Chapter 16 - 國立臺灣大學ocw.aca.ntu.edu.tw/ocw_files/099S125/ch16.pdf · Chapter 16 Slide 2...

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Chapter 16

Liquids and Solids


Chapter Preview• Intramolecular forces determine such molecular properties

as molecular geometries and dipole moments.• Intermolecular forces determine the macroscopic

physical properties of liquids and solids.• Three states of matter: solids, liquids, and gases.

– In gases and liquids, motion is mainly translational.– In solids, motion is mainly vibrational.

• This chapter describes changes from one state of matter to another and explores the types of intermolecular forces that underlie the physical properties of substances.


Table 2.11


States of Matter Compared


Dipole-Dipole Forces

• Dipole-dipole forces arise when permanent dipoles align themselves with the positive end of one dipole directed toward the negative ends of neighboring dipoles.

• When molecules come close to one another, repulsions occur between like-charged regions of dipoles.

• A permanent dipole in one molecule can induce a dipole in a neighboring molecule, giving rise to a dipole-induced dipole force.

• The more polar a molecule, the more pronounced is the effect of dipole-dipole forces on physical properties.

Dipole-Dipole Interactions

Dipole momentµ = δ ·d

E = - 2(µ1 ·µ2)/4πεr3

d

r

µ2

µ1


Dispersion Forces

• A dispersion force is the force of attraction between an instantaneous dipole and an induced dipole.

• Also called a London force after Fritz London who offered a theoretical explanation of these forces in 1928.

• The polarizability of an atom or molecule is a measure of the ease with which electron charge density is distorted by an external electrical field.

• The greater the polarizability of molecules, the stronger the intermolecular forces between them.

Dispersion Forces Illustrated

µ

E = - 2(µ2 ·α)/r6

polarizabilityMean instantaneous dipole

r

µ


Predicting Physical Properties of Molecular Substances

• Dispersion forces become stronger with increasing molar mass and elongation of molecules. In comparing nonpolarsubstances, molar mass and molecular shape are the essential factors.

• Dipole-dipole and dipole-induced dipole forces are found in polar substances. The more polar the substance, the greater the intermolecular force is expected to be.

• Because they occur in all molecular substances, dispersion forces must always be considered. Often they predominate.


Molecular Shapeand Polarizability


Effect of Molecular Weight & Dipole Moment

76.50153.8CCl4

-129088.0CF4

-40.81.4286.5CHClF2

+401.6084.9CH2Cl2

-24.21.8750.5CH3Cl

b.p. (0C)Dipole (D) moment

M.W.Compound


• A hydrogen bond is an intermolecular force in which a hydrogen atom covalently bonded to a non-metal atom in one molecule is simultaneously attracted to a non-metal atom of a neighboring molecule.

• The strongest hydrogen bonds are formed if the non-metal atoms are small and highly electronegative.

• Usually occurs with nitrogen, oxygen, and fluorine atoms.• Dotted lines are used to represent hydrogen bonds.

Hydrogen Bonds

X H YX, Y = F, O, N, Cl, S (highly electronegative elements)

Hydrogen Bonds in Water


Hydrogen Bonding in Ice


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


HF


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


Figure 25.19


Intermolecular Forces in a Liquid

Surface tension


Adhesive and Cohesive Forces


Meniscus Formation


Vaporization and Condensation

• Vaporization is the conversion of a liquid to a gas.• The enthalpy of vaporization (∆Hvapn) is the quantity of

heat that must be absorbed to vaporize a given amount of liquid at a constant temperature.

• Condensation (∆Hcondn) is the change of a gas to a liquid.

Liquid VaporVaporization

Condensation

∆Hcondn = - ∆Hvapn


Some Enthalpies of Vaporization


Vapor Pressure

• The vapor pressure of a liquid is the partial pressure exerted by the vapor when it is in dynamic equilibrium with a liquid at a constant temperature.

• The vapor pressures of liquids increases with temperature.• A vapor pressure curve is a graph of vapor pressure as a

function of temperature.


Liquid-Vapor Equilibrium


Vapor Pressure Of Water


Vapor Pressure Curves

a) Carbon disulfide: CS2

b) Methanol: CH3OH

c) Ethanol: CH3CH2OH

d) Water: H2O

e) Aniline: C6H5NH2

• The temperature of the line at P= 760 mmHgwith a vapor pressure curve is the normal boiling point.


Clausius-Clapeyron equation:

ln(P2/P1) = (∆Hvap /R)(1/T1 - 1/T2)

where, ∆Hvap = enthalpy of vaporization

Vapor Pressure as a Function of Temperature


Generalized Phase Diagram

Triple point

Critical point

Supercritical fluid

Fusioncurve

Sublimationcurve

Vapor Pressure

curve


Phase Diagram For H2O

normal boiling pointnormal melting point


Boiling Point and Critical Point

• The boiling point of a liquid is the temperature at which its vapor pressure becomes equal to the external pressure.

• The normal boiling point is the boiling point at 1 atm.• The critical temperature, Tc, is the highest temperature at

which a liquid and vapor can co-exist in equilibrium as physically distinct states of matter.

• The critical pressure, Pc, is the vapor pressure at the critical temperature.

• The condition corresponding to a temperature of Tc and a pressure of Pc is called the critical point.


The Critical Point


Phase Changes Involving Solids

• The conversion of a solid to a liquid is called melting, or fusion, and the temperature at which a solid melts is its melting point.

• The enthalpy of fusion, ∆Hfusion, is the quantity of heat required to melt a given amount of solid.

• Sublimation is the process of a molecules passing directly from the solid to the vapor state.

• Enthalpy of sublimation, ∆Hsubln, is the sum of the enthalpies of fusion and vaporization.

• The triple point is the point at which the vapor pressure curve and the sublimation curve meet.


Phase Diagram For CO2

Sublimation of dry ice


Critical Temperature and Pressure of Various Substances


Some Enthalpies of Fusion


Cooling Curve For Water

supercooledCrystallization begins

Expected m.p.


Heating Curve For H2O


Phase Diagram For HgI2

250C


Phase Diagram of Carbon


Some Characteristics ofCrystalline Solids


Network Covalent Solids• These substances contain a network of covalent

bonds that extend throughout a crystalline solid, holding it firmly together.

• The allotropes of carbon provide a good example1. Diamond has each carbon bonded to four other

carbons in a tetrahedral arrangement using sp3

hybridization.

2. Graphite has each carbon bonded to three other carbons in the same plane using sp2 hybridization.

3. Fullerenes are roughly spherical collections of carbon atoms in the shape of a soccer ball.


Crystal Structure of Diamond

Covalent bond


Crystal Structure of Graphite

Covalent bond

van der Waalsforce


Structure of a Buckyball

Covalent bond


Carbon Nano-tube

Covalent bond


Experimental Determinationof Crystal Structures

Bragg’s Law2 d sinθ = n λ


William Lawrence Bragg and William Henry Bragg


X-Ray Diffraction Image & Pattern

Single crystal Powder


Crystal Lattices

• To describe crystals, three-dimensional views must be used.• The repeating unit of the lattice is called the unit cell.• The simple cubic cell (primitive cubic) 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.• The face-centered cubic (fcc) structure has an additional

structural particle at the center of each face.


14 BravaisLattice


Unit Cells InCubic Crystal Structures

simple cubic(primitive cubic)

bcc fcc


Primitive cubic, Body-centered cubic,Face-centered cubic

Face-centered cubicBody-centered cubicPrimitive cubic


Occupancies per Unit CellsPrimitive cubic: a = 2r

1 atom/unit celloccupancy = [4/3(πr3)]/a3 = [4/3(πr3)]/(2r)3

= 0.52 = 52%Body-centered cubic: a = 4r/(3)1/2

2 atom/unit celloccupancy = 2 x [4/3(πr3)]/a3 = 2 x [4/3(πr3)]/[4r/(3)1/2]3

= 0.68 = 68%Face-centered cubic: a = (8)1/2 r

4 atom/unit celloccupancy = 4 x [4/3(πr3)]/a3 = 4 x [4/3(πr3)]/[(8)1/2 r]3

= 0.74 = 74%Closest packed


Using desity to identify structureThe atomic radius of copper is 128 pm, mass number is 63.54, and the density of copper is 8.93g/cm3. Is copper metal close packed?

Density = M/V, V= M/D

The volume of a Cu atom occupied in the lattice

= 63.54g/mol ÷ 8.93g/cm3 ÷ 6.02 x 1023atom/mol

= 1.18 x 10-23 cm3/atom = 1.18 x 107 pm3/atom

Occupancy = [4/3(πr3)]/[1.18 x 107 ]

= [4/3 π( 1283)]/[1.18 x 107 ]

= 0.744 = 74.4% Close-packed structure


Crystal Structures of Metals


Closest packeda

ab

aba abcunoccupied holes


Closest packed

abab

abcabc

= Face-centered cubic


Close-packing of Spheresin Three Dimensions


Close Packed Structures• First two layers of spheres are close-packed.• Tetrahedral holes are located above a sphere in the bottom

layer.• Octahedral holes are located above a void in the bottom

layer.• Hexagonal close-packed (hcp) arrangements occur when

the third layer covers the tetrahedral holes. These produce two-layer repeating units. ABABAB…..

• Cubic close-packed (ccp) arrangements occur when the third layer covers the octahedral holes. These produce three-layer repeating units. ABCABC….


Ionic Bonds in Ionic Solids

• There are simply inter-ionic attractions in an ionic solid.• Lattice energy is a measure of the strength of inter-ionic

attraction.• The attractive force between a pair of oppositely charged

ions increases as the charges on the ions increase and as the ionic radii decrease. Lattice energies increase accordingly.

E = (Z+Z-)/4πεr


Interionic Forces of Attraction

E = (Z+Z-)/4πεr


A Born-Haber Cycle to CalculateLattice Energy

U

1/2D(Cl-Cl)

∆Ηsublimation (Na)

IE(Na) -EA(Cl)

lattice energy U = - ∆Ηf0(NaCl) + ∆Ηsublimation (Na) + 1/2D(Cl-Cl) + IE(Na) - EA(Cl)

= (+411 +107 +122 + 496 –349) kJ/mol

= +787 kJ/mol

∆Ηf0(NaCl)

NaCl(s) Na+(g) + Cl-(g)

Na(g) + Cl(g)Na(s) + 1/2Cl2(g)


Ionic Crystal Structures• Ionic crystals have two different types of structural units -

cations and anions.• The cations and anions are different sizes.• Smaller cations can fill the voids between the larger anions.

Radii ratio:

Tetrahedral hole 0.225 < rc/ra < 0.414

Octahedral hole 0.414 < rc/ra < 0.732

Cubic hole rc/ra > 0.732


Tetrahedral, Octahedral and Cubic holes

Octahedral holesTetrahedral holes Cubic holes

Close packed structure


Radius ratio

rh/r = 0.156

rh/r = 0.225

rh/r = 0.414


Unit Cell of Rock-Salt(Sodium Chloride)

Cl- at fcc

Na+ at Oh holesCoord. #: Na+: 6; Cl-: 6atom/ unit cellNa: Cl= 4: 4 = 1: 1 NaCl


Unit Cell of Cesium Chloride

Cl- at primitive cubicCs+ at Cubic holes

Coord. #: Cs+: 8; Cl-: 8atom/ unit cellCs: Cl= 1: 1 CsCl


Unit Cell of Cubic Zinc Sulfide(Sphalerite or Zinc blende)

Coord. #: Zn2+: 4; S2-: 4atom/ unit cellZn: S = 4: 4 = 1: 1

S2- at fccZn2+ at ½ Td holes

ZnS


Quartz SiO2

Si4+ at fcc and ½ Td holesO2- in between two Si


SixOy


Table 16.4


Unit Cell of Fluorite Structure(Calcium Fluoride)

Ca2+ at fccF- at Td holesCoord. #: Ca2+: 8; F-: 4

atom/ unit cellCa: F= 4: 8 = 1: 2


Unit Cell of Rutile TiO2

O2- at hcpTi4+ at ½ Oh holes

Coord. #: Ti: 6; O: 3atom/ unit cellTi: O= 2: 4 = 1: 2


Unit Cell of PerovskiteCaTiO3

AIIBIVO3

AIIIBIIIO3

Coord. #: A: 12; B: 6atom/ unit cellA: B: O= 1: 1: 3

A and O together at ccpB at 1/4 Oh holes


Unit Cell of SpinelMgAl2O4

Normal SpinelAII[BIII]2O4, AIV[BII]2O4 , AVI[BI]2O4

e.g. NiCr2O4, Co3O4 , Mn3O4

Inverse SpinelB[AB]O4e.g. Fe3O4

O 2- at fccA at 1/8 Td holesB at 1/2 Oh holes


Unit Cell of YBa2Cu3O7


Temperature vs Resistance


Band Theory• This is a quantum-mechanical treatment of bonding in

metals.• The spacing between energy levels is so minute in metals

that the levels essentially merge into a band.• When the band is occupied by valence electrons, it is

called a valence band.• A partially filled or low lying empty band of energy levels,

which is required for electrical conductivity, is a conduction band.

• Band theory provides a good explanation of metallic luster and metallic colors.


Energy Band

bonding

Anti-bonding


The 2s Band in Lithium Metal

Bonding

Anti-bonding

e- e-Valence band

Conduction band


Band Overlap in Magnesium

Valence band

Conduction band


Band Structure of Insulatorsand Semiconductors


Table 3.1


p- and n-Type Semiconductors

e.g. Si doped with P or As

e.g. Si doped with Gaor In

e- e- e-

e- e- e-


Excesselectron

excesshole

No current flows (reverse bias)

Current flows (forward bias)

p- n junction

Chapter 16 - 國立臺灣大學ocw.aca.ntu.edu.tw/ocw_files/099S125/ch16.pdf · Chapter 16 Slide 2...

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