SimuLab 15: The Diffusion Chamber Simulation
The Diffusion Chamber program carries out the diffusing checkers model with computer speed, many more "checkers,'' and a longer chamber. With this program you can change the model in various ways in order to compare the results with experiment.
Start the Diffusion Chamber program. You will see two diffusion chambers, one above the other. Later this arrangement will allow you to compare diffusion under different circumstances. For now just use the upper chamber. In the selections on the right, choose m(green) = m(blue) which means that the two diffusing molecules have the same mass, Infinite Particles which means particles are renewed from a source at each end of the chamber, and 1D Random which means that the model is a onedimensional random walk. Start the run with the upper chamber.


Now choose a topic from the list below and carry out a brief investigation
using the Diffusion Chamber program. Different groups in
the class may choose different topics.
For comparison, you can use both chambers in the display, if you wish, running them simultaneously. To increase the statistical accuracy of your results, you can increase the number of particles using the Size menu items (but then the process will take longer).
2. Mass Ratio of Molecules: When two molecules of different mass have
the same kinetic energy, the molecule with the larger mass moves more slowly.
Here is the reason: At a given common temperature, all molecules in a gas
have the same average kinetic energy (mv^{2}/2), so one would
expect the molecules with larger mass m to move slower, on the average. Perhaps
slowermoving more massive molecules will diffuse more slowly than less massive
molecules. Therefore, perhaps the initial precipitation disk will not occur
in the middle of the tube. Is this true?
In the diffusion chamber demonstration, HCl has a molecular weight (atomic mass) of 1 + 35.5 = 36.5, while NH_{3} has a molecular weight of 14 + 3 = 17, about half as much. As a result of this difference, which molecule do you expect to diffuse faster. Do you expect the initial precipitation disk to form nearer the end of the chamber from which HCl is diffusing, or nearer the end from which NH_{3} is diffusing? How much nearer? Write down your predictions.
Test your predictions with the Diffusion Chamber program. You can try two different mass ratios in the two panels at the same time, determining the location of the initial precipitation "disk" in each case.
Do you obtain more accurate results with molecules of smaller size? Note: The "Length'' of the chamber is measured in the number of horizontal positions that can be occupied by the diffusing molecules. When you choose a smaller size for the molecules, more of them can line up from right to left in a given chamber. In this case, the number displayed for the "Length'' is larger for a chamber that shows the same size on the screen.
3. Motion of Particles: Our simplest model forces the molecules to
execute a random walk on one dimensioneach one moving back and forth along
a line. What is different if the molecules can move in two dimensions, executing
the socalled "2D random walk''? Will it take longer for the initial
precipitation disk to form? Will this disk appear in a different place? Write
down your predictions, then test them by changing the Motion of Particles
setting to 2D Random. Write down your results and compare them with
your predictions.
A third way that particles might move is ballistic. This means constant velocity in a straight line along the length of the tube. What do you expect to happen in this case? Will formation of the precipitation disk occur more quickly or more slowly than for a random walk? Will ballistic motion change the location of the initial precipitation disk? Write down your predictions.
Try the Ballistic setting for Motion of Particles and compare the results with your predictions. Predict what will happen if you carry out the ballistic experiment with the Infinite Particles setting, then the No new particles setting. Compare the results with your predictions.
Discussion  What to Expect
Before going on to a laboratory experiment with diffusion chambers made of small tubes, we try to estimate numerical values for some of the results to expect in such experiments. To simplify the analysis, we return to the onedimensional random walk model for diffusion.
From the ManyWalkers program (SimuLab 3.5) we know that in a onedimensional random walk the average of the square of distance traveled is proportional to the number of steps. Let Let x^{2} stand for this average square, let N be the number of steps, and let L_{step} be the average length of each step, the average distance between collisions. Then the result can be written as:
Why L_{step}^{2}? This must be entered in the equation as a square to make the units correct, since N here has no units. Why L_{step}^{2}? This must be entered in the equation as a square to make the units correct, since L_{step} here has no units.Notice that for uniform "ballistic'' motion in a straight line, the formula would be N = x/L (without the squares).

2. Distance between collisions. A gas molecule in the air travels a distance
between collisions (the length of one step) approximately equal to L_{step}
= 1000 x 3 x 10^{10}meters = 3 x 10^{7} meters.
How does this distance compare with the diameter of one hair on your head?
This distance is equal to how many times the diameter of an atom?
From these quantities and earlier equations, answer the following questions:




