Intermolecular Forces, Liquids and Solids

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• Intermolecular Forces, Liquids and Solids
• Solids
• Crystalline solids have an arrangement of ions,
  atoms or molecules that is highly regular and
  form a three dimensional lattice-an orderly
  arrangement of particles that can be reproduced
  by translation in three space.
• Bulk samples have flat surfaces making definite
  angles with one another.
• Crystalline solids melt at definite temperatures.

• Unit cells in crystalline solids
• The unit cell is the smallest repeating unit that
  can reproduce a lattice by translating the unit
  cell a distance equal to the length of an edge of
  the unit cell.

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• Intermolecular Forces, Liquids and Solids
• Crystalline Solids
• Unit cells in crystalline solids
• There are 7 basic crystal systems that can define
  14 kinds of unit cells reproducing the
  possible three dimensional lattices.
• These are the 14 Bravais lattices.
• The 7 basic crystal systems are shown in Fig.
  13.27, p. 612
• Three of the lattices have cubic symmetry - see
  Fig. 13.28, p. 613
• Simple cubic - 1 atom per unit cell atoms in
  contact along edge
• Body-centered cubic - 2 atoms per unit cell
  atoms in contact along body diagonal
• The alkali metals are body centered cubic
  (bcc)
• Face -centered cubic - 4 atoms per unit cell
  atoms in contact along face diagonal
• Ni, Cu, Al are facecentered cubic (fcc)

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• Intermolecular Forces, Liquids and Solids
• Crystalline Solids
• Calculations involving cubic lattices
• Atoms at the corners of a cube share their
  volumes with adjacent cubes
• Eight cubes share the volume of a corner atom

• If a cubic unit cell has an atom at each corner,
  these 8 corner atoms contribute a net of 1 atom
  to the unit cell
• For a atom in the face of a cube in a cubic
  structure
• The atom is shared equally by two cubes
• For a fcc structure with 6 atoms in 6 faces,
  these 6 atoms contribute a net of 3 atoms to the
  unit cell
• A simple cubic unit cell has 1 atom per unit cell
• A face centered cubic unit cell has 4 atoms per
  unit cell
• A body centered cubic unit cell has 2 atoms per
  unit cell

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• Intermolecular Forces, Liquids and Solids
• Crystalline Solids
• Atom contacts in cubic unit cells
• In simple cubic unit cells, the atoms are in
  contact along the cell edge
• One edge length (EL) contains two atomic radii
• In face-centered cubic unit cells, the atoms are
  in contact along the face diagonal

• Using the Pythagorian theorem,

• For bcc unit cells, the atoms are in contact
  along the body diagnal
• The Pythagorian theorem must be applied twice

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• Intermolecular Forces, Liquids and Solids
• Crystalline Solids
• Calculations involving cubic lattices
• From the cubic unit cell type and edge length,
  the atomic radius may be calculated
• From the density and the edge length, the cubic
  unit cell type may be determined
• From the density and unit cell type, the edge
  length may be calculated

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• Intermolecular Forces, Liquids and Solids
• Crystalline Solids
• Example Cu crystallizes in a fcc unit cell that
  has an edge length of 3.61 Å. a. Calculate the
  radius of a Cu atom.

b. Calculate the density of Cu.
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• Intermolecular Forces, Liquids and Solids
• Crystalline Solids
• CsCl consists of two interpenetrating simple
  cubic lattices - one for Cs and one for Cl-

• The Cs ion just fits in the octahedral hole in
  the center of the unit cell
• The corner atoms contribute a net of 1 Cl- ion
• The center atom is wholly contained in the unit
  cell
• The structure is consistent with the formula,
  CsCl

• Perovskite is a mineral of Ca, Ti and O. Its
  formula is
• 1 Ca2 from the corner atoms
• 1 Ti from the central Ti atom
• 6/2 3 Os from the face atoms
• CaTiO3

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• Intermolecular Forces, Liquids and Solids
• Crystalline Solids
• Rock salt structure NaCl. See Fig. 13.31, 619
  given on next slide.
• This structure is 2 interpenetrating FCC
  structures - one each for the Na ions and the
  other for the Cl- ions.
• The 8 corner Cl- ions contribute 1 net Cl- ions
  to the unit cell
• the 6 face Cl- ions contribute 3 net Cl- ions to
  the unit cell
• On each edge is a Na ion, one-fourth belonging
  to the unit cell for a total of 4 Na ions
• Thus the formula is NaCl
• MgO also has the rock salt structure - See p. 620

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Intermolecular Forces, Liquids and Solids Types
of Crystalline Solids
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• Intermolecular Forces, Liquids and Solids
• Phase Diagrams are two or three dimensional plots
  showing conditions under which a particular
  phase (solid, liquid or gas) is stable, the and
  conditions under which phases are in
  equilibrium.
• In a P-T diagram, areas represent the range of
  pressure and temperature that one of the phases
  of a pure substance is stable.
• A line in a P-T diagram defines the conditions
  under which equilibrium between two phases
  exists.
• The line between the solid and liquid shows the
  conditions of pressure and temperature under
  which solid and liquid are in equilibrium.
• The line between a liquid and gas shows the
  conditions of pressure and temperature under
  which vapor and liquid are in equilibrium.
• The line between a solid and gas show the
  conditions of pressure and temperature under
  which solid and gas are in equilibrium.
• A triple point - the intersection of three lines
  - defines the conditions under which
  equilibrium between three phases exits gas,
  liquid and solid are in equilibrium.

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• Intermolecular Forces, Liquids and Solids
• Phase Diagrams
• The phase diagram of H2O - see Fig. 13.37, p 630.
• The triple point is at 4.58 torr and 0.01 oC
• The slope of the solidus line is negative
  indicating that the density of ice is less than
  liquid water.
• As the pressure increases, the temperature for
  the equilibrium between solid water and liquid
  water decreases as pressure is applied to ice,
  the freezing temperature of ice decreases.
• The phase diagram of CO2 - see Fig. 13.39, p
  630.
• The triple point is at 5.11 atm and -56.4 oC.
• Above 5.11 atm it is possible to have liquid in
  equilibrium with gas and solid in equilibrium
  with liquid.
• Below 5.11 atm, it is not possible to have liquid
  CO2.
• At 1 atm, the liquid CO2 cannot exist and an
  equilibrium between gas ad solid exits at a
  temperature of -78.5 oC.
• The solidus line has a positive slope indicating
  that the solid is more dense than the liquid
  which is the most common behavior of the liquid
  and solid phases of a substance in equilibrium.

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