The Kinetic-Molecular Theory of Gases (5.2.4)

Question 1

• The kinetic-molecular theory of gases is a model linking the macroscopic
properties of gases to properties at the atomic-molecular level.

Answer 1

• The kinetic-molecular theory of gases is a model linking the macroscopic
properties of gases to properties at the atomic-molecular level.

Question 2

• By the kinetic-molecular theory of gases, P ∝ Nmu
2
/ V. This proportionality is
related to the ideal gas law, PV = nRT.

Answer 2

• By the kinetic-molecular theory of gases, P ∝ Nmu
2
/ V. This proportionality is
related to the ideal gas law, PV = nRT.

Question 3

The pressure of a gas is the force divided by the
area. Therefore, the pressure is proportional to the
frequency of collisions times the average force.
The frequency of collisions is proportional to the
average speed (u) times the number of particles (N)
divided by the volume (V). The average force is
proportional to the mass (m) times the average
speed (u). Therefore, P ∝ Nmu
2
/ V.
The number of particles (N) is proportional to the
number of moles of particles (n), and the average
kinetic energy (1/2 • mu
2
) is proportional to the
temperature (T). Therefore, P ∝ nT / V, or PV ∝ nT.
If two things are proportional to one another, they
are related by a constant (in this case the universal
gas constant, R). Therefore PV = nRT, the ideal
gas law.

Answer 3

The pressure of a gas is the force divided by the
area. Therefore, the pressure is proportional to the
frequency of collisions times the average force.
The frequency of collisions is proportional to the
average speed (u) times the number of particles (N)
divided by the volume (V). The average force is
proportional to the mass (m) times the average
speed (u). Therefore, P ∝ Nmu
2
/ V.
The number of particles (N) is proportional to the
number of moles of particles (n), and the average
kinetic energy (1/2 • mu
2
) is proportional to the
temperature (T). Therefore, P ∝ nT / V, or PV ∝ nT.
If two things are proportional to one another, they
are related by a constant (in this case the universal
gas constant, R). Therefore PV = nRT, the ideal
gas law.

Question 4

What is an Elastic Collision?

Answer 4

A collision in which no energy is lost.