Gas Law Applications
Edward A. Mottel
Department of Chemistry
Rose-Hulman Institute of Technology
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.
Gas Law Applications
Molecular weight determination Pressure measurements Isotope separation Stoichiometric reactions
Dumas Method of Molecular Weight Determination
The weight of a vapor is used to determine the approximate molecular weight of the compound.
Dumas Method of Molecular Weight Determination
A liquid is placed in anempty weighed retort.
The liquid is boiled untilis just completely
evaporates.
The tip of theglass retort issealed with a flame.
The mass of thetrapped gas is used inthe Ideal Gas equation
to calculate the MW
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 approachto determine the empirical formula
and the molecular formula of this compound.
Dumas Method of Molecular Weight Determination
Percentagecomposition
data
Approximate molecular weight
Molecularformula
Empiricalformula
GasData
1.6% H, 39.7% C,58.7% Cl
400. K and 870. torr,3.17 grams occupies 0.500 liters
Pressure MeasurementsBarometer
mercury
vacuumWhat forces determinethe height of themercuryin the glass tube?
Pressure MeasurementsManometer
mercuryPatm = 740. mm Hg
15.0 cm
10.0 cm
What is the pressureof the gas in the bulb?
open toatmosphere
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.
Kinetic Energy of Molecules
All gases at the same temperature have the same average kinetic energy.
KE mv1
22
If an oxygen molecule has a velocity of1000. m·s-1, what will be the velocity of a
nitrogen molecule at the same temperature?
Boltzmann DistributionMaxwell Speed Distribution Law
P vMW
RTv e MW v RT
42
32
2 22
/
velocity or energy
num
ber
of m
olec
ules
The same gas at a given average temperaturehas a range of different velocities.
Boltzmann DistributionMaxwell Speed Distribution Law
velocity or energy
num
ber
of m
olec
ules average Gas velocity is a measure
of energy (temperature)
KE mv1
22
T2 > T1
Graham's Law of Effusion
Isotope separation
evacuatedchamber
mixedgases
pinhole leak
Graham's Law of Effusion
Isotope separation
Rate of effusion of gas A
Rate of effusion of gas B
MW of gas B
MW of gas A
Derive this equation from KE mv1
22
Graham's Law of Effusion
evacuatedchamber
mixedgases
pinhole leak
Which gas has a lower molecular weight?
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.
Graham's Law of Effusion
How many enrichment cycles will be neededto raise the uranium-235 content from
the natural abundance 0.3% to 5%?
If the effusion method is used to separate235UF6 (MW = 349) from 238UF6 (MW = 352)
what will be the percentage enrichment per cycle?
Graham's Law of Effusion
Rate of effusion of 235UF6
Rate of effusion of 238UF6
MW of 238UF6=MW of 235UF6
352=
349= 1.0043
If the effusion method is used to separate35UF6 (MW = 349) from 238UF6 (MW = 352)
what will be the percentage enrichment per cycle?
Graham's Law of Effusion
eachenrichment
cycle1.0043 increase
1.0043 increase
1.0043 x 1.0043 increase
first cycle
second cycle
(1.0043)n increasenth cycle
Graham's Law of Effusion0.3%
naturalabundance
of U-235
5.0%required purity
of U-235for nuclearapplications
5.0%0.3% x (1.0043)n
5.0% / 0.3% = 16.7(1.0043)n
ln (16.7)n ln (1.0043)
n = 657 cycles
Non-ideal Behaviorvan der Waal Equation
intermolecular force correction (a)• collisions are not perfectly elastic
molecular volume correction (b)• molecules are not point masses
P an
VV bn nRTobs obs
2
Gas particles are molecules
Gas is composed of discrete particles of matter called molecules.• All molecules of the same substance are
the same.
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.
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).
Molecules are small
Molecules are small compared to the volume containing them.
• Molecules can be treated as point masses.• Gases are compressible because there is
a large distance between molecules.
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.