Figure 102: Partial representation of the molecular orbital energies in (a) diamond and (b) a typical metal Figure 1024: The p orbitals (a) perpendicular to the plane of the carbon ring system in graphite can combine to form (b) an extensive π-bonding network Figure 1025: Graphite consists of layers of carbon atoms Figure 1026: (top) The structure of quartz (empirical formula SiO2) Quartz contains chains of SiO4 tetrahedra (bottom) that share oxygen atoms Figure 1027: Examples of silicate anions, all of which are based on SiO44- tetrahedra Figure 1028: Twodimensional representations of (a) a quartz crystal and (b) a quartz glass 1
Figure 100: Energy-level diagrams for (a) an n-type semiconductor and (b) a ptype semiconductor Semiconductors substance in which some electrons can cross the band gap onductivity is enhanced by doping with group a or group 5a elements Figure 1029: (a) silicon crystal doped with arsenic, which has one more valence electron than silicon (b) silicon crystal doped with boron, which has one less electron than silicon Figure 101: The p-n junction involves the contact of a p-type and an n-type semiconductor Types of Solids molecular solid is a solid that consists of molecules held together by intermolecular forces Many solids are of this type Examples include solid sulfur, solid water (ice), and solid carbon dioxide (dry ice) 2
Figure 104: (a) Sulfur crystals (yellow) contain S8 molecules (b) White phosphorus (containing P4 molecules) is so reactive with the oxygen in air that it must be stored under water Figure 105: The holes that exist among closest packed uniform spheres (a) The trigonal hole formed by three spheres in a given plane (b) The tetrahedral hole formed when a sphere occupies a dimple formed by three spheres in an adjacent layer (c) The octahedral hole formed by six spheres in two adjacent layers Figure 106: (a) The location (X) of a tetrahedral hole in the face-centered cubic unit cell (b) One of the tetrahedral holes (c) The unit cell for ZnS where the S2- ions (yellow) are closest packed with the Zn2+ ions (red) in alternating tetrahedral holes Types of Solids n ionic solid is a solid that consists of cations and anions held together by electrical attraction of opposite charges (ionic bond) Examples include cesium chloride, sodium chloride, and zinc sulfide (but ZnS has considerable covalent character) Figure 107: (a) The locations (gray X) of the octahedral holes in the face-centered cubic unit cell (b) Representation of the unit cell for solid Nal
Figure 109: The rates of condensation and evaporation over time for a liquid sealed in a closed container Vapor Pressure is the of the vapor present at equilibrium is determined principally by the size of the intermolecular forces in the liquid increases significantly with Volatile liquids have high vapor s Figure 108: ehavior of a liquid in a closed container Figure 1040: (a) The vapor of a liquid can be measured easily using a simple barometer of the type shown here (b) The three liquids, water, ethanol (2H5OH), and diethyl ether [(2H5)2O], have quite different vapor s Figure 1041: iagram showing the reason vapor depends on 4
If we know the vapor, P 1, of a pure substance at, T 1, and want to determine the vapor, P 2, of the substance at a new, T 2, we can use the lausius-lapeyron equation Since for a pure substance: ln P 1 = - )H vap /RT 1 (1), and ln P 2 = - )H vap /RT 2, (2) we can subtract equation (1) from (2) to get: ln P 2 -lnp 1 = - )H vap /RT 2 -(-)H vap /RT 1 ) nd, collecting terms ln (P 2 /P 1 ) = ()H vap /R)(1/T 1-1/T 2 ) lausius-lapeyron Equation We noted earlier that vapor was a function of It has been demonstrated that the logarithm of the vapor of a liquid varies linearly with absolute, at equilibrium onsequently, the vapor of a liquid at two different s is described by: P H ln = P R 2 1 vap ( 1 T 1 1 T 2 ) Problem to onsider arbon disulfide, S 2, has a normal boiling point of 46 o (vapor = 760 mmhg) and a heat of vaporization of 268 kj/mol What is the vapor of carbon disulfide at 5 o? Substituting into the lausius-lapeyron equation, we obtain: P2 268 10 J/mol ln = ( 1 1 ) (760 mm Hg) 81 J/(mol K) 19 K 08 K = (225 K) (-112 10-4 -1 K ) = 061 Figure 1042: (a) The vapor of water, ethanol, and diethyl ether as a function of (b) Plots of In(P vap ) versus 1/T (Kelvin ) for water, ethanol, and diethyl ether Problem to onsider arbon disulfide, S 2, has a normal boiling point of 46 o (vapor = 760 mmhg) and a heat of vaporization of 268 kj/mol What is the vapor of carbon disulfide at 5 o? Taking the antiln we obtain: P 2 = antiln(-061) (760 mm Hg) P 2 = antiln(-061) 760 mm Hg P 2 = 50 mm Hg
Figure 1044: The heating curve (not drawn to scale) for a given quantity of water where energy is added at a constant rate Heat of Phase Transition To melt a pure substance at its melting point requires an extra boost of energy to overcome lattice energies The heat needed to melt 1 mol of a pure substance is called the heat of fusion and denoted Hfus For ice, the heat of fusion is 601 kj/mol H 2O(s ) H 2O(l ); H fus = 601 kj Freezing Point The at which a pure liquid changes to a crystalline solid, or freezes, is called the freezing point The melting point is identical to the freezing point and is defined as the at which a solid becomes a liquid Unlike boiling points, melting points are affected significantly by only large changes Melting Point Figure 1046: Solid and liquid phases in equilibrium with the vapor Molecules break loose from lattice points and solid changes to liquid (Temperature is constant as melting occurs) vapor of solid = vapor of liquid 6
Figure 1047: Water in a closed system with a of 1 atm exerted on the piston No bubbles can form within the liquid as long as the vapor is less than 1 atm oiling Point The at which the vapor of a liquid equals the exerted on the liquid is called the boiling point s the of a liquid increases, the vapor increases until it reaches atmospheric t this point, stable bubbles of vapor form within the liquid This is called boiling The normal boiling point is the boiling point at 1 atm Figure 1048: The supercooling of water The extent of supercooling is given by S oiling chip releasing air bubbles acts as a nucleating agent for the bubbles that form when water boils oiling Point onstant when added energy is used to vaporize the liquid vapor of liquid = of surrounding atmosphere Problem 77, p 504
Problem to onsider The heat of vaporization of ammonia is 24 kj/mol How much heat is required to vaporize 100 kg of ammonia? First, we must determine the number of moles of ammonia in 100 kg (1000 g) 1mol NH 1 00 10 g NH = 170 g NH 588 mol NH Phase iagrams elow is a typical phase diagram It consists of three curves that divide the diagram into regions labeled solid, liquid, and solid liquid Problem to onsider The heat of vaporization of ammonia is 24 kj/mol How much heat is required to vaporize 100 kg of ammonia? Then we can determine the heat required for vaporization 588 mol NH 24 kj/mol = 18 10 Problem 8, p 504 kj Phase iagrams urve, dividing the solid region from the liquid region, represents the conditions under which the solid and liquid are in equilibrium solid liquid Phase iagram Represents phases as a function of and critical : above which the vapor can not be liquefied critical : required to liquefy T the critical critical point: critical and (for water, T c = 74 and 218 atm) Phase iagrams Usually, the melting point is only slightly affected by For this reason, the melting point curve,, is nearly vertical solid liquid
Phase iagrams If a liquid is more dense than its solid, the curve leans slightly to the left, causing the melting point to decrease with Phase iagrams urve, which divides the solid region from the eous region, represents the vapor s of the solid at various s solid liquid solid liquid Phase iagrams If a liquid is less dense than its solid, the curve leans slightly to the right, causing the melting point to increase with Phase iagrams The vapor at the critical is called the critical Note that curve ends at the critical point, P crit solid liquid solid liquid (see Figure 111) T crit Phase iagrams Figure 111: Observing the critical phenomenon urve, which divides the liquid region from the eous region, represents the boiling points of the liquid for various s solid liquid
Figure 1049: The phase diagram for water Figure 1052: The phase diagram for carbon dioxide Figure 1050: iagrams of various heating experiments on samples of water in a closed system Figure 1051: The phase diagram for water t point X on the phase diagram, water is a solid 10