Download Kinetic Molecular Theory

Kinetic Molecular Theory
Making Macroscopic Sense out of
a Microscopic World
What is Kinetic Theory?
• Explains what causes pressure.
• Explains WHY the individual gas laws are
true.
• Is the theory behind the mathematics of
the Ideal Gas Law.
• Makes some assumptions…this is why it is
called the Ideal Gas Law.
The Tenets of Kinetic Theory
• Gases consist of large numbers of
molecules moving randomly.
• These molecules have negligible volume
compared to the container.
• The attractions and repulsions between
molecules is negligible.
• All collisions are elastic.
• Average kinetic energy of the molecules is
related to the absolute temperature.
Large Numbers of Random Motion
• This must be true for statistics reasons.
• This means that there are constant
collisions with each other and the side of
the container.
• These collisions exert a force on the
container. We call it pressure!!!
Pressure Defined
• If pressure is the force per area of these
collisions, then what happens if we
increase the number of collisions?
• How can we do that?
– Increase the number of molecules (P~n)
– Decrease the area for collisions (P~1/V)
• This is exactly what we observe!
Volume is Negligible
• The molecules must be thought of as
points in space.
• It throws off the physics calculations.
• Besides, molecules are really small
anyway!
Interactions are Negligible
• The basis of the theory is on collisions.
• If outside forces are involved, it throws off
the physics calculations.
• Gases are really far apart anyway and
attractions and repulsions decrease with
distance.
Collisions are Elastic
• In physics, this means that no energy is
lost when things collide.
• If this were not true, gases would lose
energy during collisions.
• This would make the gas freeze on its
own!!
Temperature is Defined
• If temperature is defined as the average
kinetic energy of all the molecules, what
would be effect of increasing the
temperature on the pressure?
• More intense collision would result in more
force and an increase in pressure (P~T)
Average Kinetic Energy
• Not all molecules
are going the same
speed!
• It is like a freeway.
• Since there are lots
of them, this is a
special statistical
state called
“normal.”
Speed and Kinetic Energy
• Kinetic Energy = ½ mass * velocity2
• If KE is constant and mass goes up,
velocity must go down by the square root
• If mass is the same, velocity is higher for
things with higher kinetic energy.
• Kinetic Energy is related to temperature!
• Temperature measures molecular speed!
Some Examples
• In light of KMT, why will an increase in the
number of molecules increase the
pressure?
• In light of KMT, why will a decrease in
temperature create a decrease in
pressure?
• In light of KMT, who is moving faster,
H2(g) or CO2(g) at STP?
What if the Theory is NOT Right?
• We did make assumptions…
– Volume is negligible
– Attractions/repulsions are negligible
• Are these true!?
– So there will be some error in what we base
off of Kinetic Theory.
• What law is based on KMT?
The Real (Non-Ideal) Gas Law
• We must correct for the assumptions
made:
– Volume is NOT negligible
– Attraction/repulsions are NOT negligible
•
nRT
P=
V – nb
n2a
Corrects for the attractions and
Repulsions between molecules.
V2
Corrects for the volume of the molecules.
Why don’t we use this then?...
• It is definitely more accurate, but the
amount of accuracy gained for the math
involved is not beneficiary.
• Especially at normal conditions, the Ideal
Gas Law gives sufficient accuracy.
So when should we use it?
• When the tenets that fail are no longer
negligible.
– When is volume of molecules not negligible?
• When the volume of container is small or there are
lots of molecules.
– So at large n values and small V values!
– When are the interactions not negligible?
• When the molecules are moving slowly and are
close together.
– So at small T values and large P values.