Equilibrium Nature of Phase Changes

Transcription

1 Equilibrium Nature of Phase Changes Chapter Twelve Highlights AP Chemistry

2 In a closed container, phase changes of many substances are reversible and reach equilibrium just as chemical changes do. The direction of the equilibrium shift can be influenced by applying LeChatelier s Principle.

3 In an open container, some fast moving molecules that are moving in the correct direction will overcome intermolecular attractions and vaporize. Energy from the surroundings allows the process to continue until the liquid is gone.

4 In a closed flask that contains a vacuum - Molecules will vaporize causing the vapor pressure to increase. At the same time, vaporized molecules will collide with the liquid surface and be captured (condensed).

5 Eventually, the rate of vaporization will equal the rate of condensation and a dynamic equilibrium is reached. The pressure of the vapor becomes constant at that temperature. Liquid Gas Vapor Pressure: pressure exerted by the vapor from a liquid at equilibrium at a given temperature.

6 Vapor Pressure of Water at Standard Pressure

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8 Liquid-gas Equilibrium

9 The equilibrium can be upset in these closed systems. Remove vapor or reduce the pressure by increasing the volume more liquid evaporates. Increase vapor or increase the pressure by reducing the volume more vapor condenses.

10 When a system at equilibrium is disturbed, it counteracts the disturbance and eventually reestablishes at state of equilibrium.

11 Effects of Temperature and Intermolecular Forces on Vapor Pressure (VP) VP depends on temperature. As the temperature increases, VP increases. As the temperature increases, a greater percentage of the molecules have the needed KE to vaporize.

12 The Effect of Temperature on the Distribution of Molecular Speed in a Liquid

13 VP depends on intermolecular forces. The weaker the intermolecular forces (attractions between particles), the higher the VP.

14 Vapor pressure as a function of temperature and intermolecular forces Small intermolecular attractions

15 The Clausius-Clapeyron Equation This equation provides a way of finding the heat of vaporization - energy needed to vaporize 1 mole of molecules from their liquid state. P ln 2 = - Hvap P R 1 1 T 2 1 T 1 P 1 and P 2 are VP

16 The Clausius-Clapeyron Equation The vapor pressure of ethanol is 115 torr at C. If H vap of ethanol is 40.5 kj/mole, calculate the temperature (in 0 C) when the vapor pressure is 760 torr. ln P 2 P 1 = - Hvap R 1 1 T T 2 1

17 C = K ln 760 torr 115 torr = x 10 3 J/mole J/mole*K 1-1 T K T 2 = 350 K = 77 0 C

18 Vapor Pressure and Boiling Point Boiling point is the temperature at which the vapor pressure equals the external pressure (atmosphere).

19 Solid-Liquid Equilibria As molecules move and enter the liquid (molten) phase (melts), some molten molecules collide with the solid and become fixed (frozen) again. A dynamic equilibrium occurs when the melting rate equals the freezing rate.

20 This temperature is the melting and freezing point. The only difference between the two is the direction of the energy flow. Because increasing or decreasing pressure has little effect on a liquid or a solid, a plot of pressure vs temperature for a S-L phase is typically or nearly a straight line.

21 Solid-Gas Equilibria Solids have much lower vapor pressures than liquids. Some solids have a large enough vapor pressure (dry ice, iodine, moth balls ) that they are capable of sublimation. Sublimation: process of a solid changing directly to a gas.

22 The solid does not melt because the intermolecular attractions and atmospheric pressure are not great enough to keep the molecules close enough together when they leave the solid phase. The pressure-temperature plot for a S-G transition shows a large effect of temperature on pressure of the vapor.

23 Phase Diagrams The Effect of Pressure and Temperature on Physical State A phase diagram combines L-G, S-L, S-G curves to describe the phase changes of a substance under varying conditions of temperature and pressure.

24 Phase diagrams for CO 2 and H 2 O

25 Regions of the Diagram Each region corresponds to one phase of the substance. Only one phase of the substance is stable in that region.

26 Lines Between Regions The lines separating phases represent the phase transition curves. Any point on the curve is a spot where the two phases exist in equilibrium with each other.

27 Note: the S-L line typically has a positive slope. The solid is typically more dense (occupies less space) than the liquid, hence an increase in pressure favors the solid phase. Water is a major exception.

28 Critical Point Point at which the L-G line ends. The critical temperature (T C ) and critical pressure (P C ) is the point past which only the vapor phase can exist.

29 Triple Point The three phase transition lines meet at the triple point. The triple point is the pressure and temperature at which all three phases can exist in equilibrium.

30 Types of Intermolecular Forces Intermolecular forces: The attraction between molecules as a result of partial charges, or the attraction between ions and molecules. Relatively weak forces because they typically involve smaller charges and greater distances.

31 The distance between two bonded atoms in the same molecule is called the bond length and ½ of this distance is the covalent radius. The longer distance between two non-bonded atoms in adjacent molecules is called the van der Waals distance.

32 The van der Waals distance is the point at which intermolecular attractions and electron cloud repulsions are balanced. ½ of this distance is the van der Waals radius. The van der Waals radius is always larger than the covalent radius.

33 Covalent and van der Waals radii

34 Periodic trends in covalent and van der Waals radii (in pm) Radii decreases across a period and increases down a group.

35 Ion-Dipole Forces When an ion and a nearby polar molecule (dipole) attract each other, an ion-dipole force results. Occurs when an ionic compound dissolves in water.

36 The ions become separated because the attractions between the ions and the charged poles of the water molecule are stronger than the attraction between the ions themselves.

37 Dipole-Dipole Forces Dipole-Dipole forces occur when the positive pole of one molecule attracts the negative pole of another. Occurs when polar molecules lie near one another in liquids or solids.

38 Orientation of Polar Molecules Because of Dipole-Dipole Forces

39 For molecular compounds of approximately the same size, the greater the dipole moment, the greater the dipole-dipole forces between the molecules. Hence, it takes more energy to separate them. This then affects melting and boiling points.

40 Dipole Moment: A measure of molecular polarity. It is the magnitude of the partial charges on the ends of the molecule times the distance between them.

41 Dipole Moment and Boiling Point

42 The Hydrogen Bond A special dipole-dipole force arises between molecules that have an H atom bound to a small highly electronegative atom with lone electron pairs. H-N, H-O, H-F are VERY polar so the electron is basically withdrawn from the H.

43 The partially positive H of one molecule is attracted to the partially negative lone pair of electrons on the N, O, and F of another molecule. This is called a hydrogen bond (H bond) F: H-O-.... Hydrogen Bond

44 O: H- N- -N: H-F:.. The small sizes of N,O, and F are essential to the formation of H bonds. 1. These atoms are so electronegative that their covalently bonded H is highly positive.

45 2. It allows the lone pair on the other N, O, or F to come close to the H.

46 PROBLEM: Drawing Hydrogen Bonds Between Molecules of a Substance Which of the following substances exhibits H bonding? For those that do, draw two molecules of the substance with the H bonds between them. O (a) C 2 H 6 (b) CH 3 OH (c) CH 3 C NH 2 PLAN: Find molecules in which H is bonded to N, O or F. Draw H bonds in the format -B: H-A-. SOLUTION: (a) C 2 H 6 has no H bonding sites. (b) H (c) H H C O H O H N CH 3 C H H CH 3 C N H O H O C H H H CH 3 C O N H H H H N CH 3 C O

47 H bonding has an impact on boiling points. Generally, boiling points typically rise as the molar mass increases. Water would be expected to boil at a very low temperature. However, additional energy is needed to break the H bonds. This increases the boiling point of water and other H bonded substances..

48 Hydrogen Bonding and Boiling Point

49 Polarizability and Charge-Induced Dipole Forces Even though electrons are localized in bonding or lone pairs, they are in constant motion (electron cloud). A nearby electric field (another ion, polar molecule ) can distort an electron cloud, pulling towards + or pushing away from a charge.

50 The electric field induces a distortion in an electron cloud. For nonpolar molecules, this distortion results in a temporary induced dipole moment. For polar molecules, the dipole moment already present is enhanced.

51 Polarizability: The ease with which a particle s electron cloud can be distorted. Small atoms (or ions) are less polarizable than larger ones because the electrons are closer to the nucleus and held more tightly. Polarizability increases down a group and decreases across a period.

52 Cations are less polarizable than their parent atom because they are smaller, whereas anions are more polarizable because they are larger.

53 Dispersion (London) Forces What forces cause nonpolar substances like octane, chlorine, and the noble gases to condense and solidify? An attractive force must be acting between the particles or the substances would stay in the gaseous form.

54 The intermolecular force primarily responsible for condensed states is the dispersion force or London force (LDF). Dispersion forces are caused by momentary oscillations of electron charge. At times, the electron density around the nucleus may be concentrated on one side.

55 This causes an instantaneous dipole that influences nearby atoms. Separated Cl 2 Molecules Instantaneous Dipoles Dispersion forces among nonpolar molecules

56 The instantaneous dipole in each atom induces a dipole in its neighbor. The result cascades throughout the sample and at low enough temperatures, the attractions keep the atoms together. Dispersion forces are instantaneous dipole-induced dipole forces.

57 Dispersion forces are weak but can exist between any particle and in many cases is the dominant intermolecular force between identical molecules. Dispersion forces increase with the number of electrons hence there is a relationship to molar mass.

58 Molar Mass and Boiling Point As the molar mass increases, LDF increase, and BP increases.

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61 Predicting the Type and Relative Strength of Intermolecular Forces For each pair of substances, identify the dominant intermolecular forces in each substance, and select the substance with the higher boiling point. (a) MgCl 2 or PCl 3 (b) CH 3 NH 2 or CH 3 F (c) CH 3 OH or CH 3 CH 2 OH CH 3 (d) Hexane (CH 3 CH 2 CH 2 CH 2 CH 2 CH 3 ) or 2,2-dimethylbutane CH 3CCH 2 CH 3 PLAN: Use the formula, structure and Table 2.2. CH 3 Bonding forces are stronger than nonbonding (intermolecular) forces. Hydrogen bonding is a strong type of dipole-dipole force. Dispersion forces are decisive when the difference is molar mass or molecular shape.

62 continued (a) Mg 2+ and Cl - are held together by ionic bonds while PCl 3 is covalently bonded and the molecules are held together by dipole-dipole interactions. Ionic bonds are stronger than dipole interactions and so MgCl 2 has the higher boiling point.

63 continued (b) CH 3 NH 2 and CH 3 F are both covalent compounds and have bonds which are polar. The dipole in CH 3 NH 2 can H bond while that in CH 3 F cannot. Therefore CH 3 NH 2 has the stronger interactions and the higher boiling point.

64 continued (c) Both CH 3 OH and CH 3 CH 2 OH can H bond but CH 3 CH 2 OH has more CH for more dispersion force interaction. Therefore CH 3 CH 2 OH has the higher boiling point.

65 continued (d) Hexane and 2,2-dimethylbutane are both nonpolar with only dispersion forces to hold the molecules together. Hexane has the larger surface area, thereby the greater dispersion forces and the higher boiling point.

66 The Major Types of Intermolecular Forces in Solutions in Decreasing Order of Strength.

67 Hydration Shells Around an Aqueous Ion

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71 Properties of the Liquid State Surface Tension Intermolecular forces have a different effect on a molecule at the surface than one in the interior. Interior molecules are attracted in all directions but surface molecules only have attractions from the side and underneath.

72 Molecular Basis of Surface Tension Surface molecules experience a net downwards attraction.

73 A liquid surface tends to have the smallest possible area, that of a sphere, and behave like a taut skin covering the interior. To increase surface area, molecules must move to the surface by breaking interior attractions. This requires energy.

74 Surface Tension: The energy required to increase the surface area by a unit amount J/m 2. The stronger the forces between particles in a liquid, the greater the surface tension.

75 Surface Tension and Forces Between Particles Substance Formula Surface Tension (J/m 2 ) at 20 0 C Major Force(s) diethyl ether CH 3 CH 2 OCH 2 CH 3 1.7x10-2 dipole-dipole; dispersion ethanol CH 3 CH 2 OH 2.3x10-2 H bonding butanol CH 3 CH 2 CH 2 CH 2 OH 2.5x10-2 H bonding; dispersion water H 2 O 7.3x10-2 H bonding mercury Hg 48x10-2 metallic bonding

76 The H-bonding Ability of the Water Molecule

77 Capillarity The rising of a liquid through a narrow space (tubes) against the pull of gravity is called capillary action, or capillarity. Attractions between the liquid and the tubes wall (adhesive forces) is greater than the intermolecular forces within the liquid (cohesive forces).

78 Shape of Water or Hg Meniscus in Glass adhesive forces stronger cohesive forces

79 Viscosity When a liquid flows, the molecules slide around and past each other. A liquid s viscosity, its resistance to flow, results from intermolecular attractions resisting the movement. Viscosity decreases with heating.

80 Viscosity of Water at Several Temperatures Temperature( 0 C) Viscosity (N*s/m 2 )* x x x x10-3 *The units of viscosity are newton-seconds per square meter. (J/m 2 )

81 Molecular shape plays a role in a liquid s viscosity. Long molecules make more contact with each other than spherical ones. Generally, these longer molecules have higher viscosities.

82 The Solid State: Structure, Properties and Bonding Crystalline solids generally have well-defined shapes. The particles atoms, molecules, ions occur in an orderly manner

83 Amorphous solids have poorly defined shapes because they lack extensive molecular level ordering of their particles.

84 Crystal Lattice and the Unit Cell In a crystal, particles are packed tightly together in an orderly 3-D array. Simplest case all particles are identical spheres The center of these particles form a regular pattern throughout the crystal.

85 This pattern is called a crystal lattice. The lattice consists of all points with identical surroundings. Unit Cell: the smallest portion of the crystal that, if repeated in all three directions, gives the crystal.

86 The Crystal Lattice and the Unit Cell

87 Coordination Number of a particle in a crystal: number of nearest neighbors surrounding it. There are 7 crystal systems and 14 types of unit cells. A very common type of crystal system is a cubic system which leads to the cubic lattice.

88 Simple Cubic Unit Cell Centers of 8 particles define the corners of the cube. Attractions pull the particles together so that they touch along the cubes edges; but they do not touch diagonally along the cube s faces or its center.

89 There are 4 particles in its own layer and one above and one below. Coordination Number = 6

90 Simple Cubic 1/8 atom at 8 corners Coordination Number = 6 Atoms/unit cell = 1/8 * 8 = 1

91 Body-Centered Cubic Particles lie in each corner and the center of the cube. The particles at the corners do not touch but they all touch the one in the center.

92 Each particle is surrounded by eight nearest neighbors, four above and four below. Coordination Number = 8

93 Body-Centered Cubic 1/8 atom at 8 corners 1 atom at center Coordination Number = 8 Atoms/unit cell = (1/8*8) + 1 = 2

94 Face-Centered Cubic A particle lies in each corner and in the center of each face but not in the center of the cube. Those at the corners touch those in the faces but not each other. Coordination Number = 12

95 Face-Centered Cubic 1/8 atom at 8 corners 1/2 atom at 6 faces Coordination Number = 12 Atoms/unit cell = (1/8*8)+(1/2*6) = 4

96 Packing Efficiency and the Creation of Unit Cells The higher the coordination number of a crystal, the more particles in a given volume. Face-Centered Cubic particles > Body-Centered Cubic particles > Simple Cubic particles.

97 Simple Cubic Cell If the next layer is placed above the first Note the diamond cut-away. Simple Cubic (52% packing efficiency)

98 Packing efficiency: the percentage of the total volume occupied by the spheres themselves.

99 Body-Centered Cubic Place the second layer inside the diamond shape. Cr, Fe, Alkali Metals Body-Centered Cubic (68% packing efficiency)

100 Hexagonal Closest Packing layer a layer b layer a Hexagonal Closest Packing closest packing of first and second layers abab (74%) hexagonal unit cell expanded side views

101 Cubic Closest Packing layer a layer b cubic closest packing layer c closest packing of first and second layers abcabc (74%) face-centered unit cell

102 There is no better way to pack spheres than hexagonal and cubic closest packing 74% packing efficiency and a coordination number of 12. Most metallic elements in these arrangements. Mg and Zn adopt the hexagonal while Ni, Cu and lead use the cubic structure.

103 Properties of Mixtures: Solutions and Colloids Chapter Thirteen Highlights AP Chemistry

104 Colligative Properties of Solutions Colligative properties: solution properties that are determined by the number of solute particles. These properties are vapor pressure lowering, boiling point elevation and freezing point depression, and osmotic pressure.

105 Vapor Pressure Lowering The vapor pressure (V.P.) of a solution is always lower than that of a pure solvent. Vapor pressure lowering ( P) is a natural process that occurs in the direction of disorder (higher entropy).

106 Since a solution is already more disordered than a pure liquid, the solvent has less tendency to vaporize in order to attain the same degree of disorder. Hence, equilibrium is reached (vaporization and condensation rates become equal) at a lower vapor pressure for the solution.

107 The Effect of a Solute on the Vapor Pressure of a Solution Fewer molecules need to condense to balance out the ones that are vaporizing.

108 Vapor pressure of a solvent above a solution (P solvent ) equals the mole fraction of the solvent in the solution (X solvent ) times the vapor pressure of the pure solvent (P O solvent ). Raoult s Law P solvent = X solvent X P O solvent

109 In a solution X solvent is always less than 1, so P solvent is always less than P O solvent. Modifying to utilize the mole fraction of solute P O solvent - P solvent = P P = X solute x P O solvent

110 Using Raoult s Law to Find the Vapor Pressure Lowering Calculate the vapor pressure lowering, P, when 10.0 ml of glycerol (C 3 H 8 O 3 ) is added to 500. ml of water at C. At this temperature, the vapor pressure of pure water is 92.5 torr and its density is g/ml. The density of glycerol is 1.26 g/ml.

111 10.0 ml C 3 H 8 O g C 3 H 8 O 3 ml C 3 H 8 O 3 mole C 3 H 8 O g C 3 H 8 O 3 = mole C 3 H 8 O ml H 2 O g H 2 O ml H 2 O mole H 2 O g H 2 O = 27.4 mole H 2 O

112 X solute = mole C 3 H 8 O mole C 3 H 8 O mol H 2 O X solute = P = X solute x P O solvent P = x 92.5 torr P = torr

113 Boiling Point Elevation A solution boils at a higher temperature than the pure solvent. B.P. (T b ) of a liquid equals the temperature at which the V.P. of a solution equals the external pressure.

114 The V.P. of a solution is always lower than that of a pure solvent. Therefore a higher temperature is needed to raise the solutions V.P. to equal the external pressure.

115 Boiling point elevation ( T b ) is proportional to the concentration of the solute particles. T b = K b m m = molality K b = molal boiling point elevation constant ( O C/m) and is specific for a given solvent.

116 T b is considered a positive value: T b = T b(solution) - T b(solvent)

117 Freezing Point Depression Just as a solute disrupts a solvents ability to boil, it also changes its ability to freeze. T f = K f m K f = molal freezing point depression constant ( O C/m) and is specific for a given solvent.

118 T f is considered a positive value: T f = T f(solvent) - T f(solution)

119 Molal Boiling Point Elevation and Freezing Point Depresssion Constants of Several Solvents Solvent Boiling Melting Point ( 0 C)* K b ( 0 C/m) Point ( 0 C) K b ( 0 C/m) Acetic acid Benzene Carbon disulfide Carbon tetrachloride Chloroform Diethyl ether Ethanol Water *at 1 atm.

120 Determining the Boiling Point Elevation and Freezing Point Depression of a Solution You add 1.00 kg of ethylene glycol antifreeze (C 2 H 6 O 2 ) to your car radiator, which contains 4450 g of water. What are the boiling and freezing points of the solution?

121 1.00 x 10 3 g C 2 H 6 O 2 X mole C 2 H 6 O g C 2 H 6 O 2 = 16.1 mole C 2 H 6 O mole C 2 H 6 O kg H 2 O = 3.62 m C 2 H 6 O 2

122 T b = C (3.62m) m T b = C T b = T b(solution) - T b(solvent) T b(solution) = T b + T b(solvent) T b(solution) = C O C BP = C

123 T fp = C m (3.62m) T fp = 6.73 O C T f = T f(solvent) - T f(solution) T f(solution) = T f(solvent) - T f T f(solution) = 0 O C C FP = C

124 Phase Diagrams of Solvent and Solution

125 Osmotic Pressure Osmotic Pressure applies to aqueous solutions. It arises when two solution of different concentrations are separated by a semipermeable membrane (allows the water but not the solute to pass through). This movement of water is called osmosis.

126 Development of Osmotic Pressure Semipermeable Membrane Net Movement of Solvent solvent molecules solute molecules

127 The solution volume increases making the concentration decrease. The difference in heights of the liquids at equilibrium creates a pressure called the Osmotic Pressure ( ).

128 Osmotic Pressure ( ) can also be defined as the applied pressure needed to prevent the volume increase.

129 = n solute RT = MRT V solution M = molarity T = Kelvin Temperature Note the similarity to the ideal gas law. Both relate the pressure of a system to temperature and concentration.

130 Determining Molar Mass from Osmotic Pressure Biochemists have discovered more than 400 mutant varieties of hemoglobin, the blood protein that carries oxygen throughout the body. A physician studying a variety associated with a fatal disease first finds its molar mass (M). She dissolves 21.5 mg of the protein in water at C to make 1.50 ml of solution and measures an osmotic pressure of 3.61 torr. What is the molar mass of this hemoglobin variant? M = π RT = 3.61 torr atm 760 torr ( L*atm/mole*K)(278.1K) = 2.08x10-4 M 2.08x10-4 mole L (1.50 ml) L 10 3 ml = 3.12x10-8 mole 21.5 mg g 10 3 mg x10-8 mole = 6.89x10 4 g/mole

131 Structure and Properties of Colloids Suspension: A heterogeneous mixture containing particles large enough to be seen by the naked eye and distinct from the surrounding fluid. Sand shaken in water is an example. The sand will eventually settle out.

132 Solution: A homogeneous mixture in which the individual molecules are distributed evenly throughout the surrounding fluid. Sugar dissolved in water is an example.

133 Between the extremes of suspensions and solutions is a large group of mixtures called colloidal dispersions or simply colloids. Colloids contain a disperesed (solute-like) substance distributed throughout a dispersing (solventlike) substance.

134 Colloidal particles are larger than simple molecules but small enough to remain distributed and not settle out. Most colloids are cloudy or opaque, but some can be transparent to the naked eye.

135 Types of Colloids Colloid Type Dispersed Substance Dispersing Medium Example Aerosol Aerosol Foam Solid foam Emulsion Solid emulsion Sol Solid sol Liquid Gas Fog Solid Gas Smoke Gas Liquid Whipped cream Gas Solid Marshmallow Liquid Liquid Milk Liquid Solid Butter Solid Liquid Paint; cell fluid Solid Solid Opal

136 Light Scattering and the Tyndall Effect.

137 Tyndall Effect: The light scattering ability of a colloidal suspension.

138 The End