Chemical Bonding Theory

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• Chemical Bonding Theory
• Metals, semiconductors and insulators MO theory
  and band theory
• Solid bulk samples of metals have a large number
  of MOs because many AOs from each metal atom
  are available to form LCAOs
• The resulting MOs are closely spaced in energy
  and are said to produce a band of delocalized
  MOs spread out throughout the bulk solid
• Each MO in a band can accommodate 2 electrons

• In a metal, there are not enough electrons to
  fill all the orbitals of the band
• The highest occupied band is called the valence
  band
• The state with lowest energy - electrons filling
  the lowest energy orbitals of a band - occurs
  only at 0 K
• The highest energy level occupied at 0 K is the
  Fermi Level
• A slight input of energy will promote an electron
  to a higher orbital resulting in two
  half-filled MOs, one above the Fermi level and
  one below the Fermi level
• Movement of electrons in these half-filled levels
  close the the energy of the Fermi level is
  responsible for electrical conduction in metals

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• Chemical Bonding Theory
• Metals, semiconductors and insulators MO theory
  and band theory
• The energy difference between the MOs in a band
  is very small and a continuum of energy states
  is produced
• There are electrons that can absorb light of
  almost any wavelength
• Absorption of light excites the electron, but it
  can immediately reemit a photon equal in
  wavelength to the incident, exciting photon
• This produces the metallic luster characteristic
  of metals
• Nonmetals behave as insulators because the
  valence band is completely filled with electrons
• The next highest MOs are a band of anitbonding
  MOs at much higher energy
• Promoting an electron in such a solid is not
  likely and the solid is not electrically
  conductive

Empty levels Conduction band

• Example the bonding in diamond can be considered
  to consist of a band of bonding MOs made up of
  C atom AOs spread out over the entire crystal
• Two bands result - a band of bonding MOs filled
  with electrons (valence band) and a band of
  empty anitibonding MOs (conduction band)
• The separation in energy of the two bands is the
  band gap

Band gap
Filled levels Valence band
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• Chemical Bonding Theory
• Metals, semiconductors and insulators MO theory
  and band theory
• Semiconductors have electrical conductivities
  between metals and insulators
• The band gap is smaller (50-300 kJ/mol) than
  insulators (500 kJ/mol)
• Some electrons can be promoted to the conduction
  band
• Si and Ge are intrinsic semiconductors
• When an electron is promoted, a positive hole is
  created in the valence band
• Both the electrons and holes carry charge - in
  opposite directions
• A hole moves as a nearby electron fills the hole
  creating a new hole some distance away
• As the temperature increases, more electrons
  occupy the conduction band

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• Chemical Bonding Theory
• Metals, semiconductors and insulators MO theory
  and band theory
• Semiconductors
• Extrinsic semiconductors have dopants added to
  control conductivity
• Substituting some of the Si atoms with Al or B
  atoms result in some bonds in the crystal to be
  electron deficient
• Group 3A elements have 3 valence electrons
  instead of the 4 valence electrons in Si or Ge
• A new band - the acceptor level - is created at
  slightly higher energy than the valence band
• Electrons are easily promoted to the acceptor
  level and positive holes are created in the
  valence band
• Such semiconductors are called p-type
  semiconductors
• Substituting some of the Si atoms with P atoms
  results in some bond in the crystal to have
  extra electrons
• P has one more valence electon than Si or Ge
• A new, filled band - the donor level - is
  established just below the conduction band
• Electrons are easily promoted to the conduction
  band and carry electric current
• Such semiconductors are called n-type
  semiconductors because they make use of
  negative charge carriers

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• Gases
• Characteristics of gases
• Often the case that gases at room temperature and
  atmospheric pressure are substances that have
  low molecular masses and are formed from
  nonmetal elements
• H2, N2, O2, F2, Cl2, CH4, HCl, H2S
• The term vapor refers the gas phase of substances
  that are liquids or solids at room temperature
  and atmospheric pressure.
• Gases take on the shape and volume of their
  container.
• Gases, as opposed to liquids or solids, are
  easily compressed.
• It is relatively easy to change the volume of a
  gas by applying pressure.
• Mixtures of gaseous substances form homogeneous
  mixtures.
• Many of the properties of gases result from the
  fact that the size of the molecules making up a
  gas are very small compared to the the total
  volume of a sample of gas.
• The molecules in a bulk sample of gas are very
  far apart.
• The physical behavior of different gaseous
  substances is very similar.

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• Gases
• Properties of gases to be examined
• Pressure
• Temperature
• Volume
• Amount of substance in bulk sample of gas
• Pressure is defined as force per unit area.
• Traditionally chemists measure the pressure of
  gases using manometers
• Closed end manometers are simpler to use because
  they requir only one measurement - the
  difference in height of the two columns of mercury

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Gases Measuring pressure of a gas with a closed
end manometer
Fg
A
FHg, r
Thus, the pressure of the gas, Pg, is directly
proportional to the net height of the Hg
column, hhr-hl
FHg, l
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Gases Using Open End Manometers the atmospheric
pressure must be taken into account
PggtPatm PgPhlPatmPhr PgPatmPhr-Phl PgPatm(P
hr-Phl) PgPatm Ph
PatmgtPg PgPhlPatmPhr PgPatmPhr-Phl PgPatm-(P
hl-Phr) PgPatm - Ph
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Gases Atmospheric pressure By definition the
standard atmoshpere will support a column of
mercury in a closed tube that is 760 mm high at 0
oC.

• The current definition of the standard atmosphere
  is
• 1 atm 1.01325 x 105 Pa
• Other useful conversions are
• 1 atm 760 mm Hg 760 torr 101.325 kPa
• Example convert 610 mm Hg to atm and kPa. This
  is the typical atmospheric pressure at UCCS.

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• Gases
• The Pressure - Volume Relationship Boyles Law
• For a fixed quantity of gas at constant
  temperature if the pressure is increases the
  volume decreases.
• Experiment shows that if the pressure is doubled
  the volume is halved

Example A gas at 255 torr and 555 mL is changed
to 325 mL. What is the new P?
Note decreasing the volume means the pressure
must increase.
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• Gases
• The Temperature - Volume Relationship Charless
  Law
• For a fixed quantity of gas at constant pressure,
  it is found that increasing the temperature
  increases the volume

-273 oC
Plots of volume vs. temperature for different
masses of the same gas at constant pressure. If
the temperature scale is converted to the K
scale, the volume (V) is directly proportional
to the temperature (T)
Example If a gas has V 255 mL at 20 oC and the
temperature is changed to 40 oC, what is the new
volume?
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Gases Combined Charless and Boyles Laws
Example A sample of He having P621 torr
occupies 375 mL at 25 oC undergoes a temperature
change so that I ts new P is 760 torr and
occupies 300 mL. What is the new temperature?
This gives rise to a 2rd law - The Pressure -
Temperature Relationship Gay-Lussacs Law
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• Gases
• The Amount of Gas - Volume Relationship
  Avogadros Law
• At constant temperature and pressure, the volume
  of a gas is directly proportional to the amount
  of gas.
• For a given gas, doubling the mass of the gas
  doubles its volume
• Avogadros law states that equal volumes of gas
  at the same temperature and pressure contain
  the same number of moles of gas.

The Ideal-Gas Equation Combine the four gas laws
into a single equation
T must be in Kelvins Most gas law problems
involve L, atm, and mol as units for variables
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• Gases
• Ideal Gas Law
• The ideal gas law is a limiting law in that it is
  valid under a set of limiting conditions.
• Most gases follow this law at temperatures that
  are high compared to the boiling temperature of
  the substance and at pressures that are low, 1
  atm or less.
• Gases will deviate from this equation when the
  temperature is near the boiling temperature of
  the substance and the pressure is high.
• Example What mass of N2 is contained in 500 mL
  at 610 torr at 25 OC?