THE KINETIC MOLECULAR THEORY OF GASES
The physical properties of gases can be explained in terms of the
motion of individual molecules.
This molecular movement is a form of energy, which is the capacity to
do work or produce change.
Work is defined as force times distance, therefore:
Energy = work done = force x distance
The Joule is the SI unit for energy
1 J = 1 kg m2/s2 = 1 N m
Kinetic energy = the energy of motion
The findings of a number of physicists resulted in a number of
generalizations about gas behaviour that are known as the kinetic
molecular theory of gases, or simply the kinetic theory of gases.
Central to the theory are the following assumptions:
1) A gas is composed of molecules that are separated from each other
by distances far greater than their own dimensions. The molecules
can be considered to be “points”, that is they possess mass but
have negligible volume.
2) Gas molecules are in constant motion in random directions, and
they frequently collide with one another. Collisions among
molecules are perfectly elastic. In other words, energy can be
transferred from one molecule to another as a result of a collision.
The total energy of all the molecules in a system remains the same.
3) Gas molecules exert neither attractive nor repulsive forces on one
4) The average kinetic energy of the molecules is proportional to the
temperature of the gas in kelvins. Any two gases at the same
temperature will have the same average kinetic energy. The
average kinetic energy of a molecule is given by:
KE = 1/2mu2
m = mass of the molecule
u = its speed
The horizontal bar denotes an average value
The quantity u2 is called the mean square speed, it is the average of
the square of the speeds of all the molecules:
u2 = u12 + u22 + … + uN2
where N = the number of molecules
Assumption 4 enables us to write:
1/2mu2 = CT
where C = proportionality constant and T = absolute temperature
According to the kinetic molecular theory, gas pressure is the result of
collisions between molecules and the walls of the container. It
depends on the frequency of collision/unit area and how “hard” the
molecules strike the wall. The theory also provides a molecular
interpretation of temperature. The temperature of a gas is a measure
of the average kinetic energy of the molecules. In other words, the
absolute temperature is an index of the random motion (thermal
motion) of the molecules – the higher the temperature, the more
energetic the molecules.
Application to the Gas Laws:
On a qualitative basis, it is possible to use the theory to account for
the general properties of substances in the gaseous state.
1) Compressibility of Gases
2) Boyle’s Law
3) Charles’s Law
4) Avogadro’s Law
5) Dalton’s Law of Partial Pressures
Distribution of Molecular Speeds
The most probable speed of gas molecules increases as temperature
increases. The larger numbers of molecules are moving at greater speed.
Lighter molecules move faster, on average, than heavier ones.
One way to estimate molecular speed is to calculate the root-mean-square
(rms) speed (urms), which is an average molecular speed. The total kinetic
energy of a mole of any gas equals 3/2RT.
Recall: average kinetic energy of one molecule = 1/2mu2
So we can write:
NA (1/2mu2) = 3/2RT
where NA = Avogadro’s number
Because NAm = M, the above equation can be rearranged to give:
u2 = 3RT
You can take the square root of each side and solve for urms.
R = 8.314 J/K · mol Molar mass –convert to kg/mol
urms will be calculated in meters per second (m/s)
Calculate the root-mean-square speeds of helium atoms and nitrogen
molecules in m/s at 25oC.