A replacement Maxwell-Boltzmann Distribution Simulation

Maxwell-Boltzmann Distribution Simulation from Wolfram

Do you ever have that Go-To demonstration or website for an activity that you really value? You've been using it for a few years, tweaked it to make it better - only to send your students there one year and have the activity fall flat on its face because the website is no longer available?

That almost happened to me this year.

As described in a previous post here on ChemEd X, I use Molecule Lab on iPads, coupled with an online simulation to introduce students to Maxwell-Boltzmann distributions. The pairing of the simulations really complemented each other, and students left with a good foundation for moving forward with energetics and kinetics discussions. In the previous post linked earlier, I take you through the process of the lesson and give some background on my discussion with students.

This week I intended to use the same process, having the students work through the two simulations as my typical introduction to Maxwell-Boltzmann. Luckily, I'm now in the habit of checking simulations I use the night before a lesson just to verify that they still work. When I found that Java simply wouldn't cooperate I started searching for replacements. I ended up stumbling upon the Wolfram Demonstrations Project (See note below about the simulations). This platform, created by the same group that put forth Mathematica and Wolfram Alpha, has a simulation "player" that uses Mathematica output for various simulations. Included in this collection is a similation that will create Maxwell-Boltzmann distribution curves for different conditions. The conditions that can be varied are temperature and molar mass of the gas. 

And while I did find this simulation quite clean and easy to use with the sliders provided so students could change conditions, I did miss the molecular motion provided by the previous simulation that no longer works for me due to Java issues. Another improvement would be adding a second gas (with its own set of sliders) to the same graph for an easier direct comparison between conditions. But linking the observations of the simulation with observations from MoleculeLab allowed students to generate a better understanding of the concept of Maxwell-Botlzmann Distribution Plots, and thus the simulation was useful.

I intend to explore the Wolfram collection more, and will share any simulations that I put into circulation within my class.

Do you have any Go-To simulations you rely on for your teaching sequence? I'd love to hear about them.

Note: In order to use these simulations, you need to download their CDF Player. Once the CDF Player is downloaded, you can download the actual simulations and save them to your hard drive. The simulations are pretty small - with many less than 100 KB. The CDF Player, however, takes up over a GB of space on your hard drive. But it's worth it! There are numerous simulations available.

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Michael Farabaugh's picture
Michael Farabaugh | Fri, 08/07/2020 - 12:26

Recently, I read a post from Jamie Benigna that appeared on the College Board's AP Teacher Community board. Jamie had shared information with everyone about using Desmos to create Maxwell-Boltzmann curves.

More information can be found here.

(Note: I'm not sure if the link shown above will actually work for everyone. It is supposed to take you to a pdf that was posted to the Resources section of the AP Teacher Community board.)

The links shown below should work, and they should take you directly to the Desmos site.

Single curve: https://www.desmos.com/calculator/k1i8zco3fz

Two curves: https://www.desmos.com/calculator/ukvmedo4ax

Three curves: https://www.desmos.com/calculator/bxvt0danbg

Jamie also posted the following information, in response to a question that someone had asked about using these types of curves to display information about the collision energy of reactant particles in relation to the activation energy for a reaction:

Add vertical line for activation energy:  https://www.desmos.com/calculator/ubnofaxgzr

Add vertical line and area under the curve to show the proportion of particles above the activation energy: https://www.desmos.com/calculator/ih5uoy4ooo

Jamie also wrote the following:

"A warning on both of these, though: for the activation energy to be related to the graph, the x-axis shouldn't be "speed," but more like "collision energy."  However, if graphing energy on the x-axis, then the first part of the curve should be more linear and not have the quadratic-like upsweep.  I don't have a function at the moment that can do that, but I'll see if I find something later on.  If you're comfortable using something that you know is flawed but illustrates something you want to show, then feel free to use it. You should be able to change the label if you open the collapsed folders (click on the arrow to open) and relabel the point that is labeled "Activation Energy" at the bottom."

Thanks to Jamie Benigna for sharing this information!