Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 109 - General Chemistry - Spring 2011

Lecture Notes 32: 13 April

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Crystal (Solid) Structure

Crystal Structure (overheads)

• Lattice
  • Unit Cell
• Crystal lattice
  • 3 kinds of cubic lattice: simple cubic, body-centered cubic, and face-centered cubic. (Figure 10.9, p 432 of Zumdahl)

  

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  • For identical spheres can get two kinds of close packing: (Figure 10.13, p 437 of Zumdahl)

  

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  • cubic close packing, which turns out to be a face-centered cubic lattice (Figure 10.15, p 437 of Zumdahl)
  • hexagonal close packing (Figure 10.14, p 437 of Zumdahl)

  The images below show the so-called cannon ball stacking in close-packing. Note that the stack is a direct result of the HCP lattice shown in the image above, where just the top ball and the next layer of three balls are darkened. Can you discern the next (triangular) layer in the diagram which cooresponds to the third layer down in the pictures below?

  

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Types of Solids

• Metallic solids: these are different in that they have ions at the lattice points in a "sea" of shared electrons (Figures 10.18-.20, p 441-2 of Zumdahl). In metals that are very hard, such as chromium, the ions are also covalently bonded to each other.
• Network (or covalent) solids - Carbon as example: carbon has allotropes (different physical forms of the same element) all of which have many atoms linked together in covalent networks, and two of which are covalent solids: (Figure 10.22, p 444 of Zumdahl)
  • Diamond (covalent solid) - each atom in the bulk solid is covalently bonded to four others in a tetrahedral arrangement. This is the secret to diamonds great hardness: to break a piece off many strong covalent bonds must be broken.
  • Graphite (covalent solid) - as in diamond the carbon atoms are covalently linked to each other, but this time in layers, where each carbon is linked to three others with strong covalent bonds in a trigonal planar geometry. The layers are then very weakly held to each other, so they can readily slide over each other, making them "slippery." Note that the sheets are very strong, thus graphite fibers are used to reinforce other materials (graphite fishing poles etc.).
  • Fullerenes (molecular solids) - graphite like sheets are rolled up to make spheres (commonly 60 C's), and tubes.
• Molecular solids: made up of a single type of covalent molecules, the crystal is held together by weak bonds which hold the molecules together. These solids tend to have low melting points.
• Ionic solids: made up of two or more types of ions (e.g. Na⁺ and Cl^-) held together by electrostatic attractions. (Figure 10.35-37, p 456-7 of Zumdahl). Note that cations (which tend to be small) often fit into the "holes of the unit cell made up the (larger) anions. (Figure 10.35, 10.37 p 456-7 of Zumdahl)

Phase Diagrams

Phase diagrams enable us to predict the behavior of a substance under different conditions of temperature and pressure. We will base our discussions on the behavior of two classic cases: water and carbon dioxide. (Note that phase diagrams strictly describe behavior only for pure substances, so they only hold exactly in closed laboratory systems. The main features do describe much of the contaminated world.)

• Water (see Figure 10.49, Zumdahl p 467).

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• First note that water is a bit unusual in that there is a negative slope for the transition from solid to liquid. This is a reflection of the fact that solid water is less dense than liquid water (a rare situation). (example: Ice skating)
• Note the unique points:
  • Critical point. Defined by two values:
    • the Critical Temperature = the temperature above which liquid cannot exist,
    • the Critical Pressure = the pressure required to give a liquid at the critical temperature. Note that above the critical point liquids no longer have an equilibrium vapor pressure, nor do they boil, rather they undergo a fluid transition to a gas as the temperature is raised.
  • Triple Point. This is a unique set of values at which the gas, liquid, and solid phases can co-exist in equilibrium. The triple point of water is used as a standard and calibration point for temperature scales because it is precisely defined and reproducible anywhere.

• Carbon Dioxide (see Figure 10.50, Zumdahl p 468).
  

  

  • Note that the solid-liquid transition has a positive slope in CO₂, which is the common situation for most substances.
  • Note that the triple point for CO₂ is above 1 atm, thus liquid CO₂ is not seen in the open on Earth's surface. Rather the solid evaporates directly to a gas (sublimes) at -78 °C at 1 atm.

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© R A Paselk

Last modified 13 April 2011