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Chemical Eye on Counting our Blessings
by Preston MacDougall


November 28, 2005

To see a world in a grain of sand,
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.

Even if the poetic genius of William Blake is new to your ears, how can you fail to hear the voice of an idealist? To my chemical ear, which has a fondness for history, I can also hear the sound of someone trying to apply the brakes to a runaway train of deterministic thinking.
jpg Preston MacDougall

To Blake, the idea of "a clockwork universe" - where the future could be determined with certainty if enough measurements could be made with high-enough precision - would be truly frightening if it wasn't totally absurd. He was right, of course, one hundred years before quantum theory forced on us a certain amount of uncertainty.

He was also right about the world of wonders that could be found in a grain of sand. Sand is mostly made out of silica, a compound of silicon and oxygen with the chemical formula SiO2. If you examine a small grain with a magnifying glass, you will notice that it is transparent, and that its differently sized faces join at various angles, some rather acute. While your magnifying glass is still handy, compare it to a grain of salt. It is also transparent, but the shape is quite different ­ that of a simple cube.

To early 19th century chemists (Blake's contemporaries), such observations led to further, more quantitative, investigations into the nature of atoms. After Blake's death, and with the advent of controlled chemical transformations, mid to late 19th century chemists eventually began to puzzle together the spatial arrangements of atoms in ever more complex molecules.

You have to learn to walk before you can run, however. So, before chemists could become masters of the atomic domain, they had to learn to count things that they couldn't see. Have you ever wondered how many atoms are in a grain of sand? The answer may surprise you.

An Italian chemist, named Amadeo Avogadro, took the first step on a fruitful path toward the answer to such a question. It is amusing to note that Avogadro and his fellow chemists were finding their passion in the wonderful world of atoms around the same time that Blake was illustrating Milton's "Paradise Lost".

On the basis of experiments done with chemically combining gases, Avogadro reasoned that equal volumes of different gases contained equal numbers of molecules of those gases. He had no idea what such numbers might be, and would surely have been astounded by their enormity. After his death, chemists, and then physicists once they accepted the existence of atoms, devised ingenious ways of counting atoms.

To honor Avogadro, the university in his hometown of Turin, where he also taught chemistry, named the large lecture hall in the chemistry building Aula Avogadro, or Avogadro Hall. Several years ago, I was invited to give a lecture in this room. I could feel some magic there, and to this day I am thankful to have had that opportunity.

In one of the greatest tributes a chemist has ever received, scientists worldwide count atoms and molecules by the Avogadro number, instead of by twelves, as a poutltry farmer counts eggs, for instance. While twelve eggs is the same thing as a dozen eggs, Avogadro's number of silicon atoms is also called a "mole" of silicon atoms.

And six of one is a half-dozen of another. Or is it? People often refer to a "baker's dozen" as meaning 13 of something. So there is some uncertainty even here. Avogadro's number of one is a mole of another, but we still don't know exactly how many that is. Extremely precise measurements, of ultra-pure materials, have so far determined that Avogadro's number is 602214199 with 15 more digits that we don't know yet, and even some uncertainty in those we do.

To put it in a more reader-friendly manner, Avogadro's number, rounded off to the nearest power-of-10, is one trillion trillion. That's a one followed by 24 zeros! To put it in more poetic terms, there are about 15 billion billion atoms in a grain of silica in sand - two oxygen atoms for every silicon atom. At least that's the approximate count for a grain that weighs half of a milligram, which is big enough to see with the naked eye, but small enough to inspire creative wonder.

As we take time to count our blessings, I hope that you are like me, and realize, with gratitude, that they are innumerable.


Preston MacDougall is a chemistry professor at Middle Tennessee State University. His "Chemical Eye" commentaries are featured in the Arts and Public Affairs portion of the Nashville/Murfreesboro NPR station WMOT (

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