5.8 The Kinetic Molecular Theory of Gases!
•  The kinetic molecular theory explains the gas laws by
examining the behavior of the gas particles at the
molecular level."
•  Main ideas: "
1.  Gas particles are in continuous, random motion:"
Figure 5.15"
The Kinetic Molecular Theory of Gases (contd.)"
2.  A sample of molecules has a distribution of speeds
(velocities) and kinetic energies (i.e. some molecules
have more energy than others)."
•
The average speed of the molecules depends on the
temperature."
Figure 5.19"
Figure 5.18"
The Kinetic Molecular Theory of Gases (contd.)"
3.  For an ideal gas, the volume of gas molecules is
negligible compared to the total space they occupy."
4.  Also for an ideal gas, interactions between gas
molecules (attractions/repulsions) are negligible."
•
How do these ideas explain the behavior of gases?"
•
Since most of the volume of a gas is just empty space
(point #3), gases can be compressed easily (unlike
liquids and solids)"
•
Pressure: Pressure is caused by collisions with
surfaces. P increases as (i) the frequency of collisions
increase and (ii) energy of collisions increases. "
•
Boyleʼs Law: If the volume is reduced, there will be
more frequent collisions, so pressure increases."
The Kinetic Molecular Theory of Gases (contd.)"
•
Charlesʼs Law: At higher temperatures, gas molecules
are moving more quickly on average, so collisions are
more frequent, and (more importantly) have more
energy."
•
So at constant volume, P increases as T increases, or if
P is held constant, V must increase (this is usually how
we express Charlesʼs Law)."
•
Avogadroʼs Law: As more moles of gas are added,
there are more frequent collisions, so P increases (or
again, V increases if P is constant). "
•
Since the sizes of the molecules themselves are
negligible (point #3), the volume of the gas does not
depend on the identity of the molecules that make it up. !
The Kinetic Molecular Theory of Gases (contd.)"
•
Returning to point #2: A sample of gas has a distribution
of the kinetic energies of all of its molecules, which only
depends on the temperature."
•
This means that the molecules have a distribution of
speeds, since kinetic energy = ½ mu2 (where m = mass
and u = speed or velocity)."
•
Average kinetic energy of a sample:" K.E. = 1 2 mu2
Ø  A bar over a quantity means the average of that
quantity."
•
Since all gases have the same average kinetic energy at
the same temperature, lighter molecules move faster
than heavier ones on average (if mass is smaller, u2
must be greater, see Figure 5.18 on the second slide)."
The Kinetic Molecular Theory of Gases (contd.)"
•
The average speed of a molecule in a gas sample can be
estimated by taking the square root of the average of the
square of the speeds,"
2
u
•
This is called the root-mean-square speed (urms). It is
close to (but not exactly the same as) the average speed
of the molecules. "
•
Remember that the average kinetic energy increases as
temperature increases (in fact, when you measure T, you
are really measuring the average KE of the molecules)"
•
So urms also increases as T increases (see Figure 5.19
on the second slide)."
•
For a mole of gas molecules, the total kinetic energy is
3/2 RT, and urms is thus" 3RT
" ", where MM is the molar
mass in kg/mol."
MM
The Kinetic Molecular Theory of Gases (contd.)"
•
Most important points from this section:"
•
Molecules have a distribution of speeds and kinetic
energies."
•
All ideal gases have the same average kinetic energy at
a given temperature, but: lighter molecules have a
greater average speed than heavier ones."
•
Gas molecules move faster on average at higher
temperatures."
5.9 Diffusion and Effusion!
•  Diffusion is the movement of one gas through another."
•  e.g. when someone walks into a room wearing strong
perfume, you will eventually smell it at the other side of
the room, due to diffusion of the perfume molecules. "
•  Gas molecules do not diffuse in a straight line, but have a
random path due to collisions with other molecules: "
Figure 5.20"
Diffusion and Effusion (contd.)"
•  Effusion is the leaking of a gas through a hole in a
container, such as when air escapes from a blown-up
balloon."
Figure 5.21"
Diffusion and Effusion (contd.)"
•  The rates of both diffusion and effusion depend on the
average speed of the gas molecules."
•  So lighter molecules diffuse and effuse faster than
heavier molecules."
•  Grahamʼs Law of Effusion: Rate of effusion "!
rate1
MM2
•  or, comparing two gases: "
=
rate2
MM1
1
MM
An Application of Grahamʼs Law of Effusion"
•  Here is part of a news article from 2009:"
An Application of Grahamʼs Law of Effusion"
•  Why do we care that Iran has centrifuges?"
•  They can be used to enrich uranium."
•  Uranium consists mainly of the isotope 238U. But a very
small amount (about 0.7 %) exists as 235U (three fewer
neutrons)."
•  But 235U is important since it can be made to undergo
nuclear fission, which releases enormous amounts of
energy. Thus it can be used as a nuclear fuel, in both
power stations and weapons."
•  In order to be useful, uranium must be produced that
contains much more than the natural amount of 235U."
Ø  About 3-5 % 235U is needed for reactors; as much
as 85 % is needed for nuclear bombs."
An Application of Grahamʼs Law of Effusion"
•  Enriched uranium (containing more 235U) can be
produced by taking advantage of the fact that 235U and
238U have different masses."
•  First the uranium is converted to UF6:"
U + 3 F2 è UF6"
•  UF6 is a molecular compound that can easily be made
into a gas."
•  Since 235UF6 (349 g/mol) is lighter than 238UF6 (352 g/
mol), it diffuses faster in a centrifuge."
•  What comes out of the centrifuge is only slightly
enriched in 235U, so this process must be repeated
many times in order to obtain the desired level of 235U."
5.10 Real Gases!
•  We have assumed up to now that all gases are ideal (they
obey PV=nRT), but real gases are not exactly ideal."
•  Under normal conditions, most gases obey the ideal gas
law adequately (volume of 1 mol is close to 22.4 L at STP):"
Figure 5.22"
Real Gases (contd)."
•  Remember these two assumptions about an ideal gas:"
1.  The volume of molecules is negligible compared to size of
container"
2.  Attractions between molecules are weak."
•  So the gases that best obey the ideal gas law are small,
with weak attractions between them (weak IMFs) e.g. H2
and the Noble Gases.!
•  Effect of Temperature: As T increases, molecules have
more kinetic energy which allows them to more easily
overcome attractions between molecules. So as T
decreases, gases become less ideal."
Real Gases (contd)."
•  Effect of Pressure: As P increases,
gas molecules become more
“concentrated” so attractions
between molecules increase. This
makes collisions with the walls of the
container weaker, thus PV is smaller
than it should be (PV < nRT). •  At even higher pressures, molecules
are packed together more tightly, so
the volume of molecules becomes
more important. This causes the
volume of container to increase, so
PV becomes larger than it should
be. (At high enough P, gas will
condense to a liquid). "
Figure 5.26"
Real Gases (contd)."
•  The van der Waals Equation is a modification of
the ideal gas equation for real gases (but you do not
need to know this equation). •
Most important points from this section:"
•
Gases are less ideal:"
Ø  When molecules are larger"
Ø  When molecules have especially strong
attractions between them"
Ø  At low temperature"
Ø  At high pressure"