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Intermolecular forces, Liquids and Solids

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1 Intermolecular forces, Liquids and Solids
Ch. 10 3/25/2017

2 Assumes shape/ volume of container –particles move past one another
Some Characteristics of Gases, Liquids and Solids and the Microscopic Explanation for the Behavior GAS LIQUID SOLID Assumes shape/ volume of container –particles move past one another Assumes shape of container –particles move/ slide past one another Retains fixed volume /shape –rigid particles locked in place Compressible-lots of free space between particles Not easily compressible -little free space between particles Not easily compressible- little free space between particles Flows easily-particles move past one another Flows easily-particles move/ slide past one another Does not flow easily-rigid particles cannot move/slide past one another Diffusion within gas occurs rapidly-expand easily to fill available space Diffusion within liquid occurs slowly-does not expand to fill container Diffusion within solid occurs extremely slowly Not dense More dense than gases More dense than liquid No significant attractive forces between molecules Significant attractive forces between molecules Most significant forces between molecules 3/25/2017

3 Intermolecular Forces
Ideal gas law used to describe gases Volume of gas molecule is too small 99.9% of gas is empty space Gas molecules so far apart No significant intermolecular attraction If gases truly ideal (zero volume/ attractive forces), couldn’t condense them to liquids 3/25/2017

4 To condense real gases Intermolecular attractive forces must overcome KE of gas molecules Increasing attractive forces by Decreasing distance between molecules Increasing pressure which forces gas molecules closer together Decreasing temperature lowers average KE 3/25/2017

5 Three recognized types of intermolecular attractions
Intramolecular Intramolecular 3/25/2017

6 Intermolecular forces (all electrostatic)
van der Waals forces (developed equation for predicting deviation of gases from ideal behavior) Dipole-Dipole attraction: dipole molecules orient themselves so that +/ ends close to each other London Dispersion Forces Relatively weak forces that exist among noble gas atoms/ nonpolar molecules. (Ar, C8H18) Caused by instantaneous dipole, in which electron distribution becomes asymmetrical Ease with which electron “cloud” of atom can be distorted-polarizability Hydrogen bonds: dipole-dipole attraction in which H is bound to highly electronegative atom (F/O/N) Ion-dipole force (solutions-also electrostatic) 3/25/2017

7 Ion-Dipole Forces Exists between ion and partial charge on end of polar molecule Important for solutions of ionic substance in polar liquids + ions surrounded by - ends of water molecules - ions surrounded by + ends of water molecule 3/25/2017

8 Dipole-Dipole Forces (about 1% strength of covalent bonds)
Weaker than ion-dipole forces Neutral polar molecules (dipoles) attract each other with δ+ / δ- ends Responsible for mutual solubility of polar molecules, such as NH3 in H2O Explains how and why polar molecules may be condensed to liquid state 3/25/2017

9 London Forces (dispersion forces, instantaneous dipole forces, induced dipole forces)
Weakest forces of attraction Main form of attraction in all nonpolar molecules No other type of van der Waals forces exist Nonpolar He/Ar can be condensed, so some kind of attractive interactions exist Movement of electrons within electron cloud cause instantaneous or momentary dipole moment (self-polarization) Resultant dipole induces polarization in neighboring molecules Mutual attraction of opposite ends of neighboring dipoles 3/25/2017

10 3/25/2017

11 An instant later, distribution of electrons shifts
As long as molecules are close together, this electron movement can occur over huge numbers of molecules Whole lattice of molecules can be held together in solid using van der Waals dispersion forces An instant later, distribution of electrons shifts 3/25/2017

12 Hydrogen Bonding special dipole-dipole attraction
Hydrogen covalently bonded to highly electronegative elements (N, O, F) Bond strength higher than other dipole-dipole attractions Important in bonding of molecules (water/DNA) 3/25/2017

13 3/25/2017

14 Strength of dispersion forces
Much weaker than covalent bonds Size of attraction varies considerably with size/shape of molecule In comparing intermolecular forces, molar mass is 1st consideration When molar masses comparable, differences in intermolecular attractions mainly due to differences in molecular polarity (strengths of dipole attraction) When molar masses differ greatly, differences in intermolecular attractions mainly due to differences in molar masses themselves (strength of London forces) 3/25/2017

15 Magnitude of self-polarization increases with increasing numbers of electrons
Polarizability indicates ease electron “cloud” of atom can be distorted to give dipolar charge distribution Large atoms with many electrons (electrons loosely held) exhibit higher polarizability than small atoms (electrons tightly held near nucleus) As atomic # increases, # electrons increases More electrons, more distance they can move Increased chance of temporary dipole and dipole interactions Bigger the dispersion forces 3/25/2017

16 In liquids and solids, molecules10x closer
Gaseous polar molecules show little attraction for each other (far apart) Rapidly become weaker as distance between dipoles increases Unimportant in gas phase due to distance between molecules In liquids and solids, molecules10x closer Boiling point (condensation point) indicative of attractive forces between molecules Measure of how much KE must be increased so that it can overcome attractive forces in liquid Greater attractive forces/polarity, higher BP Low boiling point indicates low attractive forces 3/25/2017

17 BP/MP increase going down group
# e’s/atomic radius increase Why I is solid/Br liquid at room temperature Why all halogens have much higher BPs than their neighboring noble gases More electrons = more distance they move = bigger temporary dipoles (“stickier”) = bigger dispersion forces Because of greater temporary dipoles, xenon molecules are "stickier" than smaller neon molecules Neon molecules will break away from each other at much lower temperatures than xenon molecules – neon has lower boiling point 3/25/2017

18 Shape of molecules More linear molecules w/greater contact between molecules have higher BP than more spherically shaped molecules Develop bigger temporary dipoles due to electron movement than short fat ones containing same numbers of electrons Long thin molecules lie closer together-attractions most effective if molecules really close Responsible for mutual solubility of nonpolar molecules such as Br2 in CCl4 Large electron clouds easily polarized, so they have higher BPs than neighboring noble gases 3/25/2017

19 The boiling point of Argon is -189.4oC.
Why is it so low? Argon does not interact with other substances because it is so small and has a complete octet of valence electrons. Argon must be made quite cool to allow liquefication via London dispersion forces. How does this boiling point prove that London dispersion forces exist? If these forces did not exist, Argon would never liquefy. The boiling point of Xenon is oC. Why is it higher than that of Argon? Xenon is bigger and has more electrons than Argon. The likelihood of momentary dipoles is thus greater. It has a greater polarizability than Argon. 3/25/2017

20 F2 can only exhibit intermolecular London forces.
Put the following substances in order from lowest to highest boiling points: C2H6 NH3 F2 F2 can only exhibit intermolecular London forces. C2H6 is not especially polar, but it does have a very slight electronegativity difference between the carbons and the hydrogens. NH3 exhibits hydrogen bonding, thus giving it a relatively high boiling point. F2, C2H6, NH3 3/25/2017

21 The Liquid State Properties of Liquids 3/25/2017

22 Surface Tension resistance of liquid to increase in surface area (polar molecules)
Increase in attractive forces between molecules at surface compared to forces between molecules in center Interior molecules attracted to molecules from every direction No net force on molecule (pulled in all directions) Surface molecules don’t have molecules to attract it on top side Molecule on surface drawn into bulk of liquid Same total attractive force divided between fewer adjacent molecules, resulting in stronger attractive force of surface molecule toward bulk of liquid Decreases with temperature (reduces intermolecular attractions 3/25/2017

23 Intermolecular attractive forces act to minimize surface area of liquid
Geometric shape w/smallest ratio of surface area to volume is sphere Surface molecules drawn inward and area of surface of liquid reduced Small quantities of liquid form spherical drops As drops get larger, weight deforms them into typical tear shape 3/25/2017

24 Bubbles (hollow drop) Surface tension acts to minimize surface (radius of spherical shell of liquid), but opposed by pressure of vapor within bubble Bubbles in pure water tend to collapse Bubbles with surfactant are stabilized 3/25/2017

25 Surface film Smaller surface area causes liquid to behave as though it has skin on surface Surface tension enables insects to walk on surface of water High intermolecular forces = greater surface tension 3/25/2017

26 Cohesion-Adhesion Liquids confined within a container have two types of forces present on molecules Cohesive forces-intermolecular forces among like molecules Adhesive forces-forces between unlike molecules for one another (polar molecules, oxygen in glass attracted to hydrogen in water) Cohesion causes water to form drops, surface tension causes them to be nearly spherical, and adhesion keeps the drops in place Picture 3/25/2017

27 Adhesive forces greater than cohesive forces
Water Mercury Adhesive forces greater than cohesive forces Meniscus (curved upper surface) is concave (curved downward) Cohesive forces greater than adhesive forces Meniscus is convex (curved upward) 3/25/2017

28 Capillary action Instantaneous rising of liquid in narrow tube
Combination of cohesion/adhesion Distance traveled dependent on diameter of tube 3/25/2017

29 Which would have a higher surface tension, H2O or C6H14. Why
Which would have a higher surface tension, H2O or C6H14? Why? Would the shape of the H2O meniscus in a glass tube be the same or different than C6H14? Water, having large dipole moment, has relatively large cohesive forces. Hexane is essentially nonpolar so it has low cohesive forces. Water would have higher surface tension. Water meniscus is concave because adhesive forces of water to polar constituents on surface of glass are stronger than its cohesive forces. Hexane would have a convex meniscus because it has very small adhesive forces, and the slightly larger cohesive forces would dominate. 3/25/2017

30 Viscosity measure of liquid’s resistance to flow
Increases with intermolecular forces To flow, liquid’s molecules must move past each other Move more freely in solutions with relatively low attractive forces Nonpolar molecules attracted to each other by only London forces have lower viscosities than polar liquids like water Increases with molecular size Is temperature dependent Decrease in viscosity with increased temperature Attributed to average molecular KE of liquid which overcomes attractive forces between molecules 3/25/2017

31 Homework: Read , pp Q pp , #13, 15, 36, 38, 40, 41, 42 3/25/2017

32 Solids Structure and Types 3/25/2017

33 Amorphous solids noncrystalline solids
Greek “without form” No orderly structure (arrangement) Lack well-defined faces/shapes Many are mixtures of particles that don’ stack together well Plastic, glass, rubber No distinct, sharp melting point, but soften gradually over large temperature range 3/25/2017

34 Crystalline Solids Atoms, ions, or molecules ordered in well-defined 3-D arrangements (lattice) Unit cell: smallest repeating unit of lattice Lattice: unit cells repeated in space in all three dimensions, characteristic of crystalline solid Lattice point: part of atom in lattice Way spheres arranged in layers determines what type of unit cell we have 3/25/2017

35 Primitive or Simple Cube
Shape Stacking Atom in each corner of cube Atoms in contact along cell edge Spheres in each layer lay on spheres below/above them Stacking pattern: AAAAAAA. . . 3/25/2017

36 Coordination # Atoms/unit cell
# atoms/ions surrounding atom/ion in crystal lattice 6 (in red)-has 6 immediate neighbors Value gives measure of how tightly spheres packed together Larger coordination #, closer spheres to each other Not close packed (least efficient method-52%) Very rare packing arrangement for metals (ex. Polonium) 3/25/2017

37 Body Centered Cubic (BCC)
Shape Stacking Atom at each corner/in center of cube Atoms in contact along body diagonal 2nd layer fit into depressions of 1st layer/3rd layer into 2nd Stacking pattern: ABABABAB. . . 3/25/2017

38 Coordination # Atoms/unit cell
Coordination # Atoms/unit cell 8 (each sphere in contact with 4 spheres in layer above/4 below) Not close packed (less efficient packing-68%) 3/25/2017

39 Face-centered Cube (FCC)
Shape Stacking Atom at each corner/atom in center of each face of cube Each layer diagonally next to each other. Alternating layer in crevices between spheres. Stacking pattern: ABABABAB. . . 3/25/2017

40 Coordination # Atoms/unit cell 12 (more efficient at 74% packing)
Not closest packed (Fe, alkali metals) 3/25/2017

41 Determine net number of Na+ and Cl- ions in unit cell
(¼ per edge) x (12 edges) = 3 (1 per center) x (1 center) = 1 Cl- (1/8 per corner) x (8 corners) = 1 (½ per face) x (6 faces) = 3 Correct since # Na = # Cl (4 = 4) 3/25/2017

42 Bravais lattice is infinite array of discrete points with arrangement and orientation that appears exactly the same, from whichever points array viewed 3/25/2017

43 Introduction to structures and types of solids
X-ray analysis of solids 3/25/2017

44 Diffraction Scattering of light from regular array of points or lines
Spacing between points/lines/atoms, related to wavelength of light X-rays used because their wavelengths similar to distances between atomic nuclei Reflection of X-rays of wavelength  from pair of atoms in two different layers of crystal 3/25/2017

45 If incident X-ray beam hits crystal lattice, general scattering occurs
Most scattering interferes w/itself and is eliminated (destructive interference) (b) Incident rays in phase but reflected rays out of phase: d2 (difference in distances traveled by two rays) = odd # of half wavelengths 3/25/2017

46 Diffraction occurs when scattering in certain direction is in phase with scattered rays from other atomic planes Combine to form waves that reinforce each other (constructive interference) (a) Incident/reflected rays in phase: d1 (difference in distances traveled by two rays ) = whole # of wavelengths 3/25/2017

47 X-ray diffraction One of best methods to determine crystal's structure
Intense X-ray beam strikes crystal Crystal diffracts X-ray beam differently, depending on structure/orientation Atoms in crystal interact w/x-ray waves to produce interference Diffraction pattern consists of reflections of different intensity used to determine crystal’s structure However, many different orientations of crystal collected before true structure of crystal determined 3/25/2017

48 3/25/2017

49 Bragg Equation resolution of X-ray diffraction detector
Used for analysis of crystal structures Each crystalline material has characteristic atomic structure, diffracts X-rays in unique characteristic pattern n = 2d sin  d = distance between atoms (unique for each mineral) n = an integer  = wavelength of x-rays 3/25/2017

50 X rays of wavelength 1. 54 Å were used to analyze an aluminum crystal
X rays of wavelength 1.54 Å were used to analyze an aluminum crystal. A reflection was produced at Ø = 19.3 degrees. Assuming n = 1, calculate the distance d between the planes of atoms producing this reflection. 2dsinθ = nλ 2(d)(sin 19.3) = 1(1.54 Å) 2(d)(0.3305) = 1.54 Å d = 2.33 Å = 233 pm 3/25/2017

51 A topaz crystal has a lattice spacing (d) of 1
A topaz crystal has a lattice spacing (d) of 1.36 Å (1 Å = 1 x m). Calculate the wavelength of X-ray that should be used if Ø = 15.0o (assume n = 1) 2dsinθ = nλ 2 (1.36 Å)(.259) = 1(λ) 0.704 Å = 70.4 pm 3/25/2017

52 Types of Crystalline Solids
(a) Atomic solids (b) Ionic solids (c) Molecular solids 3/25/2017

53 Structure and Bonding in Metals
Structural particles Principal attractive forces between particles Characteristics (physical behavior) Examples Atoms Nondirectional covalent bond involving positive ions and mobile valence electrons delocalized throughout crystal (metallic bond) Pure elements All solids at 25oC except Hg Wide range hardness (electrons move freely from atom to atom, bond metal atoms together with widely varying degrees of force) Wide range melting point (between ionic and covalent compounds) Excellent thermal/electrical conductors (mobile electrons quickly carry charge throughout metal) Malleable/ductile (nondirectional, so stress alters but not destroys crystal) Lustrous (interaction of electrons w/light) K Na Fe Mg Ca Zn 3/25/2017

54 Closest packing most efficient arrangement of spheres
Uniform/hard spheres most efficiently use available space Coordination number = 12 Each sphere in contact with 6 spheres in its own layer 3 spheres in layer above 3 spheres in layer below Stacking 2nd layer does not lie directly over those in 1st layer 3rd layer occupies dimples of 2nd layer in two ways Each sphere in 3rd layer lies directly over sphere in 1st layer (aba) Each sphere can occupy positions so that no sphere in 3rd layer lies over one in 1st layer (abc) 3/25/2017

55 Hexagonal closest packing (hcp)
aba arrangement Each layer identical to layer two below it Ex.: Be, Mg, Ti, Co, Zn, Cd, He (at low T) 2 atom unit cell (8 x 1/8 + 1) Packing efficiency = 74% 3/25/2017

56 Cubic close-packed (ccp)
Corresponds to face-centered cube (abc) Each layer identical to layer three below it Ex.: Ca, Sr, Ni, Pd, Pt, Cu, Ag, Au, Pb, Pt, Ne/Ar/Kr/Xe (at low T) Packing efficiency = 74% 3/25/2017

57 Coordination Numbers for Common Crystal Structures
Structure  Coordination Number  Stacking Pattern simple cubic     AAAAAAAA. . . body-centered cubic    ABABABAB. . . hexagonal closest-packed  12  ABABABAB. . . cubic closest-packed    ABCABCABC. 3/25/2017

58 Calculate density of LiF
4.02 Å on edge Same arrangement of ions as NaCl 4(6.94 amu) + 4(19.0 amu) = amu D = amu g (1 Å) = 2.65 g/cm3 4.02 Å x 1023 amu (10-8)-3 cm 3/25/2017

59 Calculating density of closest packed solid
Silver crystallizes in a cubic closest packed structure. The radius of a silver atom is 144 pm. Calculate the desnity of solid silver. Textbook-length of edge of cube: d = r8 = 1448 = 407 pm V = d3 = (407 pm)3 = 6.74 x 107 pm3 6.74 x 107 pm3 x (1 x 10-10cm)3/1pm = 6.74 x cm3 D = m = (4 atoms)(107.9 g/mol)(1 mol/6.022 x 1023 atoms) V x cm3 10.6 g/cm3 3/25/2017

60 The radius of nickel atom is 1. 24 Å (1Å = 1 x 10-8 cm)
The radius of nickel atom is 1.24 Å (1Å = 1 x 10-8 cm). Nickel crystallizes with a cubic closest packed structure. Calculate the density of solid nickel. d = r8 = 1.24 Å8 = 3.51 Å V = d3 = (3.51 Å)3 = 43.2 Å3 43.2 Å3 x (1 x 10-8cm)3/1pm = 4.32 x cm3 D = m = (4 atoms)(58.69 g/mol)(1 mol/6.022 x 1023 atoms) V x cm3 9.04 g/cm3 3/25/2017

61 Bonding Models for Metals
Electron Sea Model: regular array of metal atoms in “sea” of electrons Band (Molecular Orbital) Model: electrons assumed to travel around metal crystal in MOs formed from valence atomic orbitals of metal atoms 3/25/2017

62 Metal Alloys Substance containing mixture of elements/has metallic properties Substitutional alloy Host metal alloy atoms replaced by other atoms of similar size Brass-Cu/Zn, sterling silver-Ag/Cu, pewter-Sn/Cu/Bi/Sb, plumber’s solder-Sn/Sb Interstitial alloy Holes in closest packed metal structure occupied by small atoms Steel 3/25/2017

63 Network Crystal Diamond Graphite Quartz Nonmetal atoms (pure elements)
Structural particles Principal attractive forces between particles Characteristics (physical behavior) Examples Nonmetal atoms (pure elements) Directional covalent bonds leading to giant molecules (metallic bonds) Very hard (brittle) Insoluble in most ordinary liquids Sublime or melt at high temperatures (high MP) Poor thermal and electrical conductors (most insulators) C (diamond, graphite) SiC BN SiO2 (sand, quartz) Diamond Graphite Quartz 3/25/2017

64 Semiconductors Material w/electrical conductivity between conductor and insulator Conductivity is enhanced by doping In lattice, all atoms bond to 4 neighbors, leaving no free electrons to conduct current (insulator) Intentionally introducing impurities into extremely pure semiconductor which allows electrons in bonds to move Make electrons available for conduction (VA) Form holes which can conduct current (IIIA) 3/25/2017

65 Polar Molecular Crystals
Structural particles Principal attractive forces between particles Characteristics (physical behavior) Examples Discrete polar molecules occupy lattice point Dipole-dipole attractions Low to moderate MP Soluble in some polar liquids Poor thermal/electrical conductors HCl CHCl3 H2S C6H12O6 Molecules with H bonded to O, N, F Hydrogen bonds Soluble in some hydrogen-bonded and some polar liquids H2O NH3 HF CH3OH 3/25/2017

66 Nonpolar Molecular Crystals
Structural particles Principal attractive forces between particles Characteristics (physical behavior) Examples Atoms (8A), nonpolar molecules Dispersion forces Extremely low to moderate MP Soluble in nonpolar solvents Poor thermal/electrical conductors Ar Cl2 H2 CH4 I2 CO2 CCl4 3/25/2017

67 Ionic Crystals Structural particles Principal attractive forces between particles Characteristics (physical behavior) Examples Positive and negative ions that give strongest attractive forces in chemistry Ion-ion attraction Almost all have rigid lattice Moderate to high MP/BP (large lattice energy required to separate ions) Hard/brittle (when hit, atoms shift position which breaks +/- attraction) Nonconductors as solids but conductors as liquids Many dissolve in water KCl CaF2 CsBr MgO BaCl2 NaCl 3/25/2017

68 Trigonal holes < tetrahedral holes < octahedral holes
Packing arrangement done to minimize anion-anion and cation-cation repulsions Structure of most binary ionic solids explained by closest packing of spheres Anions usually larger than cations packed as hcp or ccp arrangements with cations filling holes Nature of holes depends on anion : cation size Trigonal holes formed by 3 spheres in same layer Tetrahedral holes formed by sphere sitting in dimple of three spheres in adjacent layer Octahedral holes formed between 2 sets of 3 spheres in adjoining layers of closest packed structures Trigonal holes < tetrahedral holes < octahedral holes 3/25/2017

69 Take anion to cation ratio in each case:
Would AlP have a closest packed structure which is more like NaCl or ZnS? Ionic radii: Al3+ = 50 pm, P3- = 212 pm Zn2+ = 74 pm, S2- = 184 pm Na+ = 95 pm. Cl- = 181 pm Take anion to cation ratio in each case: S2-/Zn2+ = 2.49 (tetrahedral holes) Cl-/Na+ = 1.91 (octahedral holes) P3-/Al3+ = 4.24 (?) Aluminum ions very small compared to phosphorus ion, so not much room is needed. Tetrahedral holes are adequate. So AlP is more like ZnS than NaCl. 3/25/2017

70 Atomic solid with metallic properties C2H6
Using table 10.7, and based on their properties, classify each of the following substances as to the type of solid it forms. Fe Atomic solid with metallic properties C2H6 Contains nonpolar molecules-molecular solid CaCl2 Contains Ca2+ and Cl- ions-ionic solid Graphite Made up of nonpolar carbon atoms covalently bonded in directional planes-network solid F2 Nonpolar fluorine molecules-molecular solid 3/25/2017

71 Homework: Read , pp Q pp , #46, 48, 60, 68, 72 3/25/2017

72 Vapor Pressure And change of state 3/25/2017

73 3/25/2017

74 Vaporization (Evaporation)
Escape of surface liquid molecules to form gas Rate depends on Nature of liquid Surface area (↑ SA, ↑ evaporation) Temperature (↑ T, ↑ proportion of molecules w/ KE above escape energy) Always endothermic (positive) Heat of vaporization (Enthalpy of vaporization, ΔHvap) -energy required to vaporize one mole of liquid at 1 atm 3/25/2017

75 Equilibrium vapor pressure
Develops in gas phase above liquid when liquid placed in closed container When evaporation occurs in closed container, gas molecules cannot escape to surroundings As more molecules enter gas phase, pressure increases, finally stopping at level (vapor pressure) dependent only on temperature Pressure of vapor present at equilibrium Gas molecules collide w/container walls/liquid Most re-condense when collide with liquid Initially, evaporation rate greater condensation rate As # gas molecules increase, collisions w/liquid surface increase Rate of evaporation eventually equals to rate of condensation-equilibrium 3/25/2017

76 At given temperature, not all molecules moving w/same KE
At given temperature, not all molecules moving w/same KE. Small # molecules moving very slow (low KE), while few moving very fast (high KE). Vast majority somewhere in between. 3/25/2017

77 3/25/2017

78 Variations in Vapor Pressure
Related to intermolecular attractive forces Liquids w/high intermolecular attraction have relatively low vapor pressures (less volatile-liquids that evaporate readily) Liquids w/low intermolecular attraction have relatively high vapor pressures (more volatile) For similar-size molecules Hydrogen-bonded substances have largest ΔHvap values (less volatile/lower vapor pressure) Polar substances have higher values than similar-size nonpolar substances Vapor pressure increases w/temperature 3/25/2017

79 Boiling Point vapor pressure of liquid = prevailing atmospheric pressure above that liquid
Increasing temperature  increases KE  increases molecular motion Forces of attraction between molecules (H bonding) disrupted Molecules break free of liquid and become gas At boiling point, liquid turns into gas Normal boiling point-BP of liquid at 1 atm 3/25/2017

80 Clausius-Clapeyron equation
Mathematical relationship between heat of vaporization and vapor pressure as measures of intermolecular forces that attract molecules together in liquid state Relationship between vapor pressure and temperature P = vapor pressure ΔHvap = heat of vaporization R = universal gas law constant T = Kelvin temperature C = constant (eliminated in 2nd equation) Based on following assumptions (fail at high P, near critical point) Volume of vaporized liquid negligible compared to volume of vapor Vapor behaves as ideal gas ΔHvao is constant over temperature interval of data External pressure doesn’t affect vapor pressure 3/25/2017

81 (b) Plots of In(Pvap) versus 1/T (Kelvin temperature) Linear
(a) Vapor pressure as function of temperature Quantitative nature of temperature dependence of vapor pressure Nonlinear 3/25/2017

82 Clausius-Clapeyron Pg. 487, Sample 10.6
The vapor pressure of water at 25oC is 23.8 torr, and the heat of vaporization of water is 43.9 kJ/mol. Calculate the vapor pressure of water at 50oC. ln (23.8 torr) = -43,900 J/mol ( – ) PvapT2 torr J/K mol K K ln (23.8) = -1.37 PvapT2 torr Take the antilog of both sides to get = = 93.7 torr 3/25/2017

83 Water has a vapor pressure of 24 mmHg at 25oC and a heat of vaporization of 40.7 kJ/mol. What is the vapor pressure of water at 67oC? Solution: Simply use the Clausius-Clapeyron Equation to figure out the vapor pressure. We have to be a bit careful about the units of R: the units we're using are kJ, so R = 8.31x10-3 kJ/mol K. ln(P2/P1) = -DHvap/R * (1/T2- 1/T1) ln(P2/24) = kJ/8.31x10-3 kJ/mol K *(1/340- 1/298) ln(P2/24) = 2.03 P2/24 = 7.62 P2 = 182 mmHg 3/25/2017

84 An unknown liquid has a vapor pressure of 88mmHg at 45oC and 39 mmHg at 25oC. What is its heat of vaporization? Solution: Again, use the Clausius-Clapeyron Equation. Here, the only thing we don't know is DHvap ln(P2/P1) = -DHvap/R * (1/T2- 1/T1) ln(88/39) = -DHvap/8.31x10-3*(1/ /298) DHvap = 32.0 kJ 3/25/2017

85 The vapor pressure of 1-propanol at 14. 7oC is 10. 0 torr
The vapor pressure of 1-propanol at 14.7oC is 10.0 torr. The heat of vaporization is 47.2 kJ/mol. Calculate the vapor pressure of 1-propanol at 52.8oC. ln(10.0/x) = kJ/mol/ kJ/K mol x (1/326 K – 1/287.9 K) 100.2 torr 3/25/2017

86 Heating curves Phase diagrams
Changes of State Heating curves Phase diagrams 3/25/2017

87 T/KE increases, PE is constant Only 1 phase present
Water starts to boil at 100oC KE constant due to heat of vaporization-539 cal/g PE increases until all water evaporated Liquid/gas in equilibrium T/KE increases and PE is constant Only 1 phase present Ice starts to melt at 0oC T/KE constant due to heat of fusion-80 calories/g (bonds not broken). PE increases until all ice melted Solid/liquid in equilibrium T/KE increases and PE constant Only 1 phase present 3/25/2017

88 Heat capacity (J/kg-oC-1) Heat of fusion (Enthalpy of fusion, ΔHfus)
Amount of energy required to raise temperature of system by 1o Energy required to convert mole of solid to mole of liquid at constant pressure Determined as length of first (solid-melting) plateau, which represents heat added, divided by # moles of sample Heat of vaporization (Enthalpy of vaporization, ΔHvap) Heat absorbed by one mole of liquid when it changes to gas at constant pressure Length of second (liquid-boiling) plateau divided by # moles of sample 3/25/2017

89 Sublimation substance goes directly from solid to gaseous state
Reasons for sublimation Solids have vapor pressure, but it is normally very low Solids with little intermolecular attraction may have substantial vapor pressures and be able to sublime at room conditions. Enthalpy of sublimation (Δhsub) Energy in solid-gas transition State function, so ΔHsub = ΔHfus + ΔHvap 3/25/2017

90 Condensation point/Crystallization point-used in place of BP/MP
Cooling Curve Reverse-all features same except start with gas and condense to get solid as heat is removed Condensation point/Crystallization point-used in place of BP/MP ΔHcond requires gas to give off heat-always negative (exothermic) ΔHvap = -ΔHcond 3/25/2017

91 Phase Diagram relationship between pressure and temperature and the three states of matter 3/25/2017

92 Fusion curve (solid-liquid line Vapor pressure curve Liquid-gas line
Sublimation curve Solid-gas line 3/25/2017

93 Diagram for closed system
Pressure plotted on y-axis/temperature on x-axis Divided into three physical states by three lines meeting at triple point Solids-upper left Liquids-upper right Gases-lower part Along each line is equilibrium mixture of two phases on two sides of that line Liquid-solid line usually straight line-changes in pressure have very little effect on solids and liquids (only slightly compressible) Gas-solid and liquid-gas lines are curved upward 3/25/2017

94 Normal melting point-temperature at which solid and liquid states have same vapor pressure under conditions where total pressure is 1 atmosphere Normal boiling point-temperature at which vapor pressure of liquid is exactly 1 atmosphere Supercooling -process of cooling liquid below its freezing point without its changing to solid Superheating -process of heating liquid above its boiling point without its boiling 3/25/2017

95 Triple Point Critical Point
Each phase has same temperature and vapor pressure All three phases exist together in equilibrium Helium-only substance that doesn’t have triple point since it has no solid phase Maximum temperature at which any liquid can exist , defined by Critical temperature-temp above which substance can’t liquefy gas, regardless of how great pressure Critical pressure-pressure above which substance can no longer exist as gas, no matter how high temp For water: 374°C and 218 atm Depends on intermolecular attraction (greater intermolecular forces, higher critical temperature) 3/25/2017

96 Non-compressible/high density fluid Obtained by either
Heating gas above its critical T Compressing liquid at higher P than its critical pressure Above critical point, differences between gases and liquids disappear Density of gas can approach density of liquid phase 3/25/2017

97 Homework: Read , pp Q pp , #23, 29, 76 (have fun), 78, 88, 90 Do 1 additional exercise and 1 challenge problem Submit quizzes by to me: 3/25/2017

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