Kinetic Molecular Theory

Pressure: Concepts

What is the origin of the pressure exerted by a gas?

The Kinetic Molecular Theory proposes that a gas is composed of a large number of particles in rapid motion. Each particle occasionally collides with a wall of the container. As a result of that collision, the particle exerts a force on the wall.

What does the Kinetic Molecular Theory predict about the pressure of a gas? Pressure is the force applied to a surface divided by the area of the surface. The force is the sum total force of all particles colliding with the surface.

The molecular dynamics simulation shown below contains helium and krypton atoms. The small red particles represent helium atoms (FW 4.00), and the larger blue particles represent krypton atoms (FW 83.80).

The graph shows the speed of one of the helium atoms (red line) and the speed one of the krypton atoms (blue line) as a function of time. The speeds fluctuate, of course, as a result of the collisions with other particles. Run the simulation, carefully observe the behaviors of the particles, and answer the following questions.

1.     Which atoms, helium or krypton, move faster? Explain why this behavior occurs in terms of the postulates of the Kinetic Molecular Theory.


2.     Why do the helium atoms (speed depicted with red line) show much more variability in speed than the krypton atoms (blue line)?


3.     Does a particular helium atom always move faster than all the krypton atoms?
4.     On average, the helium and krypton atoms move at different speeds. According to the Kinetic Molecular Theory, which atoms, on average, have the larger kinetic energy?


5.     Which atoms, helium or krypton, collide more frequently with the walls of the container?
6.     A helium atom and a krypton atom, each moving at the same speed and same direction, collide with the wall. Which atom imparts a greater force on the wall?


7.     This molecular dynamics simulations allows for intermolecular attractions between molecules. Do you see evidence of intermolecular attractions in the behavior of the particles? Which atoms, helium or krypton, show stronger intermolecular attractions?


8.     A gas that behaves all of the postulates of the Kinetic Molecular Theory is an Ideal Gas and obeys the Ideal Gas Law. The molecular dynamics simulation includes non-ideal behavior resulting from the presence of intermolecular attractions and the size of the atoms. Which gas, helium or krypton, comes closest to behaving like an Ideal Gas?

Factors affecting the Pressure

In the simulation below, you may choose one of the noble gases and the number of molecules placed in the system. One of the molecules (the small red particle) will always be helium, to make it easier to compare the behaviors of the different noble gases. The remainder of the atoms are the type chosen from the list at the right of the simulation. The manometer at the left of the simulation allows the pressure of the system to be measured.

Systematically vary the identity of the noble gas and number of particles (between 10 and 50). Note that the different noble gases have different atomic masses. Remember to reset the simulation after the conditions are changed. Your goals are to identify the effects of particle mass and number of particles on the pressure of the gas and to explain this behavior in terms of the Kinetic Molecular Theory.

Carefully observe the simulation and answer the questions listed below. Bear in mind positions of the walls are fixed. Therefore, the surface area for the container walls is constant. The temperature is also fixed, which means the average kinetic energy of a particle is constant.

1.     Select a particular noble gas, and run the simulation with 20 particles in the system. Measure the pressure of the gas. Repeat the experiment using 40 particles.
   
   How does the pressure change when the number of molecules is doubled?
   Explain this behavior in terms of the Kinetic Molecular Theory.


2.     Set the simulation to contain 40 particles. Select helium as the noble gas. Run the simulation and record the pressure. Keep the number of particles at 40 and select xenon as the noble gas. Run the simulation and record the pressure.
   
   How does the pressure change when the mass of the particles is increased?
   Explain this behavior in terms of the Kinetic Molecular Theory.


3.     As the mass of a particle increases, the particle moves more slowly (on average) and consequently collides less frequently with the container walls. Watch the simulation to observe this behavior.
   
   If collisions with the walls occur less frequently, why is the pressure unaffected by a change in particle mass?