Q & A: Arrhenius rate equation

Q:
What is arhenious equation?
- Airras khan (age 18)
Peshawer
A:

Most familiar rates of chemical reactions and of diffusion in solids and liquids approximately follow an equation devised by Arrheneius over 100 years ago. The equation runs as follows:

rate=fAexp(-B/kT)

where "fA" is the attempt rate, B is an energy barrier height, k is Boltzmann's constant , and T is absolute temperature.

Think of an extra particle rattling around in a crystal. There will be some rattle rate, fA, typically around typical vibration frequencies, say 1013/second. How often will the particle get over some barrier formed by its neighbors and get to the next similar site? The probability of being in some state in thermal equilibrium falls off with energy B as the Boltzmann factor exp(-B/kT). So the particle "tries" to make it over the barrier 1013 times per second, but only makes it over about exp(-B/kT) fraction of those times.

The Arrhenius law is very common, but there are also many cases in which it doesn't apply due to a variety of complications. Nevertheless, it's the starting point for most practical rate calculations.

Arrhenius, by the way, was the first to put together the understanding of why emitting CO2 will cause global warming. By 1906 he had the main physical ingredients right and had a good prediction of the amount of warming for a doubling of atmospheric CO2 concentration. What he didn't predict right was how rapidly people will emit CO2. He thought the doubling would take 5000 years, which would give many parts of the natural world as well as human society time to keep up. Of course, it's happening much faster, so that many corals won't have time to evolve, forests won't have time to gradually shift locations, coastal cities will have to be abandoned, etc.

Mike W.

(published on 07/03/2017)