Introduction: The Kinetic Theory of Matter is the statement of how we believe atoms and
molecules, particularly in gas form, behave (are in constant random motion) and how it
relates to the ways we have to look at the things around us. The Kinetic Theory is a good
way to relate the 'micro world' with the 'macro world.'
Since light, visible electromagnetic radiation, is required to see an object and light hitting an
object gives it energy, as soon as one is able to see an object at absolute zero, it is not at
absolute zero anymore from the new energy. Any other means of detection would add
energy to the material at absolute zero. An object at absolute zero would be as difficult to
keep as a lump of antimatter. What would you keep it in? Practically, we can cool something
down to temperatures approaching absolute zero, but we cannot get to that theoretical point,
nor can we achieve temperatures below that point. There is no such thing as a temperature
below absolute zero.
The Kinetic Theory of Matter does not, and is not intended to take into account the energy of
atoms due to excitation of electrons as you might see in glowing neon in a neon light or the
bright redness of molten iron. In fact, objects cooler than molten iron and less excited than
electrified neon will give off electromagnetic radiation, but that is another story.
In the view at this level, it is useful to look at atoms as if they were close to the hard little balls
that Dalton considered. With this very mechanical view of atoms and molecules, we are
losing some important facts to get an instructive thought on matter.
Big Idea 2
LO: 5, 6, 12
Postulates of the KMT
1. All matter is made of atoms, the smallest bit of each
element. A particle of a gas could be an atom or a group of
atoms.
2. Atoms have an energy of motion that we measure as
temperature. The motion of atoms or molecules can be in
the form of linear motion of translation, the vibration of
atoms or molecules against one another or pulling against
a bond, and the rotation of individual atoms or groups of
atoms.
3. There is a temperature to which we can extrapolate,
absolute zero, at which, theoretically, the motion of the
atoms and molecules would stop.
4. The pressure of a gas is due to the motion of the atoms or
molecules of gas striking the object bearing that pressure.
Against the side of the container and other particles of the
gas, the collisions are elastic (with no friction or attraction).
5. There is a very large distance between the particles of a
gas compared to the size of the particles such that the size
of the particle can be considered negligible.
Notes:
Difference in the States of Matter in Terms of the KMT Comparative Particle Motion by State
Kinetic Energy of Gas Particles - The kinetic energy of an ideal gas is directly proportional to its absolute temperature: Average Kinetic Energy of
The greater the temperature, the greater the average kinetic energy of gas molecules.
a Single Gas Molecule
Maxwell-Boltzmann Diagrams - A Maxwell-Boltzmann diagram shows the rang of velocities that the molecules of a gas
be found at. Molecules at a given temperature are not all moving at the same velocity. When determining the
temperature, we take the average velocity of all the molecules and use that in the relevant equation to calculate
temperature. You do not need to know the Maxwell-Boltzmann equation (unless you are taking AP Physics). All you
need to know here is that temperature is directly proportional to the kinetic energy.
KE = ½ mv2
m = mass of molecule (kg)
v = speed of the
molecules (m/s)
KE is measured in joules
This first type of Maxwell-Boltzmann diagram involves plotting the velocity
distribution for the molecules of one particular gas at multiple
temperatures. In the diagram on the next page, there are three curves
representing a sample of nitrogen gas at 100 K, 500 K, and 1000 K.
As you can see, the higher the temperature of the gas, the larger the range
is for the velocities of the individual molecules. Gases at higher
temperatures have greater KE, and as all the molecules in this example
have the same mass, the increased KE is due to the increased velocity of
the gas molecules.
Ideal Gases
Many chemists had dreamed of having an
equation that describes relation of a gas
molecule to its environment such as pressure or
temperature. However, they had encountered
many difficulties because of the fact that there
always are other affecting factors such as
intermolecular forces. Despite this fact,
chemists came up with a simple gas equation to
study gas behavior while putting a blind eye to
minor factors.
Maxwell-Boltzmann diagrams are also used to show a number of different gases at the same
temperature. The diagram below shows Helium, Neon, Argon and Xenon gases all at 300 K.
We must emphasize that this gas law is ideal. As
students, professors, and chemists, we
sometimes need to understand the concepts
before we can apply it, and assuming the gases
are in an ideal state where it is unaffected by
real world conditions will help us better
understand the behavior the gases. In order for
a gas to be ideal, its behavior must follow the
Kinetic-Molecular Theory whereas the NonIdeal Gases will deviate from this theory due to
real world conditions.
When dealing with gas, a famous equation was
used to relate all of the factors needed in order
to solve a gas problem. This equation is known
as the Ideal Gas Equation.
PV = nRT
P
=
pressure
of
the
particles
(atm/torr/mmHg/kPa)
V = group volume of the particles (L)
n = amount of particles (mol)
R = gas constant (value based on unit of P)
T = absolute temperature of particles (K)
As we have always known, anything ideal does
not exist. In this issue, two well-known
assumptions should have been made
beforehand:
1. The particles have no forces acting among
them, and
2. These particles do not take up any space,
meaning their atomic volume is completely
ignored.
An ideal gas is a hypothetical gas dreamed by
chemists and students because it would be
much easier if things like intermolecular forces
(IMF’s) do not exist to complicate the simple
Ideal Gas Law. Ideal gases are essentially point
masses moving in constant, random, straightline motion. Its behavior is described by the
assumptions listed in the Kinetic-Molecular
Theory of Gases. This definition of an ideal gas
contrasts with the Non-Ideal Gas definition,
because this equation represents how gas
actually behaves in reality. Thus our study of
gases in AP Chemistry will focus on the
application of ideal theory but with the
understandings of how this theory is flawed due
to the differences between real and ideal gases.
In this case, all of the gases have the same amount of total KE because they have identical
temperatures. However, not all of the atoms have the same mass. If the atoms have smaller
masses, they must have greater velocity in order to have a KE identical to that of atoms with
greater mass. Because helium atoms have the leas mass, they have the higher average
velocity. Xenon atoms, which have a much greater mass, have a correspondingly lower velocity.
Deviation from Ideal Behaviour- At low temperature and/or high pressure, gases behave in a
less-than-ideal manner. That is because the assumptions made in kinetic molecular theory
become invalid under conditions where gas molecules are packed too tightly together. Two things
happen when gas molecules are packed too tightly
When the volume of the gas molecules becomes significant - The ideal gas equation does not take
the volume of gas molecules into account, so the actual volume of a gas under nonideal
conditions will be larger than the volume predicted by the ideal gas equation.
Gas molecules attract one another and stick together - The ideal gas equation assumes that gas
molecules never stick together. When a gas is packed tightly together, intermolecular forces
become significant, causing some gas molecules to stick together. When gas molecules stick
together, there are fewer particles bouncing around and creating pressure, so the real pressure
in a nonideal situation will be smaller than the pressure predicted by the ideal gas equation.
Postulates of the KMT (of gases)
= “Ideal Gas”
1. A gas consists of a collection of
small particles traveling in straightline motion and obeying Newton's
Laws.
2. The molecules in a gas occupy no
volume (that is, they are points).
3. Collisions between molecules are
perfectly elastic (that is, no energy is
gained or lost during the collision
due to friction).
4. There are no attractive or repulsive
forces between the molecules.
5. The average kinetic energy of a
molecule is 3kT/2. (T is the absolute
temperature and k is the Boltzmann
constant.) As such, the relative
motion of a particle is proportional to
its absolute temperature.
Real vs. Ideal Gas
1. An ideal gas has no definite volume while real gas has
definite volume.
2. An ideal gas has no mass whereas real gas has mass.
3. Collision of ideal gas particles is elastic while non-elastic
for real gas.
4. No energy involved during collision of particles in ideal
gas. Collision of particles in real gas has attracting energy.
5. Pressure is high in ideal gas compared to real gas.
6. Ideal gas follows the equation PV=nRT. Real gas follows
the equation
Note “corrections" are being made to the pressure term and
the volume term. Since collisions of real Gases are nonelastic, the term n2a/V2 is correcting for the interactions of
these particles. The value of a is a constant, and must be
experimentally determined for each gas. Since real gas
particles have real volume, the nb term is correcting for the
excluded volume. The value of b is a constant, and must be
determined experimentally for each gas.