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CHAPTER 13 n Liquids and Solids Copyright © 2000 by Harcourt, Inc Requests for CHAPTER 13 n Liquids and Solids Copyright © 2000 by Harcourt, Inc Requests for permission to make copies of any part of the work should be mailed to: Permissions Department, Harcourt Inc, 6277 Sea Harbor Drive, Orlando, Florida 32887 -6777 1 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Chapter Goals n n n Kinetic-Molecular Description of Liquids & Solids Intermolecular Attractions & Chapter Goals n n n Kinetic-Molecular Description of Liquids & Solids Intermolecular Attractions & Phase Changes Properties of Liquids – Viscosity, Surface Tension, Capillary Action – Evaporation, Vapor Pressure, – Boiling Points & Distillation, Heat transfer Properties of Solids – Melting Points, Heat Transfer – Sublimation & Vapor Pressure – Phase Diagrams, Amorphous & Crystalline Solids – Crystal Structures, Bonding in Solids, Band Theory Synthesis Question 2 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Kinetic-Molecular Description of Liquids & Solids n Solids & liquids are condensed states – Kinetic-Molecular Description of Liquids & Solids n Solids & liquids are condensed states – – n Liquids & gases are fluids – n atoms, ions, molecules are close to one another highly incompressible easily flow Intermolecular attractions in liquids & solids are strong 3 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Kinetic-Molecular Description of Liquids & Solids gas cool heat liquid cool solid heat 4 Kinetic-Molecular Description of Liquids & Solids gas cool heat liquid cool solid heat 4 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Kinetic-Molecular Description of Liquids & Solids strengths of interactions among particles & n degree Kinetic-Molecular Description of Liquids & Solids strengths of interactions among particles & n degree of ordering of particles Gases< Liquids < Solids n Miscible liquids diffuse into one another n – n they are soluble in each other for example: – – water/alcohol gasoline/motor oil 5 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Kinetic-Molecular Description of Liquids & Solids n Immiscible liquids do not diffuse into each Kinetic-Molecular Description of Liquids & Solids n Immiscible liquids do not diffuse into each other – n they are insoluble in each other for example: – – water/oil water/cyclohexane 6 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes n Ion-ion interactions – force of attraction between two Intermolecular Attractions and Phase Changes n Ion-ion interactions – force of attraction between two oppositely charged ions is determined by Coulomb’s law 7 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes n energy of attraction between two ions is given Intermolecular Attractions and Phase Changes n energy of attraction between two ions is given by: 8 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes n Coulomb’s law & the attraction energy determine: – Intermolecular Attractions and Phase Changes n Coulomb’s law & the attraction energy determine: – – n melting & boiling points of ionic compounds the solubility of ionic compounds Example 13 -1: Arrange the following ionic compounds in the expected order of increasing melting and boiling points. Na. F, Ca. O, Ca. F 2 you do it What important points must you consider? 9 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes n Dipole-dipole interactions – consider NH 3 a very Intermolecular Attractions and Phase Changes n Dipole-dipole interactions – consider NH 3 a very polar molecule 11 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes n Hydrogen bonding – consider H 2 O 12 Intermolecular Attractions and Phase Changes n Hydrogen bonding – consider H 2 O 12 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes 13 Copyright © 2000 by Harcourt, Inc. All rights Intermolecular Attractions and Phase Changes 13 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes n London Forces very weak only attractive force in Intermolecular Attractions and Phase Changes n London Forces very weak only attractive force in nonpolar molecules consider Ar isolated atom 14 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Intermolecular Attractions and Phase Changes n Group of Ar molecules temporary dipole induces other Intermolecular Attractions and Phase Changes n Group of Ar molecules temporary dipole induces other dipoles 15 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Viscosity - resistance to flow water vs. molasses you buy The Liquid State n Viscosity - resistance to flow water vs. molasses you buy oil for your car based on this property Ostwald viscometer used to measure this property 16 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State Surface Tension - measure of the unequal attractions that occur at The Liquid State Surface Tension - measure of the unequal attractions that occur at the surface of a liquid n molecules at surface are attracted unevenly n – – water bugs floating razor blades 17 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State Capillary Action - ability of a liquid to rise (or fall) The Liquid State Capillary Action - ability of a liquid to rise (or fall) in a glass tube n cohesive forces - hold liquids together n adhesive forces - forces between a liquid another surface n – – capillary rise implies adhesive > cohesive capillary fall implies cohesive > adhesive 18 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Capillary Action water mercury 19 Copyright © 2000 by Harcourt, The Liquid State n Capillary Action water mercury 19 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Evaporation – – process in which molecules escape from the The Liquid State n Evaporation – – process in which molecules escape from the surface of a liquid T dependent 20 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Evaporation 21 Copyright © 2000 by Harcourt, Inc. All rights The Liquid State n Evaporation 21 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Vapor Pressure – n pressure exerted by a liquid’s vapor The Liquid State n Vapor Pressure – n pressure exerted by a liquid’s vapor on its surface at equilibrium Vap. Press. (torr) for 3 Liquids 0 o. C 20 o. C 30 o. C diethyl ether 185 442 647 n ethanol 12 44 74 n water 5 18 32 n Norm. B. P. 36 o. C 78 o. C 100 o. C 22 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Vapor Pressure 23 Copyright © 2000 by Harcourt, Inc. All The Liquid State n Vapor Pressure 23 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Boiling Points & Distillation – – n boiling point is The Liquid State n Boiling Points & Distillation – – n boiling point is temperature at which the liquid’s vapor pressure is equal to applied pressure normal boiling point is boiling point @ 1 atm distillation is a method we use to separate mixtures of liquids based on their differences in boiling points 24 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Distillation – – process in which a mixture or solution The Liquid State n Distillation – – process in which a mixture or solution is separated into its components on the basis of the differences in boiling points of the components Distillation is another vapor pressure phenomenon. 25 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Heat Transfer Involving Liquids – from Chapter 1 Example 13 The Liquid State n Heat Transfer Involving Liquids – from Chapter 1 Example 13 -2: How much heat is released by 200 g of H 2 O as it cools from 85. 0 o. C to 40. 0 o. C? The specific heat of water is 4. 184 J/go. C. you do it 26 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State molar heat capacity - amount of heat required to raise the The Liquid State molar heat capacity - amount of heat required to raise the T of one mole of a substance one degree C n Example 13 -3: The molar heat capacity of ethyl alcohol, C 2 H 5 OH, is 113 J/molo. C. How much heat is required to raise the T of 125 g of ethyl alcohol from 20. 0 o. C to 30. 0 o. C? 1 mol C 2 H 5 OH = 46. 0 g n you do it 28 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n energy associated with changes of state heat of vaporization amount The Liquid State n energy associated with changes of state heat of vaporization amount of heat required to change 1 g of a liquid substance to a gas at constant T units of J/g heat of condensation reverse of heat of vaporization 30 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State molar heat of vaporization or DHvap amount of heat required to The Liquid State molar heat of vaporization or DHvap amount of heat required to change 1 mol of a liquid to a gas at constant T units of J/mol molar heat of condensation reverse of molar heat of vaporization 31 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 32 Copyright © 2000 by Harcourt, Inc. All rights reserved. The Liquid State 32 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Example 13 -4: How many joules of energy must be The Liquid State n Example 13 -4: How many joules of energy must be absorbed by 500 g of H 2 O at 50. 0 o. C to convert it to steam at 120 o. C? The molar heat of vaporization of water is 40. 7 k. J/mol and the molar heat capacities of liquid water and steam are 75. 3 J/mol o. C and 36. 4 J/mol o. C, respectively. 33 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 34 Copyright © 2000 by Harcourt, Inc. All rights reserved. The Liquid State 34 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 2 nd let’s calculate the energy required to boil the water The Liquid State 2 nd let’s calculate the energy required to boil the water 35 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 2 nd let’s calculate the energy required to boil the water The Liquid State 2 nd let’s calculate the energy required to boil the water 3 rd let’s calculate the heat required to heat steam from 100 to 120 o. C 36 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State total amount of energy for this process is the sum of The Liquid State total amount of energy for this process is the sum of the 3 pieces we have calculated 37 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Example 13 -5: If 45. 0 g of steam at The Liquid State n Example 13 -5: If 45. 0 g of steam at 140 o. C is slowly bubbled into 450 g of water at 50. 0 o. C in an insulated container, can all the steam be condensed? you do it 38 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Clausius-Clapeyron equation – – – determine vapor pressure of a The Liquid State n Clausius-Clapeyron equation – – – determine vapor pressure of a liquid at a new T determine what T we must heat something to get a specified vapor pressure way to determine DHvap if we know pressure at 2 T’s 42 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n In Denver the normal atmospheric pressure is 630 torr. At The Liquid State n In Denver the normal atmospheric pressure is 630 torr. At what temperature does water boil in Denver? 43 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 44 Copyright © 2000 by Harcourt, Inc. All rights reserved. The Liquid State 44 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Boiling Points of Various Kinds of Liquids Gas MW BP(o. The Liquid State n Boiling Points of Various Kinds of Liquids Gas MW BP(o. C) 45 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State BP MW 46 Copyright © 2000 by Harcourt, Inc. All rights The Liquid State BP MW 46 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 47 Copyright © 2000 by Harcourt, Inc. All rights reserved. The Liquid State 47 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State BP MW 48 Copyright © 2000 by Harcourt, Inc. All rights The Liquid State BP MW 48 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 49 Copyright © 2000 by Harcourt, Inc. All rights reserved. The Liquid State 49 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State HF BP HI HBr HCl MW 50 Copyright © 2000 by The Liquid State HF BP HI HBr HCl MW 50 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State 51 Copyright © 2000 by Harcourt, Inc. All rights reserved. The Liquid State 51 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State H 2 O BP H 2 Te H 2 S MW The Liquid State H 2 O BP H 2 Te H 2 S MW 52 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Liquid State n Example 13 -6: Arrange the following substances in order of The Liquid State n Example 13 -6: Arrange the following substances in order of increasing boiling points. C 2 H 6, NH 3, Ar, Na. Cl, As. H 3 you do it 53 Copyright © 2000 by Harcourt, Inc. All rights reserved.

The Solid State n Normal Melting Point – – T at which the solid The Solid State n Normal Melting Point – – T at which the solid melts (liquid and solid in equilibrium) at 1 atm of pressure melting point increases as intermolecular attractions increase 55 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Heat Transfer Involving Solids n heat of fusion amount of heat required to melt Heat Transfer Involving Solids n heat of fusion amount of heat required to melt one gram of a solid at its melting point at constant T heat of crystallization reverse of heat of fusion 56 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Heat Transfer Involving Solids molar heat of fusion amount of heat required to melt Heat Transfer Involving Solids molar heat of fusion amount of heat required to melt a mole of a substance at its melting point molar heat of crystallization reverse of molar heat of fusion 57 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Heat Transfer Involving Solids n Summary of heats of transformation of water 58 Copyright Heat Transfer Involving Solids n Summary of heats of transformation of water 58 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Heat Transfer Involving Solids n Example 11 -7: Calculate the amount of heat required Heat Transfer Involving Solids n Example 11 -7: Calculate the amount of heat required to convert 150. 0 g of ice at -10. 0 o. C to water at 40. 0 o. C. specific heat of ice is 2. 09 J/go. C you do it 59 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Sublimation & Vapor Pressure of Solids n Sublimation – – solid transforms directly to Sublimation & Vapor Pressure of Solids n Sublimation – – solid transforms directly to vapor solid CO 2 or “dry” ice 61 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Phase Diagrams (P vs T) n convenient way to display all of the different Phase Diagrams (P vs T) n convenient way to display all of the different phases of a substance phase diagram for water – 62 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Phase Diagrams (P vs T) n phase diagram for carbon dioxide 63 Copyright © Phase Diagrams (P vs T) n phase diagram for carbon dioxide 63 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Amorphous & Crystalline Solids n Amorphous solids do not have a well ordered structure Amorphous & Crystalline Solids n Amorphous solids do not have a well ordered structure paraffin, glasses n Crystalline solids have well defined structures that consist of extended array of repeating units give X-ray difraction patterns see Bragg equation in book 64 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Structure of Crystals n unit cell - smallest repeating unit of a crystal bricks Structure of Crystals n unit cell - smallest repeating unit of a crystal bricks are repeating units for buildings n 7 basic crystal systems 65 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Structure of Crystals n Simple cubic 66 Copyright © 2000 by Harcourt, Inc. All Structure of Crystals n Simple cubic 66 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Structure of Crystals n Simple cubic – – each particle at a corner is Structure of Crystals n Simple cubic – – each particle at a corner is shared by 8 unit cells 1 unit cell contains 8(1/8) = 1 particle 67 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Structure of Crystals n Body centered cubic (bcc) – – 8 corners + 1 Structure of Crystals n Body centered cubic (bcc) – – 8 corners + 1 particle in center of cell 1 unit cell contains 8(1/8) + 1 = 2 particles 68 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Structure of Crystals n Face centered cubic (fcc) 69 Copyright © 2000 by Harcourt, Structure of Crystals n Face centered cubic (fcc) 69 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Structure of Crystals n Face centered cubic (fcc) – – 8 corners + 6 Structure of Crystals n Face centered cubic (fcc) – – 8 corners + 6 faces 1 unit cell contains 8(1/8) + 6(1/2) = 4 particles 70 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids n Molecular Solids – – – molecules occupy unit cells low Bonding in Solids n Molecular Solids – – – molecules occupy unit cells low melting points, volatile & insulators examples: n water, sugar, carbon dioxide, benzene 71 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids n Covalent Solids – – atoms that are covalently bonded to Bonding in Solids n Covalent Solids – – atoms that are covalently bonded to one another examples: n Si. O 2 (sand), diamond, graphite, Si. C 72 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids n Ionic Solids – – ions occupy the unit cell examples: Bonding in Solids n Ionic Solids – – ions occupy the unit cell examples: n Cs. Cl, Na. Cl, Zn. S 73 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids n Metallic Solids – – – positively charged nuclei surrounded by Bonding in Solids n Metallic Solids – – – positively charged nuclei surrounded by a sea of electrons positive ions occupy lattice positions examples: n Na, Li, Au, Ag, ……. . 74 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids Variations in Melting Points n Molecular Solids Compound Melting Point (o. Bonding in Solids Variations in Melting Points n Molecular Solids Compound Melting Point (o. C) ice 0 ammonia -77. 7 benzene, C 6 H 6 5. 5 napthalene, C 10 H 8 80. 6 benzoic acid, C 6 H 5 CO 2 H 122. 4 n 75 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids Covalent Solids Substance sand, Si. O 2 carborundum, Si. C diamond Bonding in Solids Covalent Solids Substance sand, Si. O 2 carborundum, Si. C diamond graphite n Melting Point (o. C) 1713 ~2700 >3550 3652 -3697 76 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids Ionic Solids Compound Li. F Li. Cl Li. Br Li. I Bonding in Solids Ionic Solids Compound Li. F Li. Cl Li. Br Li. I Ca. F 2 Ca. Cl 2 Ca. Br 2 Ca. I 2 n Melting Point (o. C) 842 614 547 450 1360 772 730 740 77 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Bonding in Solids Metallic Solids Metal Na Pb Al Cu Fe W n Melting Bonding in Solids Metallic Solids Metal Na Pb Al Cu Fe W n Melting Point (o. C) 98 328 660 1083 1535 3410 78 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Unit Cell Problem n A group IVA element with a density of 11. 35 Unit Cell Problem n A group IVA element with a density of 11. 35 g/cm 3 crystallizes in a face-centered cubic lattice whose unit cell edge length is 4. 95 A. Calculate the element’s atomic weight. What is the atomic radius of this element? 79 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Unit Cell Problem fcc has 4 atoms per unit cell n determine the volume Unit Cell Problem fcc has 4 atoms per unit cell n determine the volume of a single unit cell n 80 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Unit Cell Problem n n use density to determine the mass of a unit Unit Cell Problem n n use density to determine the mass of a unit cell determine the mass of one atom in a unit cell 81 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Unit Cell Problem n determine the mass of 1 mole of these atoms 82 Unit Cell Problem n determine the mass of 1 mole of these atoms 82 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Unit Cell Problem n n determine the radius of a Pb atom requires some Unit Cell Problem n n determine the radius of a Pb atom requires some geometry from high school notice there are 4 radii on the diagonal 83 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Unit Cell Problem n determine the diagonal length then divide by 4 to get Unit Cell Problem n determine the diagonal length then divide by 4 to get atomic radius 84 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Band Theory of Metals n Na’s 3 s orbitals can interact to produce overlapping Band Theory of Metals n Na’s 3 s orbitals can interact to produce overlapping orbitals 85 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Band Theory of Metals n Can also overlap with unfilled 3 p orbitals 86 Band Theory of Metals n Can also overlap with unfilled 3 p orbitals 86 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Band Theory of Metals Insulators have a large gap - forbidden zone n Semiconductors Band Theory of Metals Insulators have a large gap - forbidden zone n Semiconductors have a small gap n 87 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Synthesis Question n Maxwell House Coffee Company decaffeinates its coffee beans using an extractor Synthesis Question n Maxwell House Coffee Company decaffeinates its coffee beans using an extractor that is 7. 0 feet in diameter and 70. 0 feet long. Supercritical carbon dioxide at a pressure of 300. 0 atm and temperature of 100. 00 C is passed through the stainless steel extractor. The extraction vessel contains 100, 000 pounds of coffee beans soaked in water until they have a water content of 50%. 88 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Synthesis Question n This process removes 90% of the caffeine in a single pass Synthesis Question n This process removes 90% of the caffeine in a single pass of the beans through the extractor. Carbon dioxide that has passed over the coffee is then directed into a water column that washes the caffeine from the supercritical CO 2. How many moles of carbon dioxide are present in the extractor? 89 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Synthesis Question 90 Copyright © 2000 by Harcourt, Inc. All rights reserved. Synthesis Question 90 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Synthesis Question 91 Copyright © 2000 by Harcourt, Inc. All rights reserved. Synthesis Question 91 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Group Question n How many CO 2 molecules are there in 1. 0 cm Group Question n How many CO 2 molecules are there in 1. 0 cm 3 of the Maxwell House Coffee Company extractor? How many more CO 2 molecules are there in a cm 3 of the supercritical fluid in the Maxwell House extractor than in a mole of CO 2 at STP? 92 Copyright © 2000 by Harcourt, Inc. All rights reserved.

Chapter Goals Kinetic-Molecular Description of Liquids & Solids n Intermolecular Attractions & Phase Changes Chapter Goals Kinetic-Molecular Description of Liquids & Solids n Intermolecular Attractions & Phase Changes n Properties of Liquids n – – – n Viscosity, Surface Tension, Capillary Action Evaporation, Vapor Pressure, Boiling Points & Distillation, Heat transfer – – Melting Points, Heat Transfer Sublimation & Vapor Pressure Phase Diagrams, Amorphous & Crystalline Solids Crystal Structures, Bonding in Solids, Band Theory Properties of Solids 93 Copyright © 2000 by Harcourt, Inc. All rights reserved.

End of Chapter 13 n n Our understanding of Band Theory was a major End of Chapter 13 n n Our understanding of Band Theory was a major breakthrough in semiconductor knowledge. Why computers work! 94 Copyright © 2000 by Harcourt, Inc. All rights reserved.