1877

Maxwell-Boltzmann Distribution

James Clerk Maxwell (1831–1879), Ludwig Eduard Boltzmann (1844–1906)

A chemical sample is really just a large collection of molecules. They’re all moving around, but that doesn’t mean that they’re all moving in the same way and at the same speed. In the real world, in a container of nitrogen gas, for example, some of the nitrogen molecules will be zipping around much faster than the others, some of them much slower, with the rest spread out somewhere in between. This spread of different energies among the molecules is the Maxwell-Boltzmann distribution.

Scottish scientist James Clerk Maxwell (in 1860) and Austrian physicist Ludwig Eduard Boltzmann (in 1868) each modeled a container of gas as being full of tiny billiard balls, flying around and bouncing off of each other and off the walls. If you heat up the system (the collection of molecules), the balls fly around faster and bang harder against the inside of the container (and the pressure of the gas increases). From this simple picture, scientists began to understand the differences between the behavior of individual particles and the behavior of large groups of them, leading to further knowledge about bulk properties such as temperature, pressure, and many more. It’s also very useful in describing reaction rates in chemistry, since it’s often the case that only the most energetic molecules in a system are able to react. Learning how to deal with the behavior of large collections of particles like this is crucial to understanding the behavior of chemical systems (as well as for solving other problems in physics and even mathematics).

Though today we accept the presence of atoms without question, when these ideas were being developed, many physicists were not even sure if they believed in atoms as real things (rather than as useful little mental abstractions). Even after putting his work in its most complete form in 1877, Boltzmann in particular had great difficulty making headway with his proposals, which did not help his natural tendency toward depression (which eventually led to his suicide). Still, he and Maxwell are recognized (with American scientist Josiah Willard Gibbs, with his insights into Gibbs free energy) as discoverers of an essential way to deal mathematically with a world composed of small particles.

Maxwell and Boltzmann used billiard balls to explain the movement of molecules in a gas.