Chapter 9. Liquids and Solids

Transcription

1 Chapter 9 Liquids and Solids

2 Chapter 9 Table of Contents (9.1) (9.2) (9.3) (9.4) (9.5) (9.6) (9.7) (9.8) (9.9) (9.10) Intermolecular forces The liquid state An introduction to structures and types of solids Structure and bonding in metals Carbon and silicon: Network atomic solids Molecular solids Ionic solids The various forces in substances: Summary and comparison Vapor pressure and changes of state Phase diagrams

3 Chapter 9 Questions to Consider Why is white phosphorus stored in water and not left out in the open like sulfur? What causes the steaming of a piece of dry ice?

4 Section 9.1 Intermolecular Forces An Introduction Intramolecular bonding - Atoms form molecules by sharing electrons Bonding within the molecule Stronger than intermolecular forces Liquids and solids are the condensed states of matter They are formed by forces that may involve: Covalent bonding Ionic bonding Intermolecular forces

5 Section 9.1 Intermolecular Forces Figure Schematic Representations of the Three States of Matter

6 Section 9.1 Intermolecular Forces Phase Changes Change of state from solid to liquid to gas does not involve change in molecules, but change in forces among molecules Solid to liquid By adding energy, the motion of molecules increase Molecules eventually have greater movement and the disorder characteristics of a liquid Liquid to gas By adding more energy, individual molecules move far apart, reducing interaction

7 Section 9.1 Intermolecular Forces Table Densities of the Three States of Water

8 Section 9.1 Intermolecular Forces Intermolecular Forces They are forces that occur between molecules and include: Dipole dipole forces Hydrogen bonding London dispersion forces

9 Section 9.1 Intermolecular Forces Dipole Dipole Forces Exhibited by molecules with polar bonds that behave in an electric field Attract each other electrostatically Also called dipole dipole attraction Dipoles find the best compromise between attraction and repulsion Characteristics: Only 1% as strong as covalent or ionic bonds Forces grow weaker as distance between dipoles increase

10 Section 9.1 Intermolecular Forces Figure Dipole Dipole Forces (a) The electrostatic interaction of two polar molecules (b) The interaction of many dipoles in a condensed state

11 Section 9.1 Intermolecular Forces Hydrogen Bonding Strong dipole dipole forces can be noticed when H is bound to lone pairs on highly electronegative atoms like N, O 2, and F Strength of interactions can be characterized by: Polarity of the bond Close approach of the dipoles Small size of the hydrogen atom Such bonding affects the physical properties of elements Important in organic molecules

12 Section 9.1 Intermolecular Forces Figure 9.3 (b) - Hydrogen Bonding Among Water Molecules Blue dotted lines represent intermolecular forces between the water molecules

13 Section 9.1 Intermolecular Forces Figure The Boiling Points of the Covalent Hydrides of the Elements in Groups 4A, 5A, 6A, and 7A

14 Section 9.1 Intermolecular Forces London Dispersion Forces They exist among noble gas atoms and nonpolar molecules Instantaneous dipole that occurs accidentally in a given atom induces a similar dipole in a neighboring atom Instigates weak and short-lived interatomic attraction Polarizability - Ease with which the electron cloud of an atom can be distorted to produce dipolar charge distribution Large atoms with many electrons have high polarizability Also applies to nonpolar molecules

15 Section 9.1 Intermolecular Forces Figure 9.5 (a) - Polarization

16 Section 9.1 Intermolecular Forces Concept Check Which of the following is the stronger bond? a. Intramolecular bond b. Intermolecular bond Justify the answer with a valid reason

17 Section 9.1 Intermolecular Forces Concept Check Identify the molecule that is capable of forming stronger intermolecular forces? N 2 H 2 O Justify the choice with a valid reason

18 Section 9.1 Intermolecular Forces Concept Check Following are the Lewis structures for ethanol and dimethyl ether: H H C H H C H O H H C Compare the boiling points of the two molecules H H O H C H H

19 Section 9.1 Intermolecular Forces Concept Check Which gas would behave more ideally at the same pressure and temperature? CO N 2 Justify the choice with a valid reason

20 Section 9.2 The Liquid State Characteristics of Liquids Liquids exhibit low compressibility, lack of rigidity, and high density Surface tension is the resistance of a liquid to an increase in its surface area Liquids with large intermolecular forces tend to have high surface tensions Capillary action is exhibited by polar liquids and involves spontaneous rising of a liquid in a narrow tube Involves adhesive and cohesive forces

21 Section 9.2 The Liquid State Figure Convex and Concave Meniscus Nonpolar liquid, mercury, forms a convex meniscus in a glass tube, whereas polar water forms a concave meniscus

22 Section 9.2 The Liquid State Characteristics of Liquids Viscosity refers to the measure of a liquid s resistance to flow Liquids with large intermolecular forces or molecular complexity tend to be highly viscous Example - Glycerol possess unusually high viscosity because it forms hydrogen bonds using its O H groups

23 Section 9.2 The Liquid State Structural Model for Liquids Liquids have strong intermolecular forces and significant molecular motion Rapid changes in liquids can be studied using spectroscopy A typical liquid contains a large number of regions with more disorder The number of regions where holes appear is smaller Their nature is highly dynamic, rapidly fluctuating in both regions

24 Section 9.3 An Introduction to Structures and Types of Solids Classification of Solids Amorphous solids have disordered structures Example - Glass Crystalline solids have a highly regular arrangement of components Positions of components are represented by lattice(s) A three-dimensional system of points that designates the position of the components of a substance The smallest repeating unit is termed a unit cell

25 Section 9.3 An Introduction to Structures and Types of Solids Figure Three Cubic Unit Cells and the Corresponding Lattices

26 Section 9.3 An Introduction to Structures and Types of Solids Figure Three Cubic Unit Cells and the Corresponding Lattices (Contd)

27 Section 9.3 An Introduction to Structures and Types of Solids X-Ray Analysis of Solids X-ray diffraction is used to determine the structure of crystalline solids Diffraction occurs due to: Constructive interference when parallel beam waves are in phase Destructive interference when waves are out of phase Distance traveled by waves depends on the distance between the atoms A diffractometer is used to carry out X-ray analysis of crystals

28 Section 9.3 An Introduction to Structures and Types of Solids The Bragg Equation Used in the estimation of interatomic spacing Where n is an integer λ is the wavelength of the X rays d is the distance between atoms nλ = 2 d sin θ is the angle of incidence and reflection

29 Section 9.3 An Introduction to Structures and Types of Solids Figure Reflection of X rays of Wavelength λ from a Pair of Atoms in two Different Layers of a Crystal

30 Section 9.3 An Introduction to Structures and Types of Solids Interactive Example Using the Bragg Equation X rays of wavelength 1.54 Å were used to analyze an aluminum crystal. A reflection was produced at θ= 19.3 degrees. Assuming n = 1, calculate the distance d between the planes of atoms producing this reflection Solution To determine the distance between the planes, use the Bragg equation where n = 1 λ = 1.54 Å θ= 19.3 degrees

31 Section 9.3 An Introduction to Structures and Types of Solids Interactive Example Using the Bragg Equation Since2 d sin θ = nλ d o A nλ o = = = 2.33A = 233 pm 2 sin θ

32 Section 9.3 An Introduction to Structures and Types of Solids Types of Crystalline Solids Ionic solids possess ions at the points of the lattice that describe their structures Molecular solids have discrete covalently bonded molecules at each lattice point(s) An atomic solid has atoms at the lattice points that describe its structure Metallic solids Network solids Group 8A (18) solids

33 Section 9.3 An Introduction to Structures and Types of Solids Figure Examples of Three Types of Crystalline Solids (a) An atomic solid (b) An ionic solid (c) A molecular solid

34 Section 9.3 An Introduction to Structures and Types of Solids Table Classification of Solids

35 Section 9.4 Structure and Bonding in Metals The Closest Packing Model Closest packing is an arrangement that assumes that metal atoms are hard, uniform spheres These spheres are packed in layers Each successive layer is formed when spheres occupy a dimple formed by the spheres of the previous layer Forms of closest packing: aba packing abc packing

36 Section 9.4 Structure and Bonding in Metals aba Packing The 2 nd layer is like the 1 st, but it is displaced, so that each sphere in the 2 nd layer occupies a dimple in the 1 st layer The spheres in the 3 rd layer occupy dimples in the 2 nd layer Spheres in the 3 rd layer lie directly over those in the 1 st layer The resultant structures are called hexagonal closest packed (hcp) structures The spheres in every layer occupy the same vertical position When the spheres are aba closest packed, the unit cell is a hexagonal prism

37 Section 9.4 Structure and Bonding in Metals Figure 9.13 (a) - The Closest Packing Arrangement of Uniform Spheres

38 Section 9.4 Structure and Bonding in Metals Figure Hexagonal Closest Packing

39 Section 9.4 Structure and Bonding in Metals abc Packing The spheres in the 3 rd layer occupy dimples in the 2 nd layer Spheres in the 3 rd layer do not rest above spheres in the 1 st layer The 4 th layer is like the 1 st The resultant structure is termed a cubic closest packed (ccp) structure The spheres in every fourth layer occupy the same vertical position In abc packing, the unit cell is face-centered cubic

40 Section 9.4 Structure and Bonding in Metals Figure 9.13 (b) - The Closest Packing Arrangement of Uniform Spheres

41 Section 9.4 Structure and Bonding in Metals Figure Cubic Closest Packing

42 Section 9.4 Structure and Bonding in Metals Common Characteristics of the hcp and the ccp Structures Each sphere in both structures possesses 12 equivalent nearest neighbors

43 Section 9.4 Structure and Bonding in Metals Net Number of Spheres in a Face-Centered Cubic Unit Cell - Derivation A unit cell is defined by the centers of the spheres on the corners of the cube Net number of spheres in a face-centered cubic unit would be = 4 8 2

44 Section 9.4 Structure and Bonding in Metals Interactive Example Calculating the Density of a Closest Packed Solid Silver crystallizes in a cubic closest packed structure. The radius of a silver atom is 144 pm. Calculate the density of solid silver Solution Density is mass per unit volume It is necessary to know how many silver atoms occupy a given volume in the crystal The structure is cubic closest packed, which means the unit cell is face-centered cubic Find the volume of this unit cell for silver and the net number of atoms it contains

45 Section 9.4 Structure and Bonding in Metals Interactive Example Calculating the Density of a Closest Packed Solid In the structure, the atoms touch along the diagonals for each face and not along the edges of the cube The length of the diagonal is r + 2r + r, or 4r Use this information to find the length along the edge of the cube by the Pythagorean theorem d + d = 4r 2 d = 16r d 2 2 = 8r 2 2 d r r 2 = 8 = 8

46 Section 9.4 Structure and Bonding in Metals Interactive Example Calculating the Density of a Closest Packed Solid Since r = 144 pm for a silver atom, d = 144 pm 8 = 407 pm The volume of the unit cell is d 3, which is (407 pm) 3, or pm 3 Converting to cubic centimeters, cm pm = cm pm

47 Section 9.4 Structure and Bonding in Metals Interactive Example Calculating the Density of a Closest Packed Solid It is known that the net number of atoms in the face-centered cubic unit cell is 4 4 silver atoms are contained in a volume of cm 3 Therefore, the density is mass Density = = 3 4 atoms107.9 g / mol1 mol / atoms volume cm = 10.6 g / cm 23 3

48 Section 9.4 Structure and Bonding in Metals Concept Check Determine the number of metal atoms in a unit cell if the packing is: a. Simple cubic b. Cubic closest

49 Section 9.4 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

50 Section 9.4 Structure and Bonding in Metals Bonding Models for Metals - An Introduction A successful bonding model for metals must consider: Malleability Ductility Efficient uniform conduction of heat and electricity Bonding models for metals include: Electron sea model Band model (MO model)

51 Section 9.4 Structure and Bonding in Metals Bonding Models for Metals Electron sea model A regular array of metal cations are considered to be in a sea of mobile valence electrons Mobile electrons conduct heat and electricity Ions can freely move around when the metal is hammered or drawn into a wire

52 Section 9.4 Structure and Bonding in Metals Figure The Electron Sea Model for Metals (a) Representation of an alkali metal (Group 1A) with one valence electron (b) Representation of an alkaline earth metal (Group 2A) with two valence electrons

53 Section 9.4 Structure and Bonding in Metals Bonding Models for Metals Band model, or the molecular orbital (MO) model Electrons are assumed to be traveling in molecular orbitals formed from the valence atomic orbitals of the metal atom Interaction between metal atoms results in a virtual continuum of levels, called bands

54 Section 9.4 Structure and Bonding in Metals Figure Molecular Orbital Energy Levels Produced When Various Numbers of Atomic Orbitals Interact

55 Section 9.4 Structure and Bonding in Metals Figure Representation of Energy Levels in a Magnesium Crystal

56 Section 9.4 Structure and Bonding in Metals Metal Alloys An alloy is a substance that contains a mix of elements and possesses metallic properties Classification of alloys: Substitutional alloy, where some of the host metal atoms are replaced by other metal atoms of similar size Example - Brass Interstitial alloy, where some of the holes in the closest packed metal structure are occupied by small atoms Example - Steel

57 Section 9.4 Structure and Bonding in Metals Figure Two Types of Alloys

58 Section 9.4 Structure and Bonding in Metals Carbon and Steel Amount of carbon affects the properties of steel Mild steel - Less than 0.2% carbon Malleable and ductile Can be drawn into nails, cables, and chains Medium steel to 0.6% carbon Harder than mild steel Used in structural steel beams High-carbon steel to 1.5% carbon Used for making cutlery and tools

59 Section 9.5 Carbon and Silicon: Network Atomic Solids Network Solids - An Introduction Network solids are those atomic solids that contain directional covalent bonds which form solids that can be viewed as giant molecules Properties: Brittle nature Ineffective conductors of heat and electricity Important elements: Carbon Diamond and graphite Silicon

60 Section 9.5 Carbon and Silicon: Network Atomic Solids Forms of Carbon - Diamond Hardest naturally occurring substance Each C atom is surrounded by a tetrahedral arrangement of other C atoms Structure as per the localized electron model: Stable structure is obtained via covalent bonds Formed by the overlap of sp 3 hybridized C atomic orbitals Structure as per the molecular orbital theory: Large gaps between filled and empty levels Electron transfer is not easy

61 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure 9.22 (a) - The Structure of Diamond

62 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure 9.23 (a) - Partial Representation of the Molecular Orbital Energies in Diamond

63 Section 9.5 Carbon and Silicon: Network Atomic Solids Forms of Carbon - Graphite Slippery, black, and a conductor of heat and electricity Structure is based on layers of C atoms arranged in fused sixmembered rings Structure as per the localized electron model: Shows trigonal planar arrangement 120-degree bond angles sp 2 hybridization Three sp 2 orbitals on each C atom fuse to form σ bonds with three other C atoms One 2p orbital remains unhybridized, perpendicular to the plane

64 Section 9.5 Carbon and Silicon: Network Atomic Solids Forms of Carbon - Graphite Structure as per the molecular orbital theory: All orbitals combine to form MOs Assist in the stability of graphite Delocalized electrons account for good electrical conductivity Used as lubricants in locks Slipperiness can be attributed to the strong bonding within the C atom layers rather than between the layers By applying 150,000 atm pressure at 2800 C, graphite can be converted to a diamond

65 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure 9.22 (b) - The Structure of Graphite

66 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure The p Orbitals and the -Bonding Network in Graphite

67 Section 9.5 Carbon and Silicon: Network Atomic Solids Silicon An important constituent of the compounds that form the earth s crust Stable silicon compound involves chains with silicon oxygen bonds Fundamental silicon oxygen compound is silica (SiO 2 ) Structure Silicon does not use its 3p orbitals to form strong bonds with oxygen since the orbital size of silicon is larger Octet rule is satisfied by forming a network of SiO 4 tetrahedra with shared oxygen atoms

68 Section 9.5 Carbon and Silicon: Network Atomic Solids Structure of Quartz - A Silicate Quartz holds the same empirical formula as silica, SiO 2 It contains chains of SiO 4 tetrahedra that share O 2 atoms

69 Section 9.5 Carbon and Silicon: Network Atomic Solids Silicon and Silicates Those compounds that are closely related to silica are called silicates They constitute salts containing metal cations and polyatomic silicon oxygen anions Glass is formed when silica is heated above its melting point of 1600 C Also formed when substances like Na 2 CO 3 are added to the silica melt and then cooled Properties vary with varying additives

70 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure Examples of Silicate Anions

71 Section 9.5 Carbon and Silicon: Network Atomic Solids Table Compositions of Some Common Types of Glass

72 Section 9.5 Carbon and Silicon: Network Atomic Solids Ceramics Made from clays, based on silicates, and hardened by firing at high temperatures Nonmetallic materials that are strong, brittle, and resistant to high temperatures and attack by chemicals Heterogeneous nature Formed by the weathering action of water and CO 2 on the mineral feldspar, an aluminosilicate Weathered feldspar produces kaolinite, which consists of small, thin platelets with the empirical formula Al 2 Si 2 O 5 (OH) 4

73 Section 9.5 Carbon and Silicon: Network Atomic Solids Ceramics When dry, the platelets stick together, and finally interlock In the presence of water, they can slide over one another, illustrating the plasticity of clay After firing: Uses: Remaining water is driven off and silicates and cations form a glass which binds the tiny crystals of kaolinite Drawn into flexible superconducting wires by adding organic polymers Hold great promise with prosthetic devices

74 Section 9.5 Carbon and Silicon: Network Atomic Solids Semiconductors Electrons of certain elements like silicon can cross the energy gap at 25 C, making them a semiconducting element Conductivity increases with increasing temperature n-type semiconductor: A substance whose conductivity is increased by doping with atoms that have more valence electrons than those in the host crystal p-type semiconductors: A substance whose conductivity is increased by doping with atoms having fewer valence electrons than the atoms of the host crystal

75 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure Energy Level Diagrams for: (a) an n-type Semiconductor (b) a p-type Semiconductor

76 Section 9.5 Carbon and Silicon: Network Atomic Solids Semiconductors The connection of a p-type and an n-type form a p n junction where: A small number of electrons migrate from the n-type area to the p-type area where low-energy MOs are vacant Net effect of this migration is to place negative charge on the p-type region and positive charge on the n-type region This buildup, the contact or junction potential, prevents further migration Forward bias Reverse bias

77 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure 9.30 (a) - The Charge Carriers of the p-type and n-type Regions The charge carriers of the p-type region are holes In the n-type region the charge carriers are electrons

78 Section 9.5 Carbon and Silicon: Network Atomic Solids Figure 9.30 (b) and (c) - Reverse and Forward Bias

79 Section 9.6 Molecular Solids An Introduction to Molecular Solids Possess strong covalent bonding within molecules but weak forces between molecules Forces among the molecules depend on the nature of the molecules CO 2, I 2, P 4, and S 8 - No dipole moment; possess London dispersion forces Molecules that possess dipole moments have greater intermolecular forces, especially when hydrogen bonding is viable

80 Section 9.7 Ionic Solids Characteristics of Ionic Solids Stable with high-melting points Held together by strong electrostatic forces between oppositely charged ions Structure is based on closest packing of spheres so that: Electrostatic attraction between oppositely charged ions is maximized Repulsion among ions with like charges is minimized For spheres of a given diameter the holes increase in size in the order trigonal < tetrahedral < octahedral

81 Section 9.7 Ionic Solids Types of Holes in Closest Packed Structures Trigonal holes Formed by three spheres in a given plane Very small and are never occupied in binary ionic compounds

82 Section 9.7 Ionic Solids Types of Holes in Closest Packed Structures Tetrahedral holes Formed when a sphere occupies a dimple formed by three spheres in an adjacent layer Holes are occupied based on the relative size of the anion and the cation There are twice as many tetrahedral holes as packed anions in a closest packed structure

83 Section 9.7 Ionic Solids Figure The Tetrahedral Hole in the Face-Centered Cubic Unit Cell (a) (b) (c) The location (red X) of a tetrahedral hole in the face-centered cubic unit cell One of the tetrahedral holes The unit cell for ZnS where the S 2 ions (yellow) are closest packed with the Zn 2+ ions (red) in alternating tetrahedral holes

84 Section 9.7 Ionic Solids Types of Holes in Closest Packed Structures Octahedral holes Formed by six spheres in two adjacent layers The number of holes in a ccp structure is the same as the number of packed anions

85 Section 9.7 Ionic Solids Interactive Example Determining the Number of Ions in a Unit Cell Determine the net number of Na + and Cl ions in the sodium chloride unit cell Solution The Cl ions are cubic closest packed and thus form a facecentered cubic unit cell There is a Cl ion on each corner and one at the center of each face of the cube Thus the net number of Cl ions present in a unit cell is: = 4 8 2

86 Section 9.7 Ionic Solids Interactive Example Determining the Number of Ions in a Unit Cell The Na + ions occupy the octahedral holes located in the center of the cube and midway along each edge The Na + ion in the center of the cube is contained entirely in the unit cell, whereas those on the edges are shared by four unit cells Four cubes share a common edge Since the number of edges in a cube is 12, the net number of Na + ions present is: = 4 4

87 Section 9.7 Ionic Solids Interactive Example Determining the Number of Ions in a Unit Cell The net number of ions in a unit cell is 4 Na + ions and 4 Cl ions, which agrees with the 1:1 stoichiometry of sodium chloride

88 Section 9.7 Ionic Solids Table Types and Properties of Solids

89 Section 9.7 Ionic Solids Table Types and Properties of Solids (Contd)

90 Section 9.7 Ionic Solids Interactive Example Types of Solids Using the table on the types and properties of solids, classify each of the following substances according to the type of solid it forms a. Gold b. Carbon dioxide c. Lithium fluoride d. Krypton

91 Section 9.7 Ionic Solids Interactive Example Types of Solids Solution a. Solid gold is an atomic solid with metallic properties b. Solid carbon dioxide contains nonpolar carbon dioxide molecules and is a molecular solid c. Solid lithium fluoride contains Li + and F ions and is a binary ionic solid d. Solid krypton contains krypton atoms that can interact only through London dispersion forces It is an atomic solid but has properties characteristic of a molecular solid with nonpolar molecules

92 Section 9.8 The Various Forces in Substances: Summary and Comparison Table lntramolecular (Bonding) Forces

93 Section 9.8 The Various Forces in Substances: Summary and Comparison Table lntramolecular (Bonding) Forces (Contd)

94 Section 9.8 The Various Forces in Substances: Summary and Comparison Table Intermolecular Forces

95 Section 9.8 The Various Forces in Substances: Summary and Comparison Table Intermolecular Forces (Contd)

96 Section 9.9 Vapor Pressure and Change of State An Introduction Vaporization, or evaporation is an endothermic process whereby molecules of a liquid escape the liquid s surface and form gas Energy required to vaporize 1 mole of a liquid at a pressure of 1 atm is termed the heat of vaporization or the enthalpy of vaporization Symbolic representation - ΔH vap Example - Strong hydrogen bonding in the molecules of water in the liquid state leads to a large heat of vaporization

97 Section 9.9 Vapor Pressure and Change of State Vapor Pressure Equilibrium: A point where no further net change can be seen in the amount of liquid or vapor because evaporation and condensation balance each other The pressure of vapor present at equilibrium is also called equilibrium vapor pressure Vapor pressure increases with increase in temperature Sublimation: A substance is said to sublime when it changes directly from solid to gaseous phase without passing through the liquid phase

98 Section 9.9 Vapor Pressure and Change of State The Rates of Condensation and Evaporation The rate of evaporation remains constant and the rate of condensation increases as the number of molecules in the vapor phase increases, until the two rates become equal At this point, the equilibrium vapor pressure is attained

99 Section 9.9 Vapor Pressure and Change of State Figure Estimation of Vapor Pressure Using a Simple Barometer

100 Section 9.9 Vapor Pressure and Change of State Concept Check What is the vapor pressure of water at 100 C? Justify your answer

101 Section 9.9 Vapor Pressure and Change of State Determining Vapor Pressure Vapor pressure can be determined principally by the size of intermolecular forces in the liquid Liquids with large intermolecular forces have relatively low vapor pressures Molecules need a higher energy to escape the vapor phase Substances with large molar masses have low vapor pressures Attributed to larger dispersion forces

102 Section 9.9 Vapor Pressure and Change of State Vapor Pressure vs. Temperature Produces a straight line when plotted on a graph Where T - Temperature in Kelvin ΔH vap - Enthalpy of vaporization R - Universal gas constant ΔH vap 1 ln Pvap = + C R T C - Characteristics of a given liquid ln - Natural logarithm of vapor pressure

103 Section 9.9 Vapor Pressure and Change of State Figure 9.39(b) - Plots of In(P vap ) Versus 1/T for Water, Ethanol, and Diethyl Ether

104 Section 9.9 Vapor Pressure and Change of State The Clausius Clapeyron Equation When the values of ΔH vap and P vap at constant temperature are known, it is easy to calculate the value of P vap at another temperature Assume that C does not depend on temperature P vap, T ΔH vap 1 1 P vap, T R T 2 2 T1 1 ln =

105 Section 9.9 Vapor Pressure and Change of State Interactive Example Calculating Vapor Pressure The vapor pressure of water at 25 C is 23.8 torr, and the heat of vaporization of water at 25 C is 43.9 kj/mol. Calculate the vapor pressure of water at 50 C Solution Use the Clausius Clapeyron equation: P vap, T ΔH vap 1 1 P vap, T R T 2 2 T1 1 ln =

106 Section 9.9 Vapor Pressure and Change of State Interactive Example Calculating Vapor Pressure For water, we have: P vap,t1 = 23.8 torr T 1 = = 298K T 2 = = 323 K ΔH vap = 43.9 kj/mol R = J/K mol Thus, 23.8 torr 43,900 J / mol 1 1 ln = Pvap torr,t J / K mol 323 K 298 K ln = 1.37 P vap,t 2

107 Section 9.9 Vapor Pressure and Change of State Interactive Example Calculating Vapor Pressure Taking the antilog of both sides, 23.8 = P P vap,t vap,t 2 2 = 93.7 torr

108 Section 9.9 Vapor Pressure and Change of State Changes of State When a solid is heated, a heating curve can be observed A plot of temperature against time for a process where energy is added at a constant rate Enthalpy change that occurs at the melting point is called heat of fusion or enthalpy of fusion (ΔH fus ) Normal melting point: Temperature at which solid and liquid states have identical vapor pressure, and total pressure = 1 atm Normal boiling point: The temperature a which the vapor pressure of the liquid is exactly 1 atm

109 Section 9.9 Vapor Pressure and Change of State Figure Heating Curve for Water

110 Section 9.9 Vapor Pressure and Change of State Changes of State Water can be supercooled and remain in liquid state when: Temperature < 0 C Pressure = 1 atm Liquids can be superheated and raised to temperatures above their boiling point, when heated rapidly The supercooling of water, represented by S

111 Section 9.9 Vapor Pressure and Change of State Concept Check Which of the following should be larger for a given substance? Justify your answer H vap H fus

112 Section 9.10 Phase Diagrams Phase Diagrams - An Introduction A convenient way of representing the phases of a substance as a function of its temperature and pressure Triple point: The temperature at which all three phases exist simultaneously Critical point: The critical pressure and critical temperature, together, define this point Critical pressure: Pressure required to produce liquefaction at critical temperature Critical temperature: The temperature above which a liquid cannot be liquefied, irrespective of pressure applied

113 Section 9.10 Phase Diagrams Figure Phase Diagram for Water At point X on the phase diagram, water is a solid As the external pressure is increased while the temperature remains constant, the solid/liquid line is crossed and the ice melts

114 Section 9.10 Phase Diagrams Phase Diagram for Water - Interpretations and Observations The solid/liquid boundary line is a negative slope Melting point of ice decreases with increased external pressure At the melting point, liquid and solid are in dynamic equilibrium When pressure is applied, the volume is reduced A given mass of ice has more volume at 0 C than the same mass of water in liquid state Freezing point of water is less than 0 C when pressure is greater than 1 atm

115 Section 9.10 Phase Diagrams Phase Diagram of Water - Applications Ice skating Narrow blades of skates exert more pressure Frictional heat is caused when the skate moves over ice, contributing to further melting of ice As the blade passes by, the liquid refreezes since normal pressure and temperature are re-established Low density of ice ensures that the ice formed on rivers and lakes float, ensuring water bodies do not freeze in the winter In humid climates, snow and ice seem to sublime

116 Section 9.10 Phase Diagrams Figure Phase Diagram for Carbon Dioxide The liquid state does not exist at a pressure of 1 atm The solid/liquid line has a positive slope, since the density of solid carbon dioxide is greater than that of liquid carbon dioxide

117 Section 9.10 Phase Diagrams Phase Diagram for CO 2 - Interpretation and Applications Interpretations: Solid/liquid line is a positive slope Triple point occurs at 5.1 atm and 56.6 C Critical point can be noticed at 72.8 atm and 31 C Sublimation occurs at 78 C Applications: Dry ice - A convenient refrigerant because it does not undergo the liquid phase under normal atmospheric conditions Liquid form is used in fire extinguishers at 25 C under high pressure

118 Section 9.10 Phase Diagrams Concept Check As intermolecular forces increase, what happens to each of the following? Boiling point Viscosity Surface tension Enthalpy of fusion Freezing point Vapor pressure Heat of vaporization