Untitled - Kelly Walsh High School

86 CHEMISTRY FOR THE UTTERLY CONFUSED
5-3 The Kinetic-Molecular
Theory of Gases
The kinetic-molecular theory (KMT) represents the properties of gases by
modeling the gas particles themselves at the microscopic level. The KMT
assumes that:
• Gases are composed of very small particles, either small molecules or individual
atoms.
• The gas particles are so tiny in comparison to the distances between them, that
the KMT assumes the volume of the gas particles themselves is negligible.
• The gas particles are in constant motion, moving in straight lines in a random
fashion and colliding with each other and the inside walls of the container.
These collisions with the inside container walls comprise the pressure of
the gas.
• KMT assumes that the gas particles neither attract nor repel each other. They
may collide with each other, but if they do, it assumes the collisions are
elastic—no kinetic energy is lost, only transferred from one gas molecule to
another.
• Finally, the KMT assumes that the average kinetic energy of the gas is proportional
to the Kelvin temperature.
A gas that obeys all of these conditions is an ideal gas.
Using the KMT, we can derive several quantities related to the properties of
the gas particles. First, KMT qualitatively describes the motion of the gas particles.
The average velocity of the gas particles is the root mean square velocity
and has the symbol u rms. This is a special type of average speed. It is the
average speed of a gas particle having the average kinetic energy. We can represent
it as:
where
u rms 23RT/M
R is a molar (ideal) gas constant of 8.314 J/mol·K (8.314 kg·m 2 /s 2 ·mol·K)
T is the Kelvin temperature
M is the molar mass of the gas.
These root mean speeds are very high. Hydrogen gas, H 2, at 20. o C has a value
of approximately 2000 m/s.