1. States of Matter and Intermolecular Forces
Chapter Eleven
States of Matter and Intermolecular Forces

2. 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.

3. Molecular Forces Compared

4. States of Matter Compared
Intermolecular forces are very important.
Intermolecular forces are of little significance; why?
Intermolecular forces must be considered.

5. Vaporization and Condensation
Vaporization is the conversion of a liquid to a gas.
The enthalpy of vaporization (DHvapn) 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 (DHcondn) 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 DH must be zero:
DHvapn + DHcondn = 0
DHcondn = –DHvapn

7. Example 11.2 An Estimation Example
How much heat, in kilojoules, is required to vaporize 175 g methanol, CH3OH, at 25 °C?
Example An Estimation Example
Without doing detailed calculations, determine which liquid in Table 11.1 requires the greatest quantity of heat for the vaporization of 1 kg of liquid.

8. Vapor Pressure Liquid Vapor
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

9. Liquid–Vapor Equilibrium
… until equilibrium is attained.
More vapor forms; rate of condensation of that vapor increases …

10. Vapor pressure increases with temperature; why?

11. Vapor Pressure Curves CS2 CH3OH H2O CH3CH2OH 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?

12. Example 11.3
Suppose the equilibrium illustrated in Figure 11.3 is between liquid hexane, C6H14, and its vapor at K. A sample of the equilibrium vapor is found to have a density of g/L. What is the vapor pressure of hexane, in mmHg, at K?

13. 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.

14. At Tc, the densities of liquid and vapor are equal; a single phase.
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.

15. These four gases can’t be liquefied at room temperature, no matter what pressure is applied; why not?

16. Example 11.4 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?

17. Phase Changes Involving Solids
Melting (fusion): transition of solid  liquid.
Melting point: temperature at which melting occurs.
Same as freezing point!
Enthalpy of fusion, DHfusion, 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, DHsubln, is the sum of the enthalpies of fusion and vaporization.
Triple point: all three phases—solid, liquid, vapor—are in equilibrium.

18. Some Enthalpies of Fusion

19. 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.

20. 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.

21. 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.
A—B, solid-vapor equilibrium.
Triple point

22. HgI2 has two solid phases, red and yellow.
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?

23. Note that at 1 atm, only the solid and vapor phases of CO2 exist.
Phase Diagram for CO2
Note that at 1 atm, only the solid and vapor phases of CO2 exist.

24. Phase Diagram for H2O

25. Example 11.5 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 = 6.01 kJ/mol, ΔHvapn = 40.6 kJ/mol (at 100 °C), molar heat capacity of H2O(l) = 76 J mol–1 °C–1.

26. Intermolecular Forces
… are forces between molecules.
They determine melting points, freezing points, and other physical properties.
Types of intermolecular forces include:
dispersion forces
Dipole–dipole forces
hydrogen bonding

27. 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.

28. Dispersion Forces Illustrated (1)
At a given instant, electron density, even in a nonpolar molecule like this one, is not perfectly uniform.

29. 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 …

30. Dispersion Forces Illustrated (3)
… this molecule induces a tiny dipole moment …
… in this molecule.
Opposite charges ________.

31. 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 …

32. 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 …

33. 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.

34. Dipole–Dipole Interactions
Opposites attract!

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.

36. Example 11.6
Arrange the following substances in the expected order of increasing boiling point: carbon tetrabromide, CBr4; butane, CH3CH2CH2CH3; fluorine, F2; acetaldehyde, CH3CHO.

37. 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.

38. Example 11.7 An Estimation Example
The boiling points of the straight-chain alkanes pentane, hexane, heptane, and octane are 36.1, 68.7, 98.4, and °C, respectively. Estimate the boiling point of the straight-chain alkane decane.

39. When Y and Z are small and highly electronegative (N, O, F) …
Hydrogen Bonds
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 ~~~~
When Y and Z are small and highly electronegative (N, O, F) …
… this force is called a hydrogen bond; a special, strong type of dipole–dipole force.

40. Hydrogen Bonds in Water

41. 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).

42. Hydrogen Bonding in Acetic Acid
Hydrogen bonding occurs between molecules.

43. Hydrogen Bonding in Salicylic Acid
Hydrogen bonding occurs within the molecule.

44. Intermolecular Hydrogen Bonds
Intermolecular hydrogen bonds give proteins their secondary shape, forcing the protein molecules into particular orientations, like a folded sheet …

45. Intramolecular Hydrogen Bonds
… while intramolecular hydrogen bonds can cause proteins to take a helical shape.

46. Example 11.8
In which of these substances is hydrogen bonding an important intermolecular force: N2, HI, HF, CH3CHO, and CH3OH? Explain.

47. Liquids and Intermolecular Forces
Much behavior and many properties of liquids can be attributed to intermolecular forces.
Surface tension (g) 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.

48. Surface Tension
To create more surface, the molecules at the surface must be separated from one another.

49. 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?

50. What conclusion can we draw about the cohesive forces in mercury?
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.

51. Capillary Action
The adhesive forces wet more and more of the inside of the tiny tube, drawing water farther up the tube.

52. 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?

53. 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).

54. 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.

55. Crystal Structure of Diamond
Three-dimensional network is extremely strong, rigid.
What kind of forces must be overcome to melt diamond?

56. Crystal Structure of Graphite
Hexagons of sp2-hybridized carbon atoms.
Forces between layers are relatively weak.

57. Structure of a Buckyball
C60 molecule

58. 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.

60. 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.

61. 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.

62. Example 11.9
Arrange the ionic solids MgO, NaBr, and NaCl in the expected order of increasing melting point.

63. 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).

64. The unit cell is a cube in each case. Whole atoms shown for clarity.
Cubic Unit Cells
The unit cell is a cube in each case.
Whole atoms shown for clarity.

65. Close-Packed Structures
A close packed structure in two dimensions.

66. 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

67. 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.

68. 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 …

69. 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 >

70. Unit Cell of Cesium Chloride
How many cesium ions are inside this unit cell? How many chloride ions?

71. Unit Cell of Sodium Chloride
How many sodium ions are inside this unit cell? How many chloride ions?

72. Experimental Determination of Crystal Structures
X rays
Angle of diffraction can be used to find distance d, using simple trigonometry.

73. 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