## Behavior of Gases: Finding the Molar Mass of a Fictitious

Gas Using Temperature and Average Velocity

OBJECTIVES

• Determine the molar mass of a fictitious gas in a simulation
• Learn the relationship between temperature and kinetic energy

INTRODUCTION

The molecules of matter at ordinary temperatures can be considered to be in ceaseless, random motion at high speeds. The average translational kinetic energy for these molecules can be deduced from the Boltzmann distribution. Knowing the velocity and the temperature of these molecules at different temperatures will allow us to calculate a value for the Molar Mass.
The Boltzmann distribution of energies can be broken down to relate average velocities to temperature using the following relation:
k = 1.38 x 10-23 J/K
T in Kelvin
m of a single particle in kg
v in m/s
We can eliminate the 1/2 factor by multiplying both sides by 2 giving us:
You can see how this equation can be viewed and plotted as a linear relationship with v2 as the x-axis and 3kT as the y-axis.

PROCEDURE

A. Go to the University of Colorado website for science simulations: phet.colorado.edu.Click on the “Play with Simulation” button.

Click on “Chemistry”

Find the lab the says “Gas Properties” and click on it.

You can either use the simulation online or download it as a .jar (Java archive) file. If you click to play and you get a blank screen, you will need to download it.

Open the .jar file and run it. If you need to install Java on your computer you can do so here https://java.com/en/download/manual.jsp. You may need to restart your computer
3
2
kT = 1
2
mv
2
3kT = mv
2
y = mx + b
Page 1 of 4 after installing. You may also get a message about the developer and it won’t open. If this happens, just hold down Control and click to open the file, then open it

B. SETTING UP THE EXPERIMENT

Click on “Volume” as your Constant Parameter.

Click on “Measurement Tools”, then select “Species Information”

Click on “Advanced Options” and deselect “Molecules Collide”

Record your data from the experiment in the table below for Temperature, Pressure, and Average Speed

C. RUNNING THE EXPERIMENT

Use the pump handle to pump in between 300 and 600 particles. This is shown in the
right-hand panel.

Record the values for the Temperature, Pressure, and Average Speed in your table above. Average Speed is shown in the pop-up window.

Use the Heat Control to raise or lower the temperature and record at least 4 additional data points with a total temperature range of at least 500K between the lowest and highest temperatures and at least two below room temperature (300K)

Once you are finished recording your data points, click on the “Reset” button to begin a new experiment. (You may need to close the Measurement Tools to find the reset button).

Choose the “Light Species” for the Gas in Pump, and repeat steps 1 – 4. Be sure to choose at least one temperature in this series of measurements that is the same as the first series
Heavy Species T(K) Pressure (atm) Average Speed (m/s)
Light Species T(K) Pressure (atm) Average Speed (m/s)
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D. DATA ANALYSIS

Plot your data with v2 as the x-axis and 3kT as the y-axis as explained in the Introduction

Find the mass of a single particle in kg, and the mass of one mole of particles in g/mol.
Show your calculations below. (Note: You will need to find the slope of your line. To find the slope of your line to more than one significant figure in Excel you may need to use the SLOPE function. In a cell type =SLOPE(range of y-values),(range of x-values))

Repeat your analysis for the light species.

E. QUESTIONS

What is the relationship between temperature and average velocity?
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Using the two measurements that were at the same temperature for the two species, how did the average velocity compare between the heavy and light particles? Explain why this is.

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