Random Systems:

Random systems are those which contain an element of unpredictability. For example, before a coin is tossed, it is impossible to know whether it will land with heads or tails facing up. Before students take a test, it is impossible to know with certainty what their grades will be. If a leaf is selected from a tree and measured, its length cannot be accurately known before the leaf is chosen.

In chemistry, many processes contain a great deal of randomness. When two chemicals A and B are mixed to form new compound AB, it is not known in advance which molecules of A will react soonest and which will remain unreacted until the reaction is almost complete. In an ideal gas of colliding atoms, it is impossible to know in advance the speed of a particular atom at any given time. Each atom's speed is the by-product of all its collisions with other atoms and with the walls of the container.

Exercises to Illustrate Randomness

  1. Run the JAVA applet for 2 atoms at 500K and examine the speeds of 2 atoms by watching the histogram. For roughly how many iterations can you predict the speeds of the particles? Run the simulation several times to see if this number of iterations is reproducible.
  2. Now vary the number of atoms and the temperature. How does changing these variables affect the length of time (number of iterations) that the speeds are predictable?
  3. Again run the simulation for 2 atoms and 500K. Why aren't the starting speeds the same each time?
  4. Thought question: In an ideal gas with a mole of atoms at room temperature, for how long will the atomic speeds be predictable?

The Big Picture

Does a random system mean that we cannot know anything about it? Absolutely not! Many random systems eventually achieve equilibrium, and many properties of this equilibrium state are predictable.

© Andrew M. Rappe