button below the graph. Kinetic Theory of Gases - Computer Simulation
Dynamics on the microscopic level is often very difficult for us to comprehend, since textbook descriptions and illustrations simply do not provide an adequate picture of motion. Computer simulation of dynamics fills that gap by providing a direct picture of microscopic behavior. In this lab you will be using a powerful and sophisticated computer program called Boltzmann, that simulates the motional (dynamical) behavior of gases on the molecular level. You will learn about the kinetic theory of gases and Graham’s Law.
Start-up: Log in to your PC Network account in the ChemTech PC Lab (Foster Hall 326). Launch the Boltzmann program by clicking on Start / Programs / Chemistry / Boltzmann Kinetic Theory Program. The simulator will come up with a collection of 40 molecules, depicted as red spheres, having a mass of 2.0 amu, corresponding to H2 molecules, at a temperature of 1500 K.
Lower the temperature of the system to near 300 K. Change the mass of the molecules to 4 amu, corresponding to Helium. Now click the START button to enact that change and reset the clock.
Click on the Cum box in the middle left hand side of the window to begin accumulating statistics on the molecules for later study.
A. Qualitative Behavior of the Molecules: Now, observe the motional behavior of the molecules, and reflect on their properties relative to the following basic concepts of the kinetic-molecular theory of gases:
1. Are the gas molecule dimensions small compared to the space between them?
2. Are the molecules in continuous motion, or is the system tending toward a rest state?
3. Do the molecules travel in straight-line motion between collisions?
4. Are all the molecules traveling at the same speed, or are there a range of speeds evident?
5. Follow one molecule with your eye. To make this easier, simply click in the simulation space with the mouse, which drops a "blue" molecule into the simulation. Follow this molecule. Does the given molecule travel always at the same speed or does its speed vary?
6. Over a lengthy period of time, does the given molecule exhibit systematic motion, or is it random, chaotic motion? (The motion of a single gas molecule is characteristic of the process called diffusion.)
B. Quantitative Statistics of the Molecules: In the next set of observations, you will look at the cumulative statistics on the particles. In the upper left hand corner of the window you will see a graph showing the instantaneous speed distribution of the molecules. The white curve indicates the theoretical line of the Maxwell-Boltzmann distribution of speeds. The bars indicate actual tallies of numbers of particles traveling at various speeds. Slight discrepancies between the bar graph and the smooth curve are due to insufficient sampling data accumulated.
Other distributions may be observed by clicking on the
button below the graph.
1. Sketch the distribution of instantaneous speeds in the following axis system, being as quantitative as possible in labeling the x-axis. Record the average speed of the molecules in meters per second?
2. Next, bring up the Kinetic Energy distribution. Sketch the distribution of kinetic energies of the molecules. Record the average kinetic energy of the molecules?
3. Next, bring up the Path distribution. This is the distribution of the distance traveled between collisions. Sketch the distribution of paths of the molecules. Record the average path length between collisions in nanometers?
C. Gas Diffusion and Effusion: The final exercise involves the effusion of gas molecules through a small orifice, which is described by Graham’s Law of effusion, covered in lecture. You will set up a simulation of a mixture of two gases of different mass both effusing through the same opening. You will observe which gas makes more rapid progress in populating the region on the other side of the orifice.
Set-up: Cut down the number of molecules to 20. Adjust their mass to 4 amu for Helium. Click the DIVIDE button to divide the arena. Click the START button. Now all the red helium atoms should be on the left side of the divider. Change the mass to 28 for Nitrogen gas. Using the arrow cursor and mouse clicks, drop 20 blue Nitrogen molecules into the left side of the arena. Click the DIVIDE button again to open up the orifice (pinhole) and begin the Graham’s Law demonstration. Immediately record the start time given in the bottom left corner of the window. Observe the effusion of the two types of molecules through the orifice.
1. Occasionally hit the PAUSE button and count the number of Heliums and Nitrogens that occupy the Right side of the divider and the time in the table below:
2. Use Graham’s Law to calculate the numerical ratio of rate of effusion of Helium to Nitrogen in the space below.
3. Does the simulation agree with this calculation in a qualitative sense? In a quantitative sense?
4. If the simulation does not give a precise quantitative reflection of Graham’s Law, what could be done to improve the quantitative estimate of the simulation?
5. Describe what the gas system would be like when equilibrium is reached.