108
12-1 Intermolecular Forces: Liquids, Solids, and Phase Changes

Solids, Inter Molecular

Embed Size (px)

Citation preview

Page 1: Solids, Inter Molecular

12-1

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Intermolecular Forces:

Liquids, Solids, and Phase Changes

Page 2: Solids, Inter Molecular

12-2

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Intermolecular Forces:

Liquids, Solids, and Phase Changes

12.1 An Overview of Physical States and Phase Changes

12.2 Quantitative Aspects of Phase Changes

12.3 Types of Intermolecular Forces

12.4 Properties of the Liquid State

12.5 The Uniqueness of Water

12.6 The Solid State: Structure, Properties, and Bonding

12.7 Advanced Materials

Page 3: Solids, Inter Molecular

12-3

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

ATTRACTIVE FORCES

electrostatic in nature

Intramolecular forces bonding forces

These forces exist within each molecule.

They influence the chemical properties of the substance.

Intermolecular forces nonbonding forces

These forces exist between molecules.

They influence the physical properties of the substance.

Page 4: Solids, Inter Molecular

12-4

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Phase Changes

solid liquid gas

melting

freezing

vaporizing

condensing

sublimination

endothermic

exothermic

Page 5: Solids, Inter Molecular

12-5

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Table 12.1

A Macroscopic Comparison of Gases, Liquids, and Solids

State Shape and Volume Compressibility Ability to Flow

Gas Conforms to shape and volume

of container

high high

Liquid Conforms to shape of container;

volume limited by surface

very low moderate

Solid Maintains its own shape and

volume

almost none almost none

Page 6: Solids, Inter Molecular

12-6

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.1

Heats of vaporization and fusion for several common substances.

Page 7: Solids, Inter Molecular

12-7

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.2 Phase changes and their enthalpy changes.

Page 8: Solids, Inter Molecular

12-8

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.3

A cooling curve for the conversion of gaseous water to ice.

q = (amount)(molar heat capacity)(T) within a phase

q = (amount)(enthalpy of phase change) during a phase change

Page 9: Solids, Inter Molecular

12-9

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Within a phase, a change in heat is accompanied by a change in

temperature which is associated with a change in average Ek as

the most probable speed of the molecules changes.

Quantitative Aspects of Phase Changes

During a phase change, a change in heat occurs at a constant

temperature, which is associated with a change in Ep, as the

average distance between molecules changes.

q = (amount)(molar heat capacity)(T)

q = (amount)(enthalpy of phase change)

Page 10: Solids, Inter Molecular

12-10

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.4 Liquid-gas equilibrium.

Page 11: Solids, Inter Molecular

12-11

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.5The effect of temperature on the distribution of

molecular speed in a liquid.

Page 12: Solids, Inter Molecular

12-12

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.6 Figure 12.7

Vapor pressure as a function of

temperature and intermolecular forces.

A linear plot of vapor

pressure- temperature

relationship.

Page 13: Solids, Inter Molecular

12-13

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

The Clausius-Clapeyron Equation

ln P =

-Hvap

R

1

T

C

ln P2P1

= -Hvap

R

1

T2

1

T1

Page 14: Solids, Inter Molecular

12-14

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

SAMPLE PROBLEM 12.1 Using the Clausius-Clapeyron Equation

SOLUTION:

PROBLEM: The vapor pressure of ethanol is 115 torr at 34.90C. If Hvap of

ethanol is 40.5 kJ/mol, calculate the temperature (in 0C) when

the vapor pressure is 760 torr.

PLAN: We are given 4 of the 5 variables in the Clausius-Clapeyron

equation. Substitute and solve for T2.

ln P2P1

= -Hvap

R

1

T2

1

T1

34.90C = 308.0K

ln760 torr

115 torr=

-40.5 x103 J/mol

8.314 J/mol*K

1

T2

1

308K-

T2 = 350K = 770C

Page 15: Solids, Inter Molecular

12-15

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.8 Iodine subliming.

iodine solid

iodine vapor

iodine solid

test tube with ice

Page 16: Solids, Inter Molecular

12-16

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.9 Phase diagrams for CO2 and H2O.

CO2 H2O

Page 17: Solids, Inter Molecular

12-17

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Types of

Intermolecular forces

Page 18: Solids, Inter Molecular

12-18

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

The nature of the phases and their changes are due primarily to forces among molecules.

Bonding and nonbonding (intermolecular)

The two type of forces differ and Coulomb’s law explains why:

Bonding – strong – larger charges closer together

Intermolecular – weak – smaller charges farther apart.

Page 19: Solids, Inter Molecular

12-19

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

bond length

covalent radius

van der Waal’s distance

van der Waal’s radius

Figure 12.10 Covalent and van der Waals radii.

How far apart are the charges between molecules

that give rise to intermolecular forces?

Page 20: Solids, Inter Molecular

12-20

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.11

Periodic trends in covalent and van der Waals radii (in pm).

The van der Waals radius

of an atom is always larger

than its covalent radius,

But van der Waals radii

decrease across a period

and increase down a group,

just as covalent radii do.

Page 21: Solids, Inter Molecular

12-21

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Page 22: Solids, Inter Molecular

12-22

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Page 23: Solids, Inter Molecular

12-23

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Ion – dipole forcesWhen an ion and a nearby polar molecule (dipole)

attract each other, an ion –dipole force results.

Example: when an ionic compound dissolves in water.

Ep α - | z | µ

r2

The – sign means that the potential energy of the molecule is lowered by its interaction with the polar

solvent.

1/r2 means that the interaction depends more strongly in distance than between two ions.

Page 24: Solids, Inter Molecular

12-24

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Dipole – dipole forces

When polar molecules lie near each other, as in

liquids and solids, their partial charges act as

tiny electric fields that orient them and give

rise to dipole – dipole forces

Page 25: Solids, Inter Molecular

12-25

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.12 Polar molecules and dipole-dipole forces.

solid

liquid

Page 26: Solids, Inter Molecular

12-26

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

THE HYDROGEN BOND

a dipole-dipole intermolecular force

The elements which are so electronegative are N, O, and F.

A hydrogen bond may occur when an H atom in a molecule,

bound to small highly electronegative atom with lone pairs of

electrons, is attracted to the lone pairs in another molecule.

..

F..

..

..H O..

N.. FH

..

..

..

O.. ..

..

NH

hydrogen bond

donor

hydrogen bond

acceptor

hydrogen bond

acceptor

hydrogen bond

donor

hydrogen bond

donor

hydrogen bond

acceptor

Page 27: Solids, Inter Molecular

12-27

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.13 Dipole moment and boiling point.

For molecular compounds of approximately the same size and molar mass, the

greater the dipole-dipole forces between the molecules are, and so the more

energy it takes to separate them.

Page 28: Solids, Inter Molecular

12-28

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

SAMPLE PROBLEM 12.2 Drawing Hydrogen Bonds Between Molecules

of a Substance

SOLUTION:

PROBLEM: Which of the following substances exhibits H bonding? For

those that do, draw two molecules of the substance with the H

bonds between them.

C2H6(a) CH3OH(b) CH3C NH2

O

(c)

PLAN: Find molecules in which H is bonded to N, O or F. Draw H

bonds in the format -B: H-A-.

(a) C2H6 has no H bonding sites.

(c)(b)C O H

H

H

H

COH

H

H

H

CH3C N

O

H

H

CH3CN

O

H

H

CH3C

N

O

H

H

CH3C

N

O

H

H

Page 29: Solids, Inter Molecular

12-29

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.14 Hydrogen bonding and boiling point.

Page 30: Solids, Inter Molecular

12-30

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Polarizability and Charged-Induced Dipole Forces

distortion of an electron cloud

•Polarizability increases down a group

size increases and the larger electron clouds are further

from the nucleus

•Polarizability decreases left to right across a period

increasing Zeff shrinks atomic size and holds the electrons

more tightly

•Cations are less polarizable than their parent atom

because they are smaller.

•Anions are more polarizable than their parent atom

because they are larger.

Page 31: Solids, Inter Molecular

12-31

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.15 Dispersion forces among nonpolar molecules.

separated

Cl2molecules

instantaneous

dipoles

Page 32: Solids, Inter Molecular

12-32

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

London or dispersion forces

• Dispersion forces are caused by momentary oscillation of electron charge in atoms and, therefore, are present between all particles (atoms, ions and molecules)

• Instantaneous dipole – induced dipole forces.

• Except in cases involving small polar molecules or those with strong hydrogen bonding, the dispersion force is the dominant force

• Example: HCl - 85% dispersion and 15% dipole-dipole.

Page 33: Solids, Inter Molecular

12-33

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.16

Molar mass and boiling point.

Higher molar mass, higher

polarizability

Intermolecular forces between

the molecules.

Page 34: Solids, Inter Molecular

12-34

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.17 Molecular shape and boiling point.

more points for

dispersion

forces to act

fewer points for

dispersion

forces to act

Page 35: Solids, Inter Molecular

12-35

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

SAMPLE PROBLEM 12.3 Predicting the Type and Relative Strength of

Intermolecular Forces

PROBLEM: For each pair of substances, identify the dominant

intermolecular forces in each substance, and select the

substance with the higher boiling point.

(a) MgCl2 or PCl3

(b) CH3NH2 or CH3F

(c) CH3OH or CH3CH2OH

(d) Hexane (CH3CH2CH2CH2CH2CH3)

or 2,2-dimethylbutaneCH3CCH2CH3

CH3

CH3PLAN: Use the formula, structure and Table 2.2 (button).

•Bonding forces are stronger than nonbonding(intermolecular) forces.

•Hydrogen bonding is a strong type of dipole-dipole force.

•Dispersion forces are decisive when the difference is molar mass or

molecular shape.

Page 36: Solids, Inter Molecular

12-36

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

SOLUTION:

SAMPLE PROBLEM 12.3 Predicting the Type and Relative Strength of

Intermolecular Forcescontinued

(a) Mg2+ and Cl- are held together by ionic bonds while PCl3 is covalently

bonded and the molecules are held together by dipole-dipole interactions. Ionic

bonds are stronger than dipole interactions and so MgCl2 has the higher boiling

point.

(b) CH3NH2 and CH3F are both covalent compounds and have bonds which are

polar. The dipole in CH3NH2 can H bond while that in CH3F cannot. Therefore

CH3NH2 has the stronger interactions and the higher boiling point.

(c) Both CH3OH and CH3CH2OH can H bond but CH3CH2OH has more CH for

more dispersion force interaction. Therefore CH3CH2OH has the higher boiling

point.

(d) Hexane and 2,2-dimethylbutane are both nonpolar with only dispersion

forces to hold the molecules together. Hexane has the larger surface area,

thereby the greater dispersion forces and the higher boiling point.

Page 37: Solids, Inter Molecular

12-37

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.18

Summary diagram for analyzing the intermolecular forces in a sample.

INTERACTING PARTICLES

(atoms, molecules, ions)

ions only

IONIC BONDING

(Section 9.2)

ion + polar molecule

ION-DIPOLE FORCES

ions present ions not present

polar molecules only

DIPOLE-DIPOLE

FORCES

HYDROGEN

BONDING

polar + nonpolar

molecules

DIPOLE-

INDUCED DIPOLE

FORCES

nonpolar

molecules only

DISPERSION

FORCES only

DISPERSION FORCES ALSO PRESENT

H bonded toN, O, or F

Page 38: Solids, Inter Molecular

12-38

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

OTHER PROPERTIES OF

LIQUIDS

Page 39: Solids, Inter Molecular

12-39

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.19 The molecular basis of surface tension.

hydrogen bonding

occurs in three

dimensions

hydrogen bonding

occurs across the surface

and below the surfacethe net vector

for attractive

forces is downward

Page 40: Solids, Inter Molecular

12-40

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Surface tension

• Is the energy required to increase the surface area by a unit amount – the stronger the forces are between particles in a liquid, the greater the surface tension.

• Tendency to minimize surface area (spherical drops)

• The relatively high surface tension of water accounts for the ease with which it can be nebulized, or placed into aerosol form. Low surface tension liquids tend to evaporate quickly and are difficult to keep in an aerosol form. All liquids display surface tension to some degree.

Page 41: Solids, Inter Molecular

12-41

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Table 12.3 Surface Tension and Forces Between Particles

Substance Formula

Surface Tension

(J/m2) at 200C Major Force(s)

diethyl ether

ethanol

butanol

water

mercury

dipole-dipole; dispersion

H bonding

H bonding; dispersion

H bonding

metallic bonding

1.7x10-2

2.3x10-2

2.5x10-2

7.3x10-2

48x10-2

CH3CH2OCH2CH3

CH3CH2OH

CH3CH2CH2CH2OH

H2O

Hg

Page 42: Solids, Inter Molecular

12-42

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.20 Shape of water or mercury meniscus in glass.

adhesive forces

stronger

cohesive forces

H2O

capillarity

Hg

concaveconvex

Page 43: Solids, Inter Molecular

12-43

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Capillarity

• The rising of a liquid through a narrow space

against the pull of gravity is called capillary

action, or capillarity.

• It is the result from a competition between

intermolecular forces within the liquid

(cohesive forces) and those between the liquid

and the tube walls (adhesive forces)

Page 44: Solids, Inter Molecular

12-44

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Viscosity

• Its resistance to flow – intermolecular

attractions impede this movement.

• Gases and liquids flow, but liquid viscosities

are much higher because of intermolecular

forces.

• Viscosity decreases with heating

• Molecular shape – small, spherical molecules

make little contact and pour easily.

Page 45: Solids, Inter Molecular

12-45

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Table 12.4 Viscosity of Water at Several Temperatures

Temperature(0C)

Viscosity

(N*s/m2)*

20

40

60

80

1.00x10-3

0.65x10-3

0.47x10-3

0.35x10-3

*The units of viscosity are newton-seconds per square meter.

viscosity - resistance to flow

Page 46: Solids, Inter Molecular

12-46

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.21 The H-bonding ability of the water molecule.

hydrogen bond donor

hydrogen bond acceptor

Page 47: Solids, Inter Molecular

12-47

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

The Unique Nature of Water

•great solvent properties due to polarity and

hydrogen bonding ability

•exceptional high specific heat capacity

•high surface tension and capillarity

•density differences of liquid and solid states

Page 48: Solids, Inter Molecular

12-48

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.22 The hexagonal structure of ice.

Page 49: Solids, Inter Molecular

12-49

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.23 The expansion and contraction of water.

Page 50: Solids, Inter Molecular

12-50

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.24The macroscopic properties of water and their atomic

and molecular “roots”.

Page 51: Solids, Inter Molecular

12-51

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Solids:

- crystalline

- amorphous

Page 52: Solids, Inter Molecular

12-52

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.25 The striking beauty of crystalline solids.

celestite pyrite amethyst halite

Page 53: Solids, Inter Molecular

12-53

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Structures of solids

• Crystalline solids have a regularly repeating

pattern of atoms.

• We will consider only cubic unit cells, with

equal edges meeting at right angles (90°) when

we calculate in detail the packing efficiency.

• There are 7 crystal systems and 14 types of

unit cells that occur in nature.

Page 54: Solids, Inter Molecular

12-54

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Cubic system

• Majority of metallic elements

• Some covalent compounds

• Several ionic compounds

There are 3 types of cubic unit cells within the cubic system:

1. Simple cubic unit cell

2. Body-centered cubic unit cell

3. Face-centered cubic unit cell

Page 55: Solids, Inter Molecular

12-55

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

portion of a 3-D lattice

Figure 12.26 The crystal lattice and the unit cell.lattice point

unit

cell

portion of a 2-D lattice

unit

cell

Lattice - Consists of all points with identical surroundings

Unit cell – The smallest portion of the crystal that, if repeated in all

three directions, gives the crystal.

Page 56: Solids, Inter Molecular

12-56

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.27 (1 of 3) The three cubic unit cells.

Simple Cubic

coordination number = 6

Atoms/unit cell = 1/8 * 8 = 1

1/8 atom at

8 corners

Coordination number is the number of nearest neighbors surrounding it.

Page 57: Solids, Inter Molecular

12-57

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.27 (2 of 3) The three cubic unit cells.

Body-centered

Cubic

coordination number = 8

1/8 atom at

8 corners

1 atom at

center

Atoms/unit cell = (1/8*8) + 1 = 2

Page 58: Solids, Inter Molecular

12-58

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.27 (3 of 3) The three cubic unit cells.

Face-centered

Cubic

coordination number = 12 Atoms/unit cell = (1/8*8)+(1/2*6) = 4

1/8 atom at

8 corners

1/2 atom at

6 faces

Page 59: Solids, Inter Molecular

12-59

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.28 Packing of spheres.

simple cubic

(52% packing efficiency)

body-centered cubic

(68% packing efficiency)

Page 60: Solids, Inter Molecular

12-60

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

hexagonal

unit cell

Figure 12.28 (continued)

closest packing of first

and second layers

layer a

layer a – shifting

every other row a

layer b

layer c

hexagonal

closest

packingcubic closest

packing

abab… (74%)abcabc… (74%)

expanded

side views

face-centered

unit cell

covers

the white

space.

Hexagonal( Mg, Zn) and FCC (Ni, Cu) is the most efficient packing for identical spheres

Page 61: Solids, Inter Molecular

12-61

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Packing efficiency %

= (volume occupied by spheres) / (total volume) x 100

This calculation is carried out on the contents of the

unit cell. Therefore, our first step is to count the

number of atoms contained within the unit cell. To

do this you should keep in mind that atoms located

at the corners, edges and faces of the unit cell are

not fully contained in a single unit cell, so that they

only partially occupy the unit cell.

Page 62: Solids, Inter Molecular

12-62

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

• Atom Location Fraction Inside Unit Cell*

Corner 1/8

Edge 1/4

Face 1/2

Anywhere else 1

*For unit cells with non-orthogonal axes it is not

strictly true that an atom on a corner (edge) is

exactly 1/8 (1/4) inside the unit cell, but it is still

true that 8 (4) such atoms add up to one atom in the

unit cell

Page 63: Solids, Inter Molecular

12-63

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

• Now we can determine the number of atoms

inside the unit cell for each of the packing

arrangements we have discussed.

Face Centered Cubic (ccp) (8 ×1/8) + (6 ×1/2) = 4

Body Centered Cubic (bcc) (8 ×1/8) + 1 = 2

Simple Cubic (sc) (8 ×1/8) = 1

Hexagonal closed packed (hcp) = 6

Page 64: Solids, Inter Molecular

12-64

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

• The volume of occupied space contained

within the unit cell can now be easily

calculated by multiplying the number of atoms

per unit cell by the volume of a sphere.

V = 4/3 π r3 x ?

Page 65: Solids, Inter Molecular

12-65

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

• The next step is to determine the size

of the unit cell as a function of the

atomic radius, r:

SC, BCC, FCC

Page 66: Solids, Inter Molecular

12-66

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

a = b = c = 2r

a = 2r

V = (2r)3

V = 8r3

Packing efficiency % = 4/3 π r3 x 1 X 100 = 52 %

8r3

1/8 atom at

8 corners

Atoms/unit cell = 1/8 * 8 = 1

The volume of a sphere is

V = 4/3 π r3

Simple cubic

Page 67: Solids, Inter Molecular

12-67

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

The volume of a sphere is

V = 4/3 π r3

Atoms/unit cell = (1/8*8) + 1 = 2

Packing efficiency % = 4/3 π r3 x 2 X 100 = 68 %

(2.3r)3

Body-centered cubic

a2 + a2 = ?

a2 + ? = (4r)2

a2 + 2a2 = (4r)2

3a2 = 16r2

a = √(16/3)r

Page 68: Solids, Inter Molecular

12-68

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

a2 + a2 = (4r)2

2a2 = 16r2

a = 81/2 r

V = (81/2 r)3

V = 83/2r3

The volume of a sphere is

V = 4/3 π r3

Packing efficiency % = 4/3 π r3 x 4 X 100 = 74 %

83/2r3

Atoms/unit cell = (1/8*8)+(1/2*6) = 4

Face-centered cubic

Page 69: Solids, Inter Molecular

12-69

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Density

• d = m/V

• m = M/NAx #of spheres per unit

• V = unit cell (sc, bcc, fcc)

Page 70: Solids, Inter Molecular

12-70

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

SAMPLE PROBLEM 12.4 Determining Atomic Radius from Crystal Structure

PROBLEM: Barium is the largest nonradioactive alkaline earth metal. It has

a body-centered cubic unit cell and a density of 3.62 g/cm3.

What is the atomic radius of barium?

(Volume of a sphere: V = 4/3pr3)

PLAN: We can use the density and molar mass to find the volume of 1 mol of

Ba. Since 68%(for a body-centered cubic) of the unit cell contains

atomic material, dividing by Avogadro’s number will give us the volume

of one atom of Ba. Using the volume of a sphere, the radius can be

calculated.

density of Ba (g/cm3)

volume of 1 mol Ba metal volume of 1 Ba atom

radius of a Ba atom

multiply by packing efficiency

reciprocal divided by M V = 4/3pr3

volume of 1 mol Ba atoms

divide by Avogadro’s number

Page 71: Solids, Inter Molecular

12-71

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

SAMPLE PROBLEM 12.4 Determining Atomic Radius from Crystal Structure

SOLUTION:

continued

Volume of Ba metal =137.3 g Ba

mol Ba= 37.9 cm3/mol Ba

37.9 cm3/mol Ba x 0.68 = 26 cm3/mol Ba atoms

mol Ba atoms

6.022x1023 atoms= 4.3x10-23 cm3/atom

r3 = 3V/4p = 2.2 x 10-8cm

1 cm3

3.62 gx

26 cm3

mol Ba atomsx

r =3V

4p3

3(4.3x10-23cm3 )

4 x 3.143

Page 72: Solids, Inter Molecular

12-72

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Cu d = 8.93 g/cm3 atomic radius 128pm

M = 63.55 g/mol

Is the metal close-packed or body centered cubic?

Strategy :

• Calculate the density of the metal assuming first that is ccp and then that it is bcc.

• The structure with the density closer to the experimental value is more likely to be the actual structure.

• The mass of a unit cell is the sum of the masses of the atoms that it contains.

• The mass of each atom is given by M/NA

• Length of FCC (a = 81/2r)

• Length of BCC (a = √(16/3) r )

Page 73: Solids, Inter Molecular

12-73

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Cu d = 8.93 g/cm3

Is the metal close-packed or body centered cubic?

• FCC d = m/a3 m = 4 x M/NA

(81/2r)3

• BCC d = m/a3 m = 2 x M/NA

(√(16/3) r )3

Are these metals BCC or FCC ?

Fe d = 7.87 g/cm3 atomic radius 124 pm

Ag d = 10.5 g/cm3 atomic radius 144 pm

Page 74: Solids, Inter Molecular

12-74

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Table 12.5 Characteristics of the Major Types of Crystalline Solids

Particles

Interparticle

Forces

Physical

Behavior Examples (mp,0C)

Atomic

Molecular

Ionic

Metallic

Network

Group 8A(18)

[Ne-249 to Rn-71]

Molecules

Positive &

negative ions

Atoms

Atoms

Soft, very low mp, poor

thermal & electrical

conductors

DispersionAtoms

Dispersion,

dipole-dipole,

H bonds

Fairly soft, low to moderate

mp, poor thermal &

electrical conductors

Nonpolar - O2[-219],

C4H10[-138], Cl2

[-101], C6H14[-95]

Polar - SO2[-73],

CHCl3[-64], HNO3[-

42], H2O[0.0]

Covalent bond

Metallic bond

Ion-ion

attraction

Very hard, very high mp,

usually poor thermal and

electrical conductors

Soft to hard, low to very

high mp, excellent thermal

and electrical conductors,

malleable and ductile

Hard & brittle, high mp,

good thermal & electrical

conductors when molten

NaCl [801]

CaF2 [1423]

MgO [2852]

Na [97.8]

Zn [420]

Fe [1535]

Page 75: Solids, Inter Molecular

12-75

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.29 Figure 12.30

Cubic closest packing for

frozen argon.

Atomic solids

Individual atoms held together by

dispersion forces. Noble gases

Cubic closest packing of

frozen methane.

Molecular solids

The lattice points are occupied

by individual molecules

Page 76: Solids, Inter Molecular

12-76

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.Figure 12.31

The sodium chloride structure.

expanded view

space-filling

Ionic solids

• The unit cell contains particles with whole charge and has the same

cation:anion ratio as the empirical formula.

• The ionic bonding is stronger than intermolecular forces in atomic or molecular

solids.

• Many ionic solids use the cubic closest packing.

• Coordination number is 6 - # of ions of opposite charge surrounding a specific

ion.

1:1 ratio(8 x 1/8) + (6 x 1/2) = 4 Cl-

(12 x 1/4) + 1 (center) = 4 Na+

Page 77: Solids, Inter Molecular

12-77

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.32 The zinc blende structure.

zinc sulfide1:1 ratio

(8 x 1/8) + (6 x 1/2) = 4 S2-

4 Zn2+ tetrahedrally surrounded by four

ions of opposite charge.

Page 78: Solids, Inter Molecular

12-78

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.33 The fluorite (CaF2) structure.

1:2 ratio(8 x 1/8) + (6 x 1/2) = 4 Ca2+

F- occupy all 8 available holes.

Antifluorite is often see in a 2:1 ratio.

Page 79: Solids, Inter Molecular

12-79

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Coordination number in an Ionic solid

• (6,6) – coordination -NaCl, KBr, RbI, MgO

In this notation the first number is the cation and the

second is the anion.

0.4 to 0.7 a structure similar to NaCl is expected

> 0.7 more anions can fit around the cation where

the two ions are almost the same size.

CsCl (8,8) coordination

Page 80: Solids, Inter Molecular

12-80

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.34 Crystal structures of metals.

cubic closest packing hexagonal closest packing

Metallic solids – Metallic bonding forces hold individual atoms together.

Wide range of melting point and hardnesses related to packing

efficiency and the number of valence e- available for bonding.

Page 81: Solids, Inter Molecular

12-81

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Network covalent solids – where strong covalent bonds link the atoms together

throughout a network.

High melting point and boiling point.

Conductivity and hardness depends on the bonding

Page 82: Solids, Inter Molecular

12-82

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.35 Crystalline and amorphous silicon dioxide.

Page 83: Solids, Inter Molecular

12-83

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.36 The band of molecular orbitals in lithium metal.

Page 84: Solids, Inter Molecular

12-84

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

MOLECULAR ORBITAL BAND THEORY

The electrons in a substance must move within the conduction band in order to conduct electricity.

• The conduction band is a partially filled band or a band of vacant energy levels just higher in energy than a filled band.

• Metals conduct electricity because the highest energy electrons can easily move in a conduction band.

• For a metal, the electrical conductivity decreases as the temperature increases. The metal ions move more, which slows down the flow of electrons when an electric field is applied.

• A typical metalloid is a semiconductor where there is a gap between the highest energy electrons and the conduction band and they do not conduct electricity at low temperatures. A small increase in temperature will excite some of the highest energy electrons into the empty conduction band. Therefore, electrical conductivity increases with increasing temperature for a metalloid.

Page 85: Solids, Inter Molecular

12-85

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.37

Electrical conductivity in a conductor, semiconductor, and insulator.

conductor

semiconductor

insulator

•Metallic luster

•Malleability

•Thermal conductivity

Page 86: Solids, Inter Molecular

12-86

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.38

The levitating power of a superconducting oxide.

rare earth magnet

superconducting ceramic disk

liquid nitrogen

Superconductivity –

to conduct with no energy loss

requires extreme cooling to minimize atom movement.

It has been observed by cooling metals to near absolute zero.

Page 87: Solids, Inter Molecular

12-87

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.39

Crystal structures and band

representations of doped

semiconductors.

Doping – adding small amounts of other elements to increase or decreae the

number of valence electrons in the bands.

extra negative charges (electrons) are present the empty orbitals act as positive holes

INCREASING CONDUCTIVITY

Page 88: Solids, Inter Molecular

12-88

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Forward bias

Reverse bias

p-n junctionFigure 12.40 The p-n junction.

Page 89: Solids, Inter Molecular

12-89

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

heat in furnace with O2

treat with photoresist apply template •expose to light

and solvent

•remove template

•etch SiO2 with HF

• remove photoresist

•treat with Ga vapor

•remove SiO2

Figure 12.41 Steps in manufacturing a p-n junction.

Page 90: Solids, Inter Molecular

12-90

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.42

Structures of two typical molecules that form liquid crystals.

Page 91: Solids, Inter Molecular

12-91

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.43 The three common types of liquid crystal phases.

nematic smecticcholesteric

Page 92: Solids, Inter Molecular

12-92

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.44 Liquid crystals in biological systems.

nematic arrays of

tobacco mosaic virus particles

actin and myosin protein

filaments in voluntary muscle cells

Page 93: Solids, Inter Molecular

12-93

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.45

Schematic of a liquid

crystal display (LCD).

Page 94: Solids, Inter Molecular

12-94

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Table 12.7 Some Uses of Modern Ceramics and Ceramic Mixtures

Ceramic Applications

SiC, Si3N4, TiB2, Al2O3 Whiskers(fibers) to strength Al and other ceramics

Si3N4 Car engine parts; turbine rotors for “turbo” cars;

electronic sensor units

Si3N4, BN, Al2O3 Supports or layering materials(as insulators) in

electronic microchips

SiC, Si3N4, TiB2, ZrO2,

Al2O3, BN

ZrO2, Al2O3

Cutting tools, edge sharpeners(as coatings and

whole devices), scissors, surgical tools, industrial

“diamond”

BN, SiC Armor-plating reinforcement fibers(as in Kevlar

composites)

Surgical implants(hip and knee joints)

Page 95: Solids, Inter Molecular

12-95

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.46 Unit cells of some modern ceramic materials.

SiC

silicon

carbide

BN

cubic boron

nitride

(borazon)

YBa2Cu3O7

high

temperature

superconductor

Page 96: Solids, Inter Molecular

12-96

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Table 12.8 Molar Masses of Some Common Polymers

Name Mpolymer (g/mol) n Uses

Acrylates 2 x105 2 x103 Rugs, carpets

Polyamide(nylons) 1.5 x104 1.2 x102 Tires, fishing line

Polycarbonate 1 x105 4 x102 Compact discs

Polyethylene 3 x105 1 x104 Grocery bags

Polyethylene (ultra-

high molecular weight)

5 x106 2 x105 Hip joints

Poly(ethylene

terephthalate)

2 x104 1 x102 Soda bottles

Polystyrene 3 x105 3 x103 Packing; coffee cups

Poly(vinyl chloride) 1 x105 1.5 x103 Plumbing

Page 97: Solids, Inter Molecular

12-97

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.47 The random coil shape of a polymer chain.

Page 98: Solids, Inter Molecular

12-98

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.48 The semicrystallinity of a polymer chain.

Page 99: Solids, Inter Molecular

12-99

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.49 The viscosity of a polymer in solution.

Page 100: Solids, Inter Molecular

12-

100

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Table 12.9 Some Common Elastomers

Name Tg (0C)*

*Glass transition temperature

Uses

Poly(dimethyl siloxane) -123

-106

-65

-43

Polybutadiene

Polyisoprene

Polychloroprene (neoprene)

Breast implants

Rubber bands

Surgical gloves

Footwear, medical tubing

Page 101: Solids, Inter Molecular

12-

101

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.50 Manipulating atoms.

tip of an atomic force microscope (AFM)

Page 102: Solids, Inter Molecular

12-

102

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure 12.50 Manipulating atoms.

nanotube gear

Page 103: Solids, Inter Molecular

12-

103

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure B12.1

Diffraction of x-rays by crystal planes.

Tools of the Laboratory

Page 104: Solids, Inter Molecular

12-

104

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Figure B12.2

Formation of an x-ray diffraction pattern of the

protein hemoglobin.

Tools of the Laboratory

Page 105: Solids, Inter Molecular

12-

105

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Tools of the Laboratory

Figure B12.3 Scanning tunneling micrographs.

gallium arsenide semiconductor metallic gold

Page 106: Solids, Inter Molecular

12-

106

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Page 107: Solids, Inter Molecular

12-

107

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Page 108: Solids, Inter Molecular

12-

108

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Other properties of liquids

• Surface tension- energy required to disrupt a

drop and spread it out as a film- tendency to

minimize surface area (spherical drops)

• Capillary action- creeping up a surface

cohesive vs. adhesive

• Viscosity: resistance to flow

depends on intermolecular forces

less inter.forces high viscosity.