The Grotthuss Mechanism

If you could watch an individual water molecule, once in a while you’d see it do this.

As it bounces around, every so often it hits another water molecule hard enough enough for one to steal a hydrogen nucleus—that is, a proton—from the other!

The water molecule with the missing proton is called a hydroxide ion, OH⁻. The one with an extra proton is called a hydronium ion, H₃O⁺.

This process is called the ‘autoionization’ of water. Thanks to this, a few molecules in a glass of water are actually OH⁻ or H₃O⁺, not the H₂O you expect.

And this gives a cool way for protons to move through water. Here’s a a little movie of how it works, made by Mark Petersen:

A positively charged proton gets passed from one molecule to another! This is called the ‘Grotthuss mechanism’, because Theodor Grotthuss proposed this theory in his paper “Theory of decomposition of liquids by electrical currents” back in 1806. It was quite revolutionary at the time, since ions were not well understood.

Something like this theory is true. But in fact, I believe all the pictures I’ve shown so far are oversimplified! A hydronium ion is too powerfully positive to remain a lone H₃O⁺. It usually attracts a bunch of other water molecules by the van der Waals force and creates larger structures. You can see these here:

• Water, Azimuth, 29 November 2013.

I have a couple of questions:

Puzzle 1. What fraction of water molecules are autoionized at any time? It should be possible to compute this for water at 25℃ knowing that

at this temperature.

Puzzle 2. How often, on average, does an individual water molecule autoionize? Wikipedia says it happens about once every 10 hours, and cites this paper:

• Manfred Eigen and L. De Maeyer, Untersuchungen über die Kinetik der Neutralisation I, Z. Elektrochem. 59 (1955), 986.

But I don’t know how this was estimated, so I don’t know how seriously to take it.

If we knew answers to Puzzles 1 and 2, maybe we could compute how long an individual molecule remains ionized each time it autoionizes, on average. But I’m worried about a lot of subtleties that I don’t really understand.

For more, read:

• Wikipedia, Self-ionization of water.

• Wikipedia, Grotthuss mechanism.