# Workout: A Boltzmann distribution example

Read the page, Example: The Boltzmann distribution,

## Launch

Launch the PhET simulation, Reversible Reactions

## Set up

On the screen is represented a metastable state of a set of molecules. The molecules on the left are at a higher PE than their ground state, but they stay at the higher state because there is an energy barrier that they don't often get over.

Set the barrier at 40 by pulling up on the top of the ruler. Put 200 molecules in chamber A. Your result might look like the figure at the right.

On the left, the molecules are starting in a higher energy state than they would be if they were at the bottom of the PE well on the right. If there were no barrier, we would expect most of the molecules to move over to the right.

(Note this is an energy plot, not a free energy plot. We are asking whether something is physically possible given energy conservation, not whether it makes a transition spontaneously.)

1.  Let the program run for a while. Describe what happens. How many molecules go over? (The numbers are shown in the "Molecules in the chamber" box at the upper right.) What is the temperature of the system? (shown on the thermometer)

2. Now add heat to the system until the temperature reaches about 300 K. What happens?

3. Notice that while the program runs, the temperature on the thermometer is fluctuating. Is this because the total energy in the chamber is fluctuating? Do you think this is an error in the program? What could the programmers be trying to represent?

4.If the program ran for a very long time do all the molecules run to the right side? Does it matter what the temperature is? How does the Boltzmann factor help explain what is happening?

5. Now pause the program. Lower the barrier to 20. Now what happens? What does the barrier affect? What does it not affect? What is the role of the Boltzmann factor in the change that takes place?

6. The program is titled "Reversible Reactions." To what extent are these reactions "reversible" and what is the relevance for biological systems?

Joe Redish 2/27/18, 4/11/19

Article 616