Gas Law Applications

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Gas Law Applications

• Edward A. Mottel
• Department of Chemistry
• Rose-Hulman Institute of Technology

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Gas Law Applications

• Reading Assignment
• Zumdahl Chapter 5.4, 5.6-5.8
• This lecture concludes the topic of gas laws by
  describing the kinetic theory of gases and
  applying gaseous relationships to solve a variety
  of problems.

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Gas Law Applications

• Molecular weight determination
• Pressure measurements
• Isotope separation
• Stoichiometric reactions

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Dumas Method of Molecular Weight Determination

• The weight of a vapor is used to determine the
  approximate molecular weight of the compound.

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Dumas Method of Molecular Weight Determination
A liquid is placed in an empty weighed retort.
The mass of the trapped gas is used in the Ideal
Gas equation to calculate the MW
The tip of the glass retort is sealed with a
flame.
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Dumas Method of Molecular Weight Determination

• A gaseous sample was found to have the following
  composition
• 1.6 H, 39.7 C, 58.7 Cl
• At 400. K and 870. torr, a 3.17 gram sample
  occupies 0.500 liters.

Diagram an approach to determine the empirical
formula and the molecular formula of this
compound.
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Dumas Method of Molecular Weight Determination
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Pressure MeasurementsBarometer
What forces determine the height of
the mercury in the glass tube?
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Pressure MeasurementsManometer
open to atmosphere
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Kinetic Theory of Gases

• Gas is composed of discrete molecules.
• Molecules are in continuous motion.
• Molecular collisions are elastic.
• Molecules are small.
• The absolute temperature is proportional to the
  average kinetic energy.

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Kinetic Energy of Molecules

• All gases at the same temperature have the same
  average kinetic energy.

If an oxygen molecule has a velocity of 1000.
ms-1, what will be the velocity of a nitrogen
molecule at the same temperature?
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Boltzmann DistributionMaxwell Speed Distribution
Law
The same gas at a given average temperature has a
range of different velocities.
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Boltzmann DistributionMaxwell Speed Distribution
Law
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Graham's Law of Effusion

• Isotope separation

evacuated chamber
mixed gases
pinhole leak
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Graham's Law of Effusion

• Isotope separation

Derive this equation from
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Graham's Law of Effusion
Which gas has a lower molecular weight?
evacuated chamber
mixed gases
pinhole leak
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Graham's Law of Effusion

• Uranium hexafluoride (UF6) is a gas that has been
  used as a method to enrich the amount of
  uranium-235 used in nuclear reactions.
• Uranium has two principle isotopes, uranium-235
  and uranium-238.

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Graham's Law of Effusion

• If the effusion method is used to separate 235UF6
  (MW 349) from 238UF6 (MW 352) what will be
  the percentage enrichment per cycle?
• How many enrichment cycles will be needed to
  raise the uranium-235 content from the natural
  abundance (0.3) to 5?

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Non-ideal Behaviorvan der Waal Equation
2
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P
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nRT

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obs
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• intermolecular force correction (a)
• collisions are not perfectly elastic
• molecular volume correction (b)
• molecules are not point masses

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Gas Particles are Molecules

• Gas is composed of discrete particles of matter
  called molecules.
• All molecules of the same substance are the same.

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Molecules are in continuous motion

• Collide with each other and the walls that
  contain them.
• The pressure of a gas is due to the collision of
  molecules with the wall.

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Molecular collisions are elastic

• There is no net loss of kinetic energy.
• A perfectly insulated vessel will maintain the
  same total kinetic energy (the temperature will
  remain constant).

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Molecules are small

• Molecules are small compared to the volume
  containing them.
• Molecules can be treated as point masses.

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Kinetic energy is proportional to absolute
temperature

• The absolute temperature of a gas is directly
  proportional to the average kinetic energy of the
  molecules.
• The translational velocity of a molecule (a
  measure of its kinetic energy) is proportional to
  its temperature.

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