Download presentation
Presentation is loading. Please wait.
1
Chapter 10 Liquids and Solids
2
States of Matter and Intermolecular Forces
Unit ch.5, 10, 11 States of Matter and Intermolecular Forces Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
3
10.1 Intermolecular Forces 10.2 The Liquid State
Chapter 10 Table of Contents Intermolecular Forces The Liquid State An Introduction to Structures and Types of Solids Structure and Bonding in Metals Carbon and Silicon: Network Atomic Solids 10.6 Molecular Solids 10.7 Ionic Solids 10.8 Vapor Pressure and Changes of State 10.9 Phase Diagrams Copyright © Cengage Learning. All rights reserved
4
Links to visuals & review
Click on the link below and use as you get to visual animations and vocabulary. ahl/chemistry/7e/resources/fae/index.html?l ayer=item&src=ch10/qtiflash_ch10_overvi ew_p1.xml&w=645&h=428 Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
5
Links to visuals & review
Click on the link below and use as you get to visual animations and vocabulary. Alternate 2 link to ch. 10 site ahl/chemistry/7e/improve/improve10.html Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
6
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Chapter Preview Intramolecular forces (bonds) govern molecular properties such as molecular geometries and dipole moments. Intermolecular forces determine the macroscopic physical properties of liquids and solids. This chapter: describes changes from one state of matter to another. explores the types of intermolecular forces that underlie these and other physical properties of substances. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
7
Intramolecular Bonding
Section 10.1 Intermolecular Forces Intramolecular Bonding “Within” the molecule. Molecules are formed by sharing electrons between the atoms. Return to TOC Copyright © Cengage Learning. All rights reserved
8
Molecular Forces Compared
Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
9
Intermolecular Forces EXAMPLES
Section 10.1 Intermolecular Forces Intermolecular Forces EXAMPLES Forces that occur between molecules. They determine melting points, freezing points, and other physical properties. Types of intermolecular forces include: dispersion forces - London dispersion forces Dipole–dipole forces Hydrogen bonding Intramolecular bonds are stronger than intermolecular forces. Return to TOC Copyright © Cengage Learning. All rights reserved
10
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Dispersion Forces … exist between any two particles. Also called London forces (after Fritz London, who offered a theoretical explanation of these forces in 1928). Dispersion forces arise because the electron cloud is not perfectly uniform. Tiny, momentary dipole moments can exist even in nonpolar molecules. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
11
London Dispersion Forces
Section 10.1 Intermolecular Forces London Dispersion Forces Instantaneous dipole that occurs accidentally in a given atom induces a similar dipole in a neighboring atom. Significant in large atoms/molecules. Occurs in all molecules, including nonpolar ones. Return to TOC Copyright © Cengage Learning. All rights reserved
12
London Dispersion Forces
Section 10.1 Intermolecular Forces London Dispersion Forces Pull from the following link layer=item&src=ch10/qtiflash_ch10_overview_p1.xml&w=645&h=428 Return to TOC Copyright © Cengage Learning. All rights reserved
13
Dispersion Forces Illustrated (1)
At a given instant, electron density, even in a nonpolar molecule like this one, is not perfectly uniform. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
14
Dispersion Forces Illustrated (2)
… the other end of the molecule is slightly (+). The region of (momentary) higher electron density attains a small (–) charge … When another nonpolar molecule approaches … Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
15
Dispersion Forces Illustrated (3)
… this molecule induces a tiny dipole moment … … in this molecule. Opposite charges ________. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
16
Strength of Dispersion Forces
Dispersion force strength depends on polarizability: the ease with which the electron cloud is distorted by an external electrical field. The greater the polarizability of molecules, the stronger the dispersion forces between them. Polarizability in turn depends on molecular size and shape. Heavier molecule => more electrons => a more- polarizable molecule. As to molecular shape … Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
17
Molecular Shape and Polarizability
… can have greater separation of charge along its length. Stronger forces of attraction, meaning … Long skinny molecule … … higher boiling point. … giving weaker dispersion forces and a lower boiling point. In the compact isomer, less possible separation of charge … Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
18
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Dipole–Dipole Forces A polar molecule has a positively charged “end” (δ+) and a negatively charged “end” (δ–). When molecules come close to one another, repulsions occur between like-charged regions of dipoles. Opposite charges tend to attract one another. The more polar a molecule, the more pronounced is the effect of dipole–dipole forces on physical properties. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
19
Dipole–Dipole Interactions
Opposites attract! Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
20
Only about 1% as strong as covalent or ionic bonds.
Section 10.1 Intermolecular Forces Dipole-Dipole Forces Dipole moment – molecules with polar bonds often behave in an electric field as if they had a center of positive charge and a center of negative charge. Molecules with dipole moments can attract each other electrostatically. They line up so that the positive and negative ends are close to each other. Only about 1% as strong as covalent or ionic bonds. Return to TOC Copyright © Cengage Learning. All rights reserved
21
Intermolecular Forces
Section 10.1 Intermolecular Forces Dipole-Dipole Forces Pull from the following link layer=item&src=ch10/qtiflash_ch10_overview_p1.xml&w=645&h=428 Return to TOC Copyright © Cengage Learning. All rights reserved
22
Hydrogen Bonds Y ––– H - - - Z ~~~~
A hydrogen bond is an intermolecular force in which: a hydrogen atom that is covalently bonded to a (small, electronegative) nonmetal atom in one molecule … is simultaneously attracted to a (small, electronegative) nonmetal atom of a neighboring molecule. Y ––– H Z ~~~~ … this force is called a hydrogen bond; a special, strong type of dipole–dipole force. When Y and Z are small and highly electronegative (N, O, F) … Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
23
Hydrogen Bonding in Water
Section 10.1 Intermolecular Forces Hydrogen Bonding in Water Blue dotted lines are the intermolecular forces between the water molecules. Return to TOC Copyright © Cengage Learning. All rights reserved
24
Intermolecular Forces
Section 10.1 Intermolecular Forces Hydrogen Bonding Pull from the following link layer=item&src=ch10/qtiflash_ch10_overview_p1.xml&w=645&h=428 Return to TOC Copyright © Cengage Learning. All rights reserved
25
Strong dipole-dipole forces.
Section 10.1 Intermolecular Forces Hydrogen Bonding Strong dipole-dipole forces. Hydrogen is bound to a highly electronegative atom – nitrogen, oxygen, or fluorine. Return to TOC Copyright © Cengage Learning. All rights reserved
26
Hydrogen Bonds in Water
Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
27
Hydrogen Bonding in Ice
Hydrogen bonding arranges the water molecules into an open hexagonal pattern. “Hexagonal” is reflected in the crystal structure. “Open” means reduced density of the solid (vs. liquid). Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
28
Hydrogen Bonding in Acetic Acid
Hydrogen bonding occurs between molecules. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
29
Hydrogen Bonding in Salicylic Acid
Hydrogen bonding occurs within the molecule. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
30
Intermolecular Hydrogen Bonds
Intermolecular hydrogen bonds give proteins their secondary shape, forcing the protein molecules into particular orientations, like a folded sheet … Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
31
Animation and Questions for Intermolecular Forces
Click link below for Intermolecular forces and animations. (needed add’l downloads) /imf2.html Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
32
Intramolecular Hydrogen Bonds
… while intramolecular hydrogen bonds can cause proteins to take a helical shape. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
33
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Example 11.8 In which of these substances is hydrogen bonding an important intermolecular force: N2, HI, HF, CH3CHO, and CH3OH? Explain. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
34
Which are stronger, intramolecular bonds or intermolecular forces?
Section 10.1 Intermolecular Forces Concept Check Which are stronger, intramolecular bonds or intermolecular forces? How do you know? Intramolecular bonds are stronger because it would take a lot more energy to overcome covalent bonds and break apart the molecule than to overcome intermolecular forces in between the atoms (to make it become a liquid or gas). Return to TOC Copyright © Cengage Learning. All rights reserved
35
Predicting Physical Properties of Molecular Substances
Dispersion forces become stronger with increasing molar mass and elongation of molecules. In comparing nonpolar substances, 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 substances, dispersion forces must always be considered. Often they predominate. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
36
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Example 11.6 Arrange the following substances in the expected order of increasing boiling point: carbon tetrabromide, CBr4; butane, CH3CH2CH2CH3; fluorine, F2; acetaldehyde, CH3CHO. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
37
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Homology A series of compounds whose formulas and structures vary in a regular manner also have properties that vary in a predictable manner. This principle is called homology. Example: both densities and boiling points of the straight-chain alkanes increase in a continuous and regular fashion with increasing numbers of carbon atoms in the chain. Trends result from the regular increase in molar mass, which produces a fairly regular increase in the strength of dispersion forces. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
38
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
QUESTION Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
39
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Videoclip summary Watch the following for intermolecular forces. Click below. try/chemical-bonds/intermolecular-forces/ Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
40
States of Matter Compared
Intermolecular forces are very important. Intermolecular forces are of little significance; why? Intermolecular forces must be considered. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
41
Section 10.1 Intermolecular Forces Phase Changes When a substance changes from solid to liquid to gas, the molecules remain intact. The changes in state are due to changes in the forces among molecules rather than in those within the molecules. Return to TOC Copyright © Cengage Learning. All rights reserved
42
Schematic Representations of the Three States of Matter
Section 10.1 Intermolecular Forces Schematic Representations of the Three States of Matter Return to TOC Copyright © Cengage Learning. All rights reserved
43
Section 10.1 Intermolecular Forces Phase Changes Solid to Liquid As energy is added, the motions of the molecules increase, and they eventually achieve the greater movement and disorder characteristic of a liquid. Liquid to Gas As more energy is added, the gaseous state is eventually reached, with the individual molecules far apart and interacting relatively little. Return to TOC Copyright © Cengage Learning. All rights reserved
44
Densities of the Three States of Water
Section 10.1 Intermolecular Forces Densities of the Three States of Water Return to TOC Copyright © Cengage Learning. All rights reserved
45
Melting and Boiling Points
Section 10.1 Intermolecular Forces Melting and Boiling Points In general, the stronger the intermolecular forces, the higher the melting and boiling points. Return to TOC Copyright © Cengage Learning. All rights reserved
46
Intermolecular Forces
Section 10.1 Intermolecular Forces The Boiling Points of the Covalent Hydrides of the Elements in Groups 4A, 5A, 6A, and 7A Return to TOC Copyright © Cengage Learning. All rights reserved
47
Which molecule is capable of forming stronger intermolecular forces?
Section 10.1 Intermolecular Forces Concept Check Which molecule is capable of forming stronger intermolecular forces? N2 H2O Explain. H2O has the stronger intermolecular forces because it exhibits hydrogen bonding, whereas N2 only exhibits London dispersion forces. Return to TOC Copyright © Cengage Learning. All rights reserved
48
Section 10.1 Intermolecular Forces Concept Check Draw two Lewis structures for the formula C2H6O and compare the boiling points of the two molecules. One Lewis structure could be ethanol and one Lewis structure could be dimethyl ether. Ethanol will have a higher boiling point than dimethyl ether because ethanol exhibits hydrogen bonding and dimethyl ether exhibits dipole-dipole interactions. Hydrogen bonding is an especially strong type of dipole-dipole interaction and will thus raise the boiling point of ethanol. Return to TOC Copyright © Cengage Learning. All rights reserved
49
Which gas would behave more ideally at the same conditions of P and T?
Section 10.1 Intermolecular Forces Concept Check Which gas would behave more ideally at the same conditions of P and T? CO or N2 Why? N2 would behave more ideally because it is nonpolar and only exhibits London dispersion forces, therefore the intermolecular forces between N2 molecules are weak (and thus the collisions will be more “elastic”). CO also exhibits dipole-dipole interactions. Return to TOC Copyright © Cengage Learning. All rights reserved
50
Section 10.2 The Liquid State Atomic Masses Liquids Low compressibility, lack of rigidity, and high density compared with gases. Surface tension – resistance of a liquid to an increase in its surface area: Liquids with large intermolecular forces tend to have high surface tensions. Return to TOC Copyright © Cengage Learning. All rights reserved
51
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Surface Tension To create more surface, the molecules at the surface must be separated from one another. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
52
Liquids and Intermolecular Forces
Much behavior and many properties of liquids can be attributed to intermolecular forces. Surface tension (γ) is the amount of work required to extend a liquid surface and is usually expressed in J/m2. Adhesive forces are intermolecular forces between unlike molecules. Cohesive forces are intermolecular forces between like molecules. A meniscus is the interface between a liquid and the air above it. Viscosity is a measure of a liquid’s resistance to flow. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
53
Capillary action – spontaneous rising of a liquid in a narrow tube:
Section 10.2 The Liquid State Atomic Masses Liquids Capillary action – spontaneous rising of a liquid in a narrow tube: Cohesive forces – intermolecular forces among the molecules of the liquid. Adhesive forces – forces between the liquid molecules and their container. Return to TOC Copyright © Cengage Learning. All rights reserved
54
Meniscus Formation What conclusion can we draw about the cohesive forces in mercury? Water wets the glass (adhesive forces) and its attraction for glass forms a concave-up surface. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
55
Convex Meniscus Formed by Nonpolar Liquid Mercury
Section 10.2 The Liquid State Atomic Masses Convex Meniscus Formed by Nonpolar Liquid Mercury Which force dominates alongside the glass tube – cohesive or adhesive forces? cohesive forces Return to TOC Copyright © Cengage Learning. All rights reserved
56
Concave Meniscus Formed by Polar Water
Section 10.2 The Liquid State Atomic Masses Concave Meniscus Formed by Polar Water Which force dominates alongside the glass tube – cohesive or adhesive forces? adhesive forces Return to TOC Copyright © Cengage Learning. All rights reserved
57
Adhesive and Cohesive Forces
The liquid spreads, because adhesive forces are comparable in strength to cohesive forces. The liquid “beads up.” Which forces are stronger, adhesive or cohesive? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
58
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Capillary Action The adhesive forces wet more and more of the inside of the tiny tube, drawing water farther up the tube. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
59
Viscosity – measure of a liquid’s resistance to flow:
Section 10.2 The Liquid State Atomic Masses Liquids Viscosity – measure of a liquid’s resistance to flow: Liquids with large intermolecular forces or molecular complexity tend to be highly viscous. Return to TOC Copyright © Cengage Learning. All rights reserved
60
Comparing Viscosity Which oil flows more readily?
Which oil has stronger intermolecular forces between its molecules? Oil is mostly hydrocarbons; what kind of forces are these? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
61
Disorder in the structures Glass Crystalline Solids:
Section 10.3 An Introduction to Structures and Types of Solids The Mole Solids Amorphous Solids: Disorder in the structures Glass Crystalline Solids: Ordered Structures Unit Cells Return to TOC Copyright © Cengage Learning. All rights reserved
62
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Types of Solids Amorphous solids have no significant long-range order. Crystalline solids have atoms/ions/molecules arranged in a regular pattern. Types of crystalline solids include: Molecular solids, containing molecules held to one another by dispersion/dipole–dipole/ hydrogen bonding forces. Network (covalent) solids. Ionic solids. Metallic solids (metals). Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
63
Three Cubic Unit Cells and the Corresponding Lattices
Section 10.3 An Introduction to Structures and Types of Solids The Mole Three Cubic Unit Cells and the Corresponding Lattices Return to TOC Copyright © Cengage Learning. All rights reserved
64
Ionic Bonds as “Intermolecular” Forces
There are no molecules in an ionic solid, and therefore there can’t be any intermolecular forces. The attractions are electrostatic interionic attractions. Lattice energy (Chapter 9) is a measure of the strength of interionic attraction. The attractive force between a pair of oppositely charged ions increases: as the charges on the ions increase. as the ionic radii decrease. Lattice energies increase accordingly. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
65
Interionic Forces of Attraction
Mg2+ and O2– have much stronger forces of attraction for one another than do Na+ and Cl– . Melting point of MgO is about 2800 oC. Melting point of NaCl is about 801 oC. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
66
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Example 11.9 Arrange the ionic solids MgO, NaBr, and NaCl in the expected order of increasing melting point. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
67
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Crystal Lattices To describe crystals, three-dimensional views must be used. The repeating unit of the lattice is called the unit cell. There are a number of different types of unit cell; hexagonal, rhombic, cubic, etc. The three types of cubic unit cells are: simple cubic, body-centered cubic (bcc), face-centered cubic (fcc). Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
68
Cubic Unit Cells The unit cell is a cube in each case.
Whole atoms shown for clarity. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
69
Used to determine the interatomic spacings.
Section 10.3 An Introduction to Structures and Types of Solids The Mole Bragg Equation Used to determine the interatomic spacings. n = integer = wavelength of the X rays d = distance between the atoms = angle of incidence and reflection Return to TOC Copyright © Cengage Learning. All rights reserved
70
An Introduction to Structures and Types of Solids The Mole
Section 10.3 An Introduction to Structures and Types of Solids The Mole Bragg Equation Return to TOC Copyright © Cengage Learning. All rights reserved
71
Types of Crystalline Solids
Section 10.3 An Introduction to Structures and Types of Solids The Mole Types of Crystalline Solids Ionic Solids – ions at the points of the lattice that describes the structure of the solid. Molecular Solids – discrete covalently bonded molecules at each of its lattice points. Atomic Solids – atoms at the lattice points that describe the structure of the solid. Return to TOC Copyright © Cengage Learning. All rights reserved
72
Examples of Three Types of Crystalline Solids
Section 10.3 An Introduction to Structures and Types of Solids The Mole Examples of Three Types of Crystalline Solids Return to TOC Copyright © Cengage Learning. All rights reserved
73
Classification of Solids
Section 10.3 An Introduction to Structures and Types of Solids The Mole Classification of Solids Return to TOC Copyright © Cengage Learning. All rights reserved
74
Assumes that metal atoms are uniform, hard spheres.
Section 10.4 Structure and Bonding in Metals Closest Packing Model Closest Packing: Assumes that metal atoms are uniform, hard spheres. Spheres are packed in layers. Return to TOC Copyright © Cengage Learning. All rights reserved
75
Animations for Closest Packing
Section 10.4 Structure and Bonding in Metals Animations for Closest Packing Simple Cubic Animation ement/chemistry_chang10e/animations/sphere_packing _simple.swf Cubic Closest Packing Animation ement/chemistry_chang10e/animations/sphere_packing _cubic_close.swf Return to TOC Copyright © Cengage Learning. All rights reserved
76
Close-Packed Structures
A close packed structure in two dimensions. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
77
Close Packing in Three Dimensions
Third layer directly above first layer: HCP Two layers, stacked, give two different locations for the third layer … Third layer over the octahedral holes in the second layer: CCP Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
78
The Closest Packing Arrangement of Uniform Spheres
Section 10.4 Structure and Bonding in Metals The Closest Packing Arrangement of Uniform Spheres aba packing – the 2nd layer is like the 1st but it is displaced so that each sphere in the 2nd layer occupies a dimple in the 1st layer. The spheres in the 3rd layer occupy dimples in the 2nd layer so that the spheres in the 3rd layer lie directly over those in the 1st layer. Return to TOC Copyright © Cengage Learning. All rights reserved
79
The Closest Packing Arrangement of Uniform Spheres
Section 10.4 Structure and Bonding in Metals The Closest Packing Arrangement of Uniform Spheres abc packing – the spheres in the 3rd layer occupy dimples in the 2nd layer so that no spheres in the 3rd layer lie above any in the 1st layer. The 4th layer is like the 1st. Return to TOC Copyright © Cengage Learning. All rights reserved
80
Hexagonal Closest Packing
Section 10.4 Structure and Bonding in Metals Hexagonal Closest Packing Return to TOC Copyright © Cengage Learning. All rights reserved
81
Structure and Bonding in Metals
Section 10.4 Structure and Bonding in Metals Cubic Closest Packing Return to TOC Copyright © Cengage Learning. All rights reserved
82
The Indicated Sphere Has 12 Nearest Neighbors
Section 10.4 Structure and Bonding in Metals The Indicated Sphere Has 12 Nearest Neighbors Each sphere in both ccp and hcp has 12 equivalent nearest neighbors. Return to TOC Copyright © Cengage Learning. All rights reserved
83
The Net Number of Spheres in a Face-Centered Cubic Unit Cell
Section 10.4 Structure and Bonding in Metals The Net Number of Spheres in a Face-Centered Cubic Unit Cell Return to TOC Copyright © Cengage Learning. All rights reserved
84
Determine the number of metal atoms in a unit cell if the packing is:
Section 10.4 Structure and Bonding in Metals Concept Check Determine the number of metal atoms in a unit cell if the packing is: Simple cubic Cubic closest packing 1 metal atom 4 metal atoms 1 metal atom 4 metal atoms Return to TOC Copyright © Cengage Learning. All rights reserved
85
A metal crystallizes in a face-centered cubic structure.
Section 10.4 Structure and Bonding in Metals Concept Check A metal crystallizes in a face-centered cubic structure. Determine the relationship between the radius of the metal atom and the length of an edge of the unit cell. Length of the edge = r×sqrt(8) Return to TOC Copyright © Cengage Learning. All rights reserved
86
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Example 11.10 Copper crystallizes in the cubic close-packed arrangement. The atomic (metallic) radius of a Cu atom is pm. (a) What is the length, in picometers, of the unit cell in a sample of copper metal? (b) What is the volume of that unit cell, in cubic centimeters? (c) How many atoms belong to the unit cell? Example 11.11 Use the results of Example 11.10, the molar mass of copper, and Avogadro’s number to calculate the density of metallic copper. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
87
Calculate the density of the silver metal. Density = 10.5 g/cm3
Section 10.4 Structure and Bonding in Metals Concept Check Silver metal crystallizes in a cubic closest packed structure. The face centered cubic unit cell edge is 409 pm. Calculate the density of the silver metal. Density = 10.5 g/cm3 The density is 10.5 g/cm3. There are four silver atoms per unit cell. The volume of the unit cell is d3, which is (409 pm)3, or 6.84 × 107 pm3. This is equivalent to 6.84 × cm3. Density = mass/volume = [(4 atoms)(107.9 g/mol)(1 mol/6.022×1023 atoms)] / 6.84 × cm3 = 10.5 g/cm3 Return to TOC Copyright © Cengage Learning. All rights reserved
88
Bonding Models for Metals
Section 10.4 Structure and Bonding in Metals Bonding Models for Metals Electron Sea Model Band Model (MO Model) Return to TOC Copyright © Cengage Learning. All rights reserved
89
A regular array of cations in a “sea” of mobile valence electrons.
Section 10.4 Structure and Bonding in Metals The Electron Sea Model A regular array of cations in a “sea” of mobile valence electrons. Return to TOC Copyright © Cengage Learning. All rights reserved
90
Structure and Bonding in Metals
Section 10.4 Structure and Bonding in Metals Molecular Orbital Energy Levels Produced When Various Numbers of Atomic Orbitals Interact Return to TOC Copyright © Cengage Learning. All rights reserved
91
The Band Model for Magnesium
Section 10.4 Structure and Bonding in Metals The Band Model for Magnesium Virtual continuum of levels, called bands. Return to TOC Copyright © Cengage Learning. All rights reserved
92
Section 10.4 Structure and Bonding in Metals Metal Alloys Substitutional Alloy – some of the host metal atoms are replaced by other metal atoms of similar size. Interstitial Alloy – some of the holes in the closest packed metal structure are occupied by small atoms. Return to TOC Copyright © Cengage Learning. All rights reserved
93
Brass is a substitutional alloy.
Section 10.4 Structure and Bonding in Metals Two Types of Alloys Brass is a substitutional alloy. Steel is an interstitial alloy. Return to TOC Copyright © Cengage Learning. All rights reserved
94
Carbon and Silicon: Network Atomic Solids
Section 10.5 Carbon and Silicon: Network Atomic Solids Network Solids Pull from the following link l?layer=item&src=ch10/qtiflash_ch10_overview_p1.xml&w=645&h=428 Return to TOC Copyright © Cengage Learning. All rights reserved
95
The Structures of Diamond and Graphite
Section 10.5 Carbon and Silicon: Network Atomic Solids The Structures of Diamond and Graphite Return to TOC Copyright © Cengage Learning. All rights reserved
96
Network Covalent Solids
Network solids have a network of covalent bonds that extend throughout the solid, holding it firmly together. The allotropes of carbon provide good examples. Diamond has each carbon bonded to four other carbons in a tetrahedral arrangement using sp3 hybridization. Graphite has each carbon bonded to three other carbons in the same plane using sp2 hybridization. Fullerenes are roughly spherical collections of carbon atoms in the shape of a soccer ball. A nanotube can be thought of as a plane of graphite rolled into a tube. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
97
Crystal Structure of Diamond
Three-dimensional network is extremely strong, rigid. What kind of forces must be overcome to melt diamond? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
98
Crystal Structure of Graphite
Hexagons of sp2-hybridized carbon atoms. Forces between layers are relatively weak. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
99
Structure of a Buckyball
C60 molecule Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
100
Structure of a Nanotube
A nanotube can be thought of as a sheet of graphite, rolled into a tube, capped with half of a buckyball. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
101
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
102
Carbon and Silicon: Network Atomic Solids
Section 10.5 Carbon and Silicon: Network Atomic Solids Partial Representation of the Molecular Orbital Energies in a) Diamond b) a Typical Metal Return to TOC Copyright © Cengage Learning. All rights reserved
103
The p Orbitals and Pi-system in Graphite
Section 10.5 Carbon and Silicon: Network Atomic Solids The p Orbitals and Pi-system in Graphite Return to TOC Copyright © Cengage Learning. All rights reserved
104
Section 10.5 Carbon and Silicon: Network Atomic Solids Ceramics Typically made from clays (which contain silicates) and hardened by firing at high temperatures. Nonmetallic materials that are strong, brittle, and resistant to heat and attack by chemicals. Return to TOC Copyright © Cengage Learning. All rights reserved
105
Section 10.5 Carbon and Silicon: Network Atomic Solids Semiconductors n-type semiconductor – substance whose conductivity is increased by doping it with atoms having more valence electrons than the atoms in the host crystal. p-type semiconductor – substance whose conductivity is increased by doping it with atoms having fewer valence electrons than the atoms of the host crystal. Return to TOC Copyright © Cengage Learning. All rights reserved
106
Carbon and Silicon: Network Atomic Solids
Section 10.5 Carbon and Silicon: Network Atomic Solids Energy Level Diagrams for (a) an n-type Semiconductor (b) a p-type Semiconductor Return to TOC Copyright © Cengage Learning. All rights reserved
107
Silicon Crystal Doped with (a) Arsenic and (b) Boron
Section 10.5 Carbon and Silicon: Network Atomic Solids Silicon Crystal Doped with (a) Arsenic and (b) Boron Return to TOC Copyright © Cengage Learning. All rights reserved
108
Pull from the following link
Section 10.6 Molecular Solids Pull from the following link layer=item&src=ch10/qtiflash_ch10_overview_p1.xml&w=645&h=428 Return to TOC Copyright © Cengage Learning. All rights reserved
109
Pull from the following link
Section 10.7 Ionic Solids Pull from the following link layer=item&src=ch10/qtiflash_ch10_overview_p1.xml&w=645&h=428 Return to TOC Copyright © Cengage Learning. All rights reserved
110
Three Types of Holes in Closest Packed Structures
Section 10.7 Ionic Solids Three Types of Holes in Closest Packed Structures Trigonal holes are formed by three spheres in the same layer. Return to TOC Copyright © Cengage Learning. All rights reserved
111
Three Types of Holes in Closest Packed Structures
Section 10.7 Ionic Solids Three Types of Holes in Closest Packed Structures Tetrahedral holes are formed when a sphere sits in the dimple of three spheres in an adjacent layer. Return to TOC Copyright © Cengage Learning. All rights reserved
112
Three Types of Holes in Closest Packed Structures
Section 10.7 Ionic Solids Three Types of Holes in Closest Packed Structures Octahedral holes are formed between two sets of three spheres in adjoining layers of the closest packed structures. Return to TOC Copyright © Cengage Learning. All rights reserved
113
trigonal < tetrahedral < octahedral
Section 10.7 Ionic Solids For spheres of a given diameter, the holes increase in size in the order: trigonal < tetrahedral < octahedral Return to TOC Copyright © Cengage Learning. All rights reserved
114
Types and Properties of Solids
Section 10.7 Ionic Solids Types and Properties of Solids Return to TOC Copyright © Cengage Learning. All rights reserved
115
Ionic Crystal Structures
Ionic crystals have two different types of structural units—cations and anions. The cations and anions ordinarily are different sizes. Smaller cations can fill the voids between the larger anions. Where the cations go depends on the size of the cations and on the size of the voids. The smallest voids are the tetrahedral holes, then the octahedral holes, and finally the holes in a cubic structure. Therefore … Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
116
Ionic Crystal Structures
Tetrahedral hole filling occurs when the cations are small; when the radii ratio is: 0.225 < rc/ra < 0.414 Octahedral filling occurs with larger cations, when the radii ratio is: 0.414 < rc/ra < 0.732 The arrangement is cubic if rc/ra > Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
117
Unit Cell of Cesium Chloride
How many cesium ions are inside this unit cell? How many chloride ions? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
118
Unit Cell of Sodium Chloride
How many sodium ions are inside this unit cell? How many chloride ions? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
119
Experimental Determination of Crystal Structures
X rays Angle of diffraction can be used to find distance d, using simple trigonometry. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
120
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Cumulative Example Here are some data about an organic compound: Its normal boiling point is a few degrees below that of H2O(l), and its vapor density at 99.0 °C and 752 Torr is within 5% of 2.0 g/L. Using these data and other information from this and previous chapters, determine which one of the following compounds it is most likely to be: (CH3)2O CH3CH2CH2OH CH3CH2OCH3 HOCH2CH2OH Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
121
Vaporization and Condensation
Vaporization is the conversion of a liquid to a gas. The enthalpy of vaporization (ΔHvapn) is the quantity of heat that must be absorbed to vaporize a given amount of liquid at a constant temperature. Condensation is the reverse of vaporization. The enthalpy of condensation (ΔHcondn) accompanies this change of a gas to a liquid. Enthalpy is a function of state: therefore, if a liquid is vaporized and the vapor condensed at constant temperature, the total ΔH must be zero: ΔHvapn + ΔHcondn = 0 ΔHcondn = –ΔHvapn Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
122
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
123
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Vapor Pressure The vapor pressure of a liquid is the partial pressure exerted by the vapor when it is in dynamic equilibrium with the liquid at a constant temperature. vaporization Liquid Vapor condensation Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
124
Vapor Pressure Animation
vanced_placement/chemistry_chang10e/ani mations/vapor_pressure.swf Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
125
Liquid–Vapor Equilibrium
… until equilibrium is attained. More vapor forms; rate of condensation of that vapor increases … Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
126
Vapor pressure increases with temperature; why?
Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
127
Vapor Pressure and Changes of State
Section 10.8 Vapor Pressure and Changes of State Behavior of a Liquid in a Closed Container a) Initially b) at Equilibrium Return to TOC Copyright © Cengage Learning. All rights reserved
128
The Rates of Condensation and Evaporation
Section 10.8 Vapor Pressure and Changes of State The Rates of Condensation and Evaporation Return to TOC Copyright © Cengage Learning. All rights reserved
129
Pressure of the vapor present at equilibrium.
Section 10.8 Vapor Pressure and Changes of State Vapor Pressure Pressure of the vapor present at equilibrium. The system is at equilibrium when no net change occurs in the amount of liquid or vapor because the two opposite processes exactly balance each other. Return to TOC Copyright © Cengage Learning. All rights reserved
130
What is the vapor pressure of water at 100°C? How do you know?
Section 10.8 Vapor Pressure and Changes of State Concept Check What is the vapor pressure of water at 100°C? How do you know? 1 atm The vapor pressure of water at 100oC is 1 atm. You know this because atmospheric pressure is 1 atm and this is the temperature at which we observe water to boil. Return to TOC Copyright © Cengage Learning. All rights reserved
131
Vapor Pressure and Changes of State
Section 10.8 Vapor Pressure and Changes of State Vapor Pressure Return to TOC Copyright © Cengage Learning. All rights reserved
132
Vapor pressure increases significantly with temperature.
Section 10.8 Vapor Pressure and Changes of State Vapor Pressure Liquids in which the intermolecular forces are strong have relatively low vapor pressures. Vapor pressure increases significantly with temperature. Return to TOC Copyright © Cengage Learning. All rights reserved
133
Vapor Pressure vs. Temperature
Section 10.8 Vapor Pressure and Changes of State Vapor Pressure vs. Temperature Return to TOC Copyright © Cengage Learning. All rights reserved
134
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Vapor Pressure Curves CS2 CH3OH CH3CH2OH H2O C6H5NH2 What is the vapor pressure of H2O at 100 °C, according to this graph? What is the significance of that numeric value of vapor pressure? Which of the five compounds has the strongest intermolecular forces? How can you tell? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
135
Clausius–Clapeyron Equation
Section 10.8 Vapor Pressure and Changes of State Clausius–Clapeyron Equation Pvap = vapor pressure ΔHvap = enthalpy of vaporization R = J/K·mol T = temperature (in kelvin) Return to TOC Copyright © Cengage Learning. All rights reserved
136
Section 10.8 Vapor Pressure and Changes of State Concept Check The vapor pressure of water at 25°C is torr, and the heat of vaporization of water at 25°C is 43.9 kJ/mol. Calculate the vapor pressure of water at 65°C. 194 torr ln(23.8 torr/Pvap,T2) = [(43900 J/mol)/( J/K·mol)][(1/338 K) – (1/298)] Pvap,T2 = 194 torr Return to TOC Copyright © Cengage Learning. All rights reserved
137
Vapor Pressure and Changes of State
Section 10.8 Vapor Pressure and Changes of State Changes of State Pull from the following link layer=item&src=ch10/qtiflash_ch10_overview_p1.xml&w=645&h=428 Return to TOC Copyright © Cengage Learning. All rights reserved
138
Vapor Pressure and Changes of State
Section 10.8 Vapor Pressure and Changes of State THURS - Left Left off here with quick discussion Return to TOC Copyright © Cengage Learning. All rights reserved
139
Heating Curve for Water
Section 10.8 Vapor Pressure and Changes of State Heating Curve for Water Return to TOC Copyright © Cengage Learning. All rights reserved
140
Section 10.8 Vapor Pressure and Changes of State Concept Check Which would you predict should be larger for a given substance: ΔHvap or ΔHfus? Explain why. ΔHvap should be larger because it will take a lot more energy to break the intermolecular forces between the liquid molecules to completely break apart to form a gas. Return to TOC Copyright © Cengage Learning. All rights reserved
141
Phase equilibrium lines
Section 10.9 Phase Diagrams A convenient way of representing the phases of a substance as a function of temperature and pressure: Triple point Critical point Phase equilibrium lines Return to TOC Copyright © Cengage Learning. All rights reserved
142
Boiling Point and Critical Point
Boiling point: the temperature at which the vapor pressure of the liquid equals the external pressure. Normal boiling point: boiling point at 1 atm. Critical temperature (Tc): the highest temperature at which a liquid can exist. 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. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
143
The Critical Point At Tc, the densities of liquid and vapor are equal; a single phase. At room temperature there is relatively little vapor, and its density is low. At higher temperature, there is more vapor, and its density increases … … while the density of the liquid decreases; molecular motion increases. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
144
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
These four gases can’t be liquefied at room temperature, no matter what pressure is applied; why not? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
145
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Example A Conceptual Example To keep track of how much gas remains in a cylinder, we can weigh the cylinder when it is empty, when it is full, and after each use. In some cases, though, we can equip the cylinder with a pressure gauge and simply relate the amount of gas to the measured gas pressure. Which method should we use to keep track of the bottled propane, C3H8, in a gas barbecue? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
146
Phase Changes Involving Solids
Melting (fusion): transition of solid liquid. Melting point: temperature at which melting occurs. Same as freezing point! Enthalpy of fusion, ΔHfusion, is the quantity of heat required to melt a set amount (one gram, one mole) of solid. Sublimation: transition of solid vapor. Example: Ice cubes slowly “disappear” in the freezer. Enthalpy of sublimation, ΔHsubln, is the sum of the enthalpies of fusion and vaporization. Triple point: all three phases—solid, liquid, vapor—are in equilibrium. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
147
Some Enthalpies of Fusion
Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
148
Cooling Curve for Water
Once all of the liquid has solidified, the temperature again drops. The liquid water cools until … … the freezing point is reached, at which time the temperature remains constant as solid forms. If the liquid is cooled carefully, it can supercool. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
149
Heating Curve for Water
… until the solid begins to melt, at which time the temperature remains constant … The temperature of the solid increases as it is heated … … until all the solid is melted, at which time the temperature again rises. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
150
Phase Diagrams A—D, solid-liquid equilibrium. A—C, liquid-vapor equilibrium. A phase diagram is a graphical representation of the conditions of temperature and pressure under which a substance exists as a solid, liquid, a gas, or some combination of these in equilibrium. Triple point A—B, solid-vapor equilibrium. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
151
Phase Diagram for HgI2 HgI2 has two solid phases, red and yellow.
As the vessel is allowed to cool, will the contents appear more red or more yellow? Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
152
Phase Diagram for CO2 Note that at 1 atm, only the solid and vapor phases of CO2 exist. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
153
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Phase Diagram for H2O Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
154
General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
Example A Conceptual Example In Figure 11.14, 50.0 mol H2O(g) (steam) at °C and 1.00 atm is added to an insulated cylinder that contains 5.00 mol H2O(s) (ice) at 0 °C. With a minimum of calculation, use the data provided to determine which of the following will describe the final equilibrium condition: (a) ice and liquid water at 0 °C, (b) liquid water at 50 °C, (c) steam and liquid water at 100 °C, (d) steam at 100 °C. Data you will need are ΔHfusion = kJ/mol, ΔHvapn = 40.6 kJ/mol (at 100 °C), molar heat capacity of H2O(l) = 76 J mol–1 °C–1. Prentice Hall © 2005 Chapter Eleven General Chemistry 4th edition, Hill, Petrucci, McCreary, Perry
155
Phase Diagram for Carbon Dioxide
Section 10.9 Phase Diagrams Phase Diagram for Carbon Dioxide Return to TOC Copyright © Cengage Learning. All rights reserved
156
Phase Diagram for Water
Section 10.9 Phase Diagrams Phase Diagram for Water Return to TOC Copyright © Cengage Learning. All rights reserved
157
Phase Diagrams Concept Check
Section 10.9 Phase Diagrams Concept Check As intermolecular forces increase, what happens to each of the following? Why? Boiling point Viscosity Surface tension Enthalpy of fusion Freezing point Vapor pressure Heat of vaporization Boiling point increases Viscosity increases Surface tension increases Enthalpy of fusion increases Freezing point increases Vapor pressure decreases Heat of vaporization increases Return to TOC Copyright © Cengage Learning. All rights reserved
158
Chapter 10 review questions - pg. 472-474
Section 10.9 Phase Diagrams Chapter 10 review questions - pg m - 20 questions for review Born-Haber Cycles 22 question quiz on phase diagrams ms.htm 16 questions Phase-Energy Diagrams #2 ms2.htm Return to TOC Copyright © Cengage Learning. All rights reserved
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.