molecules often more polarizableo Larger number of less tightly held

electrons o Magnitude of resulting partial

charge is largero Larger electron cloud

GroupProblem

Which is more polarizable?F2 or I2?

Table 12.1 Boiling Points of Halogens and Noble Gases

Larger molecules have stronger London forces and thus higher boiling points.

Number of Atoms in Molecule

o London dispersion forces increase with the number atoms in molecule because more points of attraction

Formula BP at 1 atm, C Formula BP at 1 atm, CCH4 –161.5 C5H12 36.1

C2H6 –88.6 C6H14 68.7C3H8 –42.1 : :C4H10 –0.5 C22H46 327

Hexane, C6H14

BP 68.7 °C27

Which of the following molecules will have the highest boiling point?

Propane, C3H8

BP –42.1 °C

GroupProblem

Molecular Shapeo Increased surface area available for contact =

increased points of contact = increase in London Dispersion forces.oMore compact molecules:

Less surface area to interact with other molecules

oLess compact molecules:More surface area to interact with other molecules

• Small area for interaction

• Larger area for interaction

More compact – lower BP Less compact – higher BP

Which of the following molecules experience the strongest Dispersion forces?

GroupProblem

Dipole-Dipole Attractions

o Occurs only between polar molecules

o Proportional to distance between molecules

o Polar molecules tend to align their partial charges: + / -

o As dipole moment increases, intermolecular force increases

Dipole-Dipole AttractionsTumbling molecules

oMixture of attractive and repulsive dipole-dipole forces

o Attractions (- -) are maintained longer than repulsions(- -)

oGet net attraction o ~1–4% of covalent bond

In the liquid state, which species has the strongest intermolecular forces, CH4, Cl2, O2 or HF?

HFThe polar molecule

GroupProblem

Hydrogen Bondso Very strong dipole-dipole attraction: ~10% of a covalent

o Occurs between H and highly electronegative atom (O, N, or F): H—F, H—O, and H—N bonds very polaroElectrons are drawn away from H giving atoms high

partial chargesoH only has one electron, so +

H presents almost bare proton

o –X almost full –1 charge

oElement’s small size, means high charge density

Examples of Hydrogen BondingH O

H F H O

H F H N

Hydrogen Bonding in Water

Hydrogen Bonds are strong!o Responsible for the high boiling point of watero Responsible for expansion of water as it freezes o Hydrogen bonding (dotted lines) between

water molecules in ice form tetrahedral configuration

Hydrogen Bonding in Water

0.957 Å1.97 Å

List all intermolecular forces for CH3CH2OH.

Hydrogen-bonds, dipole-dipole attractions, London dispersion forces

GroupProblem

Ion-Dipole Attractionso Attractions between ion and charged end of

polar moleculeso Ions have full charges, increasing the attraction

(a) Negative ends of water dipoles surround cation (b) Positive ends of water dipoles surround anion

AlCl3·6H2O

o Positive charge of Al3+ ion attracts partial negative charges – on O of water molecules

o Ion-dipole attractions hold water molecules to metal ion in hydrateo Water molecules are found

at vertices of octahedron around aluminum ion

Attractions between ion and polar molecules

Ion-Induced Dipole Attractionso Attractions between ion and dipole it induces on

neighboring moleculesoDepends on

oIon charge and oPolarizability of its neighbor

o Attractions can be quite strong as ion charge is constant, unlike instantaneous dipoles of London-dispersion forces

GroupProblem

How many water molecules would be attracted to this molecule by Ion-Dipole interactions?

GroupProblem

List the intermolecular forces and rank in order of strength for the liquids of each molecule.

o Ion-DipoleoHydrogen BondingoDipole-DipoleoLondon Forces

• Larger, longer, and therefore heavier molecules often have stronger intermolecular forces

• Smaller, more compact, lighter molecules have generally weaker intermolecular forces

Weakest

Strongest

GroupProblem

Intermolecular Forces and Temperature

Decrease with increasing temperatureo Increasing kinetic energy overcomes attractive

forceso If allowed to expand, increasing temperature

increases distance between gas particles and decreases attractive forces

GroupProblem

GROUP PROBLEM SET 12.1

More properties of gases,

liquids, & solids

Compressibility Surface Tension

Diffusion

Retention of Volume & shape

Wetting Viscosity

MeltingPoint

BoilingPoint

Melting & Boiling PointOften can predict physical properties by comparing strengths of intermolecular attractions:

Boiling Point increases when intermolecular forces increase

Melting Point increases when intermolecular forces increase

Compressibility

Measure of the ability of a substance to be forced into smaller volume

oDetermined by strength of intermolecular forcesoGases highly compressible

oMolecules far apartoWeak intermolecular forces

o Solids and liquids nearly incompressibleoMolecules very close togetheroStronger intermolecular forces

Retention of volume and shape

o Solids retain both volume and shapeoStrongest intermolecular attractionsoMolecules closest

o Liquids retain volume, but not shapeoAttractions intermediate

oGases, expand to fill their containersoWeakest intermolecular attractionsoMolecules farthest apart

DiffusionIn Gases

o Molecules travel long distances between collisions

o Diffusion rapidIn Liquids

o Molecules closero Encounter more collisionso Takes a long time to move

from place to placeIn Solids

o Diffusion close to zero at room temperature

o Will increase at high temperature

Surface Tension

Inside body of liquido Intermolecular forces are

the same in all directionsMolecules at surface

o Potential energy increases when removing neighbors

o Molecules move together to reduce surface area and potential energy

sphere

Why does H2O bead up on a freshly waxed car instead of forming a layer?

Surface Tension

Liquids containing molecules with strong intermolecular forces have high surface tension

Allows us to fill glass above rimoGives surface rounded

appearanceoSurface resists expansion and

pushes back

o Surface tension increases as intermolecular forces increase

o Surface tension decreases as temperature increases

Wettingo Ability of liquid to spread

across surface to form thin film

o Greater similarity in attractive forces between liquid and surface, yields greater wetting effect

o Occurs only if intermolecular attractive force between surface and liquid about as strong as within liquid itself

Wetting: Surfactants (Detergents)o Detergents added to water to lower surface tension so water

can spread on greasy glasso Substances that have both polar and non-polar characteristicso Long chain hydrocarbons with polar tail

o Nonpolar end dissolves in nonpolar greaseo Polar end dissolves in polar H2Oo Thus increasing solubility of grease in water

Viscosity o Resistance to flowo Measure of fluid’s

resistance to flow or changing form

o Decreases as Temp increases

o Not just a property of liquids: o Gas: respond to instantly

to form changing forceo Amorphous solids, like

Viscosity

Acetone Polar molecule

oDipole-dipole ando London forces

Ethylene glycolPolar molecule

oHydrogen-bondingoDipole-dipole and o London forces

Which is more viscous?

GroupProblem

For each pair given, which is has more viscosity?

CH3CH2CH2CH2OH, CH3CH2CH2CHO

C6H14, C12H26

NH3(l ), PH3(l )

GroupProblem

Changes of State

Heating/CoolingCurves ΔH

Phase Diagrams

Phase Changes = changes of physical state with temperature ( α to KE)

SOLID LIQUID GASfusion

freezing

evaporation

condensation

deposition

sublimation

endothermic

exothermic

System absorbs energy from surrounds in the form of heato Requires the addition of heat

System releases energy into surrounds in the form of heat or lighto Requires heat to be decreased

Phase Changes of Water

ICE WATER VAPORmelting

freezing

evaporation

forming dew

deposition

sublimation

Phase ChangesE

Liquid

Meltingor Fusion

Vaporization Condensation

Freezing

SublimationDeposition

Exothermic, releases heat Endothermic, absorbs heat

Heating CurveIf heat added at constant rate

Horizontal lineso Phase changeso Melting pointo Boiling point

Diagonal lines o Heating of solid,

liquid or gas

Cooling CurveHeat removed at constant rate

Diagonal lines o Cooling of

solid, liquid or gas

Horizontal lineso Phase changeso Melting pointo Boiling point

Supercooling o Temperature of liquid dips below its freezing point

Boiling Point (bp)

Bp increases as strength of intermolecular forces increase

Normal Boiling Point • T at which vapor pressure of liquid = 1 atm

Rate of Evaporationo Depends on

o Temperatureo Surface areao Strength of

intermolecular attractions

o Molecules that escape from liquid have larger than minimum escape KE

o When they leave the average KE of remaining molecules is less and so T lower

Effect of Temperature on Evaporation Rate

For given liquid the rate of evaporation per unit surface area increases as T increases

Why?o At higher T, total fraction

of molecules with KE large enough to escape is larger

o Result: rate of evaporation is larger

Kinetic Energy Distributionin 2 different liquids

o Smaller intermolecular forces

o Lower KE required to escape liquid

o A evaporates faster

o Larger intermolecular forces

o Higher KE required to escape liquid

o B evaporates slower

GroupProblem

What is an example of gas A and gas B?

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

freezing

evaporation

condensation

deposition

sublimation

Hfus Hvap

HsubMolar 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

Energies of Phase Changes

Measuring Hvap

o Clausius-Clapeyron equation o Measure pressure at various temperatures, then

o Two point form of Clausius-Clapeyron equationo Measure pressure at two temperatures and solve

equation

HP vap

1221 11ln

PP vap

Vapor Pressure Diagram

RT = 25 C

o Variation of vapor pressure with T

o Ether o Volatile o High vapor pressure

near RTo Propylene glycol

o Non-volatileo Low vapor pressure

near RT

Temp (K) Vapor P 1/T lnP280 32.4 0.003571429 3.478158423300 92.5 0.003333333 4.527208645320 225 0.003125 5.416100402330 334 0.003030303 5.811140993340 483 0.002941176 6.180016654

HP vap

Slope = Hvap/R = -4288.1KHvap = 8.3145 Jmol/K x 4288.1K Hvap = 35.65 x 103 J/molHvap = 35.65 kJ/mol

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.

1221 11ln

PP vap

6109.04928.021 e

216109.0 PP

T1 = 273.15 + 18 = 291.15 KT2 = 273.15 + 32 = 305.15 K

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

GroupProblem

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

Phase Diagram

X axis – temperatureY axis – pressure

o As P increases(T constant), solid most likely more compact

o As T increases (P constant), gas most likely higher energy

o Each point = T and Po B = o E =o F =

0.01 °C, 4.58 torr100 °C, 760 torr–10 °C, 2.15 torr

Phase Diagram of Water

AB = vapor pressure curve for iceBD = vapor pressure curve for liquid waterBC = melting point lineB = triple point: T and P where all three phases are in equilibriumD = critical point

T and P above which liquid does not exist

Phase Diagram – CO2

o Now line between solid and liquid slants to right

o More typicalo Where is triple

point?o Where is critical

point?

Supercritical Fluid

o Substance with temperature above its critical temperature (TC) and density near its liquid density

o Have unique properties that make them excellent solvents

o Values of TC tend to increase with increased intermolecular attractions between particles

At 89 °C and 760 mmHg, what physical state is present?

A.SolidB.LiquidC.GasD.Supercritical fluidE.Not enough information

is given

GroupProblem

The Before & After of Phase Changes

freezing

evaporation

condensation

deposition

sublimation

endothermic

exothermic

System absorbs energy from surrounds in the form of heato Requires the addition of heat

System releases energy into surrounds in the form of heat or lighto Requires heat to be decreased

The molar heat of a phase change (H) describes the heat needed for a phase change to go to completion.

The specific heat of a phase change (q) describes the heat needed for an amount of a substance to completely undergo a phase change.

q = n x H

Enthalpy Of Phase ChangesEndothermic Phase Changes

1. Must add heat2. Energy entering system (+)

Sublimation: Hsub > 0Vaporization: Hvap > 0Melting or Fusion: Hfus > 0

Exothermic Phase Changes3. Must give off heat4. Energy leaving system (–)

Deposition: H < 0 = –Hsub Condensation: H < 0 = –Hvap Freezing: H < 0 = –Hfus

Dynamic Equilibria

Equilibria Exist During a Phase Change

• 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 another

condensedphase

separatedphase

Le Chatelier’s Principle

o Equilibria are often disturbed or upseto When dynamic equilibrium of system is

upset by a disturbanceoSystem responds in direction that tends to

counteract disturbance and, if possible, restore equilibrium

o Position of equilibrium oUsed to refer to relative amounts of substance on

each side of double (equilibrium) arrows

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

Equilibrium & Phase Diagrams

T1 = 78°CP1 = 330 atm

To increaseT2 = 100°CThe system must respond by increasing P2 = 760 to restore equilibrium:o T is highero Volume of liquid

is lower o P of vapor higher

Le Chatelier’s Principle

Liquid + Heat Vapor

Initial V1 T1 P1

ChangeVolume lost

in evaporation

Increase Temperature

Pressure increases

Final V2 T2 P2

Evaporation Rate

Before System Reaches Equilibrium

o Liquid is placed in empty, closed, containero Begins to evaporate

o Once in gas phaseoMolecules can condense

by o Striking surface of liquid

and giving up some kinetic energy

System At Equilibrium

o Rate of evaporation = rate of condensation

o Occurs in closed systems where molecules cannot escape

Enthalpy Of Phase ChangesEndothermic:

Liquid+ heat of vaporization ↔ GasLiquid + Hvap ↔ Gas

Solid + heat of fusion ↔ LiquidSolid + Hfus ↔ Liquid

Solid + heat of sublimation ↔ GasSolid + Hsub ↔ Liquid

Exothermic:Liquid ↔ Gas - Hvap Solid ↔ Liquid - Hfus Solid ↔ Liquid - Hsub

liquid + heat of vaporization ↔ gasEquilibrium Vapor Pressure

o Pressure of gas when liquid or solid is at equilibrium with its gas phase

o Usually referred to as simply vapor pressureo Increasing temperature increases vapor pressure

because vaporization is endothermic

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

Effect of Volume on Vapor Pressure

Initial(equilibrium

exists)

Volume of Container

Volume of liquid P1

ChangeVolume

manually increased

Rate condensation

decreases

Pressure decreases

System changes to establish new

equilibrium

Volumeof container

greater

Volume of liquid

decreases

(P2 = P1)

Similar Equilibria Reached in Melting

Melting Point (mp)o Solid begins to change

into liquid as heat added

Dynamic equilibria exists between solid and liquid states

oMelting (red arrows) and freezing (black arrows) occur at same rate

o As long as no heat added or removed from equilibrium mixture

Equilibria Reached in Sublimation

At equilibrium molecules sublime from solid at same rate as molecules condense from vapor

Do Solids Have Vapor Pressures?

o At given temperature some solid particles have enough KE to escape into vapor phase

o When vapor particles collide with surface they can be captured

o Yes equilibrium vapor pressure of solid exists

Solid Structures

Types of Solids• Crystalline Solids

– Solids with highly regular arrangements of components

• Amorphous Solids– Solids with considerable disorder in their

structures

Crystalline Solids

• Unit Cell– Smallest

segment that repeats regularly

– Smallest repeating unit of lattice

– Two-dimensional unit cells

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

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

Most efficient arrangement of spheres in two dimensions

Each sphere has 6 nearest neighbors Second layer with atoms in holes on the first

layer 113

Close Packing of Spheres1st layer 2nd layer

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

3-D Simple Cubic Lattice

Portion of lattice—open view

Unit Cell

Space filling model

Other Cubic Lattices

Face Centered Cubic

Body Centered Cubic

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

Common Ionic SolidsRock salt or NaCl– Face centered cubic lattice of Cl– ions (green)– Na+ ions (blue) in all octahedral holes

Other Common Ionic Solids

Cesium Chloride, CsCl

Zinc Sulfide, ZnS

Calcium Fluoride, CaF2

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

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 cellsBody 1 1Face 1/2 2Edge 1/4 4

Corner 1/8 8

Example: NaCl

Site # of Na+ # of Cl–

Body 1 0Face 0Edge 0

Corner 0Total 4 4

36 21 312 41

FaceEdge Corner

Center

1:1CsCl

Determine the number of each type of ion in the unit cell.

4:4ZnS

4:8CaF2

Some Factors Affecting Crystalline Structure

• Size of atoms or ions involved• Stoichiometry of salt• Materials involved

– Some substances do not form crystalline solids

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

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

X-ray Diffraction

Experimental Setup Diffraction Pattern

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

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

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

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.

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

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

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.

GroupProblem

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

Ex. Covalent (Network) Solid • Diamond (all C)

– Shown

• SiO2 silicon oxide– Alternating Si and O– Basis of glass and quartz

• Silicon carbide (SiC)

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

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

GroupProblem

Intermolecular Attractions & the Properties of Liquids & Solids CHAPTER 12

Documents