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X. Solid and Liquid States
A) Types of Solids
- Crystalline Solid
Crystals result from an orderly arrangement of atoms, ions, or molecules. Crystals have planar surfaces that intersect at specific angles.
Example : A crystal of CsCl is cubic. The unit cell (smallest repeating unit in the crystal) of CsCl is illustrated below.
The physical properties of crystals are anisotropic (not the same in all directions). Crystalline solids have sharp melting points. For example the melting point of CsCl is 1290 EC.
Several Types of Unit Cells
The lengths of the edges of the unit cell are a , b , and c. The angle between the b and c edges is called , the angle between the a and c edges is called , and the angle between the a and b edges is called.
- Amorphous Solids
Amorphous solids result from the unorderly arrangement of atoms, ions, or molecules. Amorphous solids do not have characteristic shapes.
Example : Window glass
The physical properties of amorphous solids are isotropic (same in all directions). Amorphous solids melt over a broad temperature range. For example Pyrex glass softens at 800EC but does not completely liquefy until 1250EC.
B) Phase Change
- Sublimation: Solid Vapor
Molecules with KE (^) T(kinetic energy of translation) greater than the energy of the van der Waals forces in the solid will escape from the surface of the solid and enter the vapor phase. When molecules that are in the vapor phase and have a KE (^) Tless than the energy of the van der Waals forces in the solid collide with the surface of the solid, the molecules will stick to the surface.
liquid vapor
and
Gvapor ' Gliquid
and
Gvap ' Gvapor & Gliquid ' 0
ln( Pvapor ) 2 '
ð
Hvap
R ëð^
T 2 & T 1
T 2 T 1 ë^
% ln( Pvapor ) 1
Gvap ' Hvap & T Svap ' 0
Hvap ' T Svap
When the number of molecules leaving the liquid and entering the vapor phase equals the number of molecules leaving the vapor and entering the liquid phase, then the system is in equilibrium.
The pressure exerted by the vapor that is in equilibrium with the liquid is called the vapor pressure of the liquid. The magnitude of the vapor pressure depends on the magnitude of the van der Waals forces in the liquid and the temperature. Over a narrow temperature range the vapor pressure is related to temperature by the equation
where H (^) vap, the enthalpy of vaporization , is the amount of heat required to convert one mole of a liquid into a vapor.
At equilibrium
Dividing by T
Svap '
Hvap T
- Phase Diagram
A plot of the temperatures and pressures at which two or more phases are in equilibrium.
Salient Features of a Phase Diagram
C Points on the curves indicate the temperatures and pressures at which two phases are in equilibrium. The triple point is the temperature and pressure at which all three phases are in equilibrium.
C Vapor pressures at specific temperatures can be read from the phase diagram.
Example : The vapor pressure of water at 80EC is 355 torr (see above phase diagram for H O). 2
C Boiling points at specific external pressures can be read from the phase diagram. The boiling point is the temperature at which the vapor pressure of a liquid equals the external pressure.
- Ionic Crystals
Component unit : ions Cohesive forces of attraction : electrostatic attractions between the ions (ionic bond) Properties : hard and brittle, high melting points, nonvolatile, nonconductors in the solid state
Example : SnO , mp = 1630 2 EC
- Covalent Crystals
Component unit : atoms Cohesive forces of attraction : covalent bonds Properties : very hard, very high melting points, nonvolatile, insulator
Example : Diamond, mp = 3500EC
- Metallic Crystals
Component unit : atoms Cohesive forces of attraction : electrostatic attractions Properties : malleable and ductile, high melting points, nonvolatile, good conductors
Band Theory: An Explanation of Bonding in Metallic Crystals
Band gap
Empty band
Empty levels
Occupied levels
Band
g
0 1 Probability that an electron occupies energy level g
Rectangles Represent Bands of 6.022. 1023 Energy Levels
A band is a collections of closely associated molecular orbital energies. As the number of energy levels in the band increases, the difference in energy between the levels decreases.
At room temperature a number of the energy levels in the partially filled band are half- filled (see diagram above). Electrons in the half-filled levels are mobile and free to move anywhere in the solid. When an electrostatic potential is applied to the solid, there will be a net flow of electrons toward the positive charge. A partially filled band is called a conduction band.
