Kinetic Molecular Theory – Chapter 21
Let’s derive the famous equation:
M
RT
u
3
=
where u = “average” speed and M = Mol.Wt.
[u is actually the
root mean square
(rms) speed]
What is Pressure?
Area
Force
P
=
But what causes this Force?
It is the collisions that the gas molecules make with the surface of the container (or balloon).
The more molecules, the higher the pressure, and the more collisions the molecules make.
So, let’s
derive this force that the molecules exert on the container.
What is Force?
t
v
m
dt
dv
m
a
m
force
that
recall
∆
∆
=
=
=
When a molecule strikes the wall and is bounced back, its initial velocity, v, is converted into –v.
So, the force for this one molecule will be given by:
L
mv
v
L
v
m
t
v
m
F
x
x
x
x
2
2
2
=
=
∆
∆
=
And the pressure will be given by:
V
mv
LA
mv
A
F
P
x
x
2
2
=
=
=
where V is the volume of the container.
So far, we have only considered the velocity in the xdirection.
But, we are generally more interested
in the speed of the molecule, u.
In three dimensions, the resulting speed from molecules having
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 Spring '09
 BERKOWITZ
 KineticMolecular Theory, Mole, pH, Kinetic Energy, Mass, Velocity, Molecule, Kinetic theory

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