# Entropy Activity

-Introduction

-The reaction coordinate

-The energy landscape

-Population distributions

-Motion at constant temperature, and exchange of energy with the heat bath

-Thermally activated processes

-Energy and temperature determine the populations

-Entropy and free energy

-Mathematical derivation of free energy

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## Thermally activated processes

In the previous activity, we considered the number of molecules that will be on a high-energy vs. low-energy platform. In this activity, we explore the consequences of this on the rate of thermally activated processes. In the simulation, we will mimic the energy landscape with three platforms that represent the metastable, activated and stable states as shown below.

Virtual Activity

- Thermally activated processes (Java Required) [Opens in a separate window.]

In order to reach the stable state, a ball must first be activated by getting sufficient energy from the bath to reach the activated (middle) platform. Once on the activated platform, some balls will fall to the right onto the stable platform. The number of balls reaching the stable platform in a given time is then proportional to the number of activated molecules, which we saw above is proportional to where Ea is the difference in energy between the activated and stable platforms. The rate of a thermally activated process is therefore proportional to .

If you watch the simulation for a while, you'll notice that every so often a ball gets a very strong kick from the platform. Although these strong kicks are rare, they are important since they give the system enough energy to make it to the activated state. Even small increases in temperature can substantially increase the number of times a system gets a strong enough kick to reach the activated state, represented here by the middle platform. Some thermally-activated processes take minutes or hours to occur. For instance, when you cook an egg, it takes a few minutes for the egg white to solidify and even longer for the yolk to solidify. On a molecular scale, the molecules are bouncing at about 1012 times per second. If we were to use our simulation to model a reaction that takes one second to occur, a ball would have to bounce an average of about 1012 times before it got a kick strong enough to knock it onto the activated platform.

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