## Equilibrium in Chemical Systems:

### Distributing Energy

Chemical systems are random systems; the fundamental random process is the flow of energy throughout the system. For example, one molecule can collide with another one, so that the two molecules change their direction and speed. It is quite possible to create a chemical system which is not at equilibrium. If a system is heated up suddenly, portions of the system will contain a great deal of energy, and this will not be distributed in an equilibrium way. As an example, imagine an ideal billiard table with no friction and no pockets. At the opening break, the cue ball is given a high velocity and all the other balls are at rest. This is not an equilibrium situation.

For a system to come to equilibrium, flow of energy between the parts of the system must be able to occur. In the case of the billiard balls, they bounce into each other, and a fast one can give some of its kinetic energy to other balls. Usually, the faster balls will lose energy with each collision, and the slower balls will gain energy (although this need not always be the case). After some number of collisions, the energetic particles will have given away enough energy so that different particles are now the most energetic. They in turn distribute their energy, and so on. After a period of time, the system will come to equilibrium.

To understand equilibrium in this system, imagine a huge billiard table with a million billiard balls. We can take the velocities of the particles and make a histogram. At each moment in time, the system will have a certain number of particles in each velocity range. Consider one velocity range (let's say 10 m/s--10.1 m/s). A short time later, some of the particles in this range will have gained or lost enough velocity to move out of this range. At the same time, some other particles will have gained or lost enough velocity to move into this range. At equilibrium, these two processes balance, and the number of particles in this range remains constant as time goes on.

## Exercises Illustrating Chemical Energy Flow

1. Based on the description above, how is the energy equilibrium in a chemical system similar to chemical equilibrium between reactants and products? How is it different?
2. Other than the examples given, think of two systems which arrive at energy equilibrium and two systems which cannot achieve equilibrium. Explain.
3. Once a system of colliding particles is at equilibrium, describe three ways to put it out of equilibrium.
4. Thought question: How can two billiard balls collide so that the slower one gives energy to the faster one?

## The Big Picture

You have now observed a system achieve equilibrium. The average value and the most probable value aren't the only facets of an equilibrium system which are predictable; the probability distribution provides a great deal of information about the system.