Kinetic Theory

Objectives

• Describe how the kinetic-molecular theory is used to explain how gases behave at different temperatures. (Exploration 1) • Analyze data that shows how gas particle mass affects that gas’s behavior. (Exploration 2) • Describe the Maxwell-Boltzmann Distribution. (Explorations 1 and 2)

Description of Activity

The kinetic-molecular theory states that a collection of gas molecules’ average kinetic energy has a specific value at any given temperature. In this activity, you will study how temperature and gas particle mass affect the frequency distribution of gas particle speeds. You will examine and analyze speed frequency distribution graphs. This distribution is called the Maxwell-Boltzmann Distribution.

Jump Start

1. What is kinetic energy? 2. What is thermal energy? 3. What happens to a gas’s thermal energy as that gas’s temperature increases? 4. What happens to the average speeds of the particles in a gas when one increases that gas’s temperature?

Safety Discussion

If you conduct this experiment in a laboratory setting, be aware that gases heated in a closed container could result in the container exploding.

Exploration 1: The Effect of Temperature on Gas Behavior

Procedure 1. Choose any gas from the list box. 2. Set Temperature to any value. Observe the shape of the frequency distribution of speeds graph. Sketch this graph. Record the most probable particle speed (vp) and the average particle speed (vavg) in Table 1. 3. Repeat step 2 for four additional temperatures. Increase the value each time. 4. Choose another gas and repeat steps 2 and 3.

Observations and Analysis
Table 1

|Gas |Temperature (K) |Most Probable Particle |Average Particle Speed |
| | |Speed (m/s) |(m/s) |
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1. What happens to the particle speed as the temperature is increased? 2. How does the speed frequency distribution graph change for a given gas as the temperature is increased? 3. At a given temperature, why does the most probable particle speed (vp) differ from the average particle speed (vavg)? 4. Does the trend of the change in shape of the graph as temperature increases differ when a different gas is examined?

Exploration 2: The Effect of Mass on Gas Behavior

Procedure 1. Set the temperature to 500 K. Maintain this temperature throughout this Exploration. 2. Select Hydrogen gas from the list box. Record the most probable particle speed and the average particle speed in Table 2. 3. Calculate the mass of a gas particle from step 2 in amu. Refer to the periodic table for the masses of individual atoms. Be aware that a hydrogen gas particle contains two hydrogen atoms, and an oxygen gas particle contains two oxygen atoms. Record your result in Table 2. 4. Repeat steps 2 and 3 for Oxygen, Carbon dioxide, and Xenon.

Observations and Analysis
Table 2 (Temperature = 500 K)

|Gas |Most Probable Particle |Average Particle Speed |Mass of a Single Atom|
| |Speed (m/s) |(m/s) |or Molecule (amu) |
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1. At a given temperature, what relationship appears to exist between a gas particle’s mass and its speed? 2. How does the graph change as particle mass increases? 3. Isra fills two identical balloons at identical temperatures. She fills one with O2 gas and the other with O3 gas. Which balloon will deflate faster? Why?

Conclusions

What can you conclude about gas molecule speeds in a container?

Inquiry Extension

Using what you learned from this activity, explain why a balloon expands when heated and contracts when cooled.