AP Chemistry - Gases
The Kinetic-Molecular Theory of Gases
|Any law is an empirical generalization which describes the
results of several experiments. A law, however, only describes results;
not explain why they have been obtained. A theory is a description
explains the results of experiments. The kinetic-molecular theory of
is a theory of great explanatory power. We shall see how it explains
ideal gas law, which includes the laws of Boyle and of Charles;
law of partial pressures; and the law of combining volumes.
|The kinetic-molecular theory of gases can be stated as
1. A gas consists of molecules in
constant random motion.
2. Gas molecules influence each other
only by collision; they exert no other forces on each other.
3. All collisions between gas
molecules are perfectly elastic; all kinetic energy is conserved.
4. The volume actually occupied by
the molecules of a gas is negligibly small; the vast majority of the
volume of the gas is empty space through which the gas molecules are
|These postulates, which correspond to a physical model of
a gas much like a group of billiard balls moving around on a billiard
table, describe the behavior of an ideal gas. At room temperatures and
pressures at or below normal atmospheric pressure, real gases seem to
be accurately described by these postulates, and the consequences of
this model correspond to the empirical gas laws in a quantitative way.
|In the KMT, pressure is the force exerted against the wall
a container by the continual collision of molecules against it.
Newton's second law of motion tells us that the force exerted on a wall
by a single gas molecule is equal to the mass of the molecule
multiplied by the velocity of the molecule. The molecule rebounds
elastically and no kinetic
energy is lost in a collision. All the molecules in a gas do not
the same velocity. The average velocity is used to describe the overall
in a container of gas.
|The pressure-volume product of the ideal gas equation is
directly proportional to the average velocity of the gas
molecules. If the
velocity of the molecules is a function only of the temperature, then
KMT gives us Boyle's Law.
|The statement that the pressure-volume product of an ideal
gas is directly proportional to the total kinetic energy of the gas is
statement of Boyle's Law, since the total kinetic energy of an ideal
gas depends only upon the temperature.
|If you look at the ideal gas law equation carefully you
will see that it shows that the total kinetic energy of a collection of
gas molecules is directly proportional to the absolute temeprature of
the gas. The ideal gas law can be rearranged to give an explicit
expression for temperature. Temperature is a function only of the mean
kinetic energy, the mean velocity and the mean molar mass.
|As the absolute temperature decreases, the kinetic energy
must decrease and thus the mean velocity of the molecules must decrease
also. At T=0, the absolute zero of temperautre, all motion of gas
molecules would cease and the pressure would then also be zero No
molecules would be moving. Experimentally, the absolute zero of
temperature has never been attained, although modern experiments have
made it to temperatures as low as 0.01
|It has been necessary to use the average velocity of the
molecules of a gas because the actual velocities are distributed over a
range. This distribution, can be described by Maxwell's law
distribution of velocities, or you can think of a superhighway.
is an average speed on the highway. Some cars are travelling
some faster, some at exactly the right speed. Even those on
control are never exactly on the right speed because of the
in the speed control on each individual engine and the ground geometry
which the car must be moved.
|It is not necesary to use a Maxwell-Boltzmann distribution
velocities to explain either the nature of temperature or Charles' law,
although it is the correct expression of the distribution. Charles' law
can be obtained for any distribution in which the velocities of the gas
molecules are a function of the nature of the gas and the
|Dalton's law of partial pressures follows from the KMT of
gases. If the gas molecules in a mixture are in constant and
random motion and
if there are no forces operating between the molecules except
then on the average, the net effect of collisions with other molecules
be zero. For this reason each gas acts as if it were present
|The root mean square velocity of a molecule can be
obtained by using the formula
|Example: Calculate the root-mean-square velocity of oxygen
moleules at room temperature, 25oC. M is the
molarcular mass of
oxygen which is 31.9998 g/mol; the molar gas constant is 8.314 J/mol K,
the temperature is 298.15 K. The molecular mass must be divideved
1000 to convert it into a usable form, therefore
vrms = (3(8.314)(298.15)/(0.0319998))1/2
= 481.2 m/s
So an oxygen molecule travels through the air at 481.2 m/s
which is 1726 km/h, much faster than a jetliner can fly and faster than
that of most rifle bullets.
|The very high speed of gas molecules under normal room
conditions would indicate that a gas molecule would travel across a
room almost instantly. In fact, gas molecules do not do
so. If a small sample of a
very odorous (and poisonous) gas, H2S is released in one
of a room, our noses will not detect it in another corner of the room
several minutes unless the air is vigorously stirred by a mechanical
The slow diffusion of gas molecules which are moving very quickly
because the gas molecules travel only short distances in straight lines
they are deflected in a new direction by collision with other gas
|The distance any single molecule travels between
collisions will vary from very short to very long distances, but the
average distance that a molecule travels between collisions in a gas
can be calculated. This distance is called the mean free path of the
gas molecules. If the root-mean-square velocity is divided by the mean
free path of the gas molecules, the result will be the number of
collisions one molecule undergoes per second. This number is
called the collision frequency of the gas molecules.
|The postulates of the KMT of gases permit the calculation
of the mean free path of gas molecules. The gas molecules are
visualized as small hard spheres. Without going into the
mathmatical detail; as the temperature rises the mean free path
increases; it also rises as the pressure decreases, and as the size of
the molecules decrease. Taking all this
into account, the oxygen molecules from above have a mean free path of
nm. Diffusion takes place slowly because even though
are moving very fast, they travel only short distances in any one