Happy Mole Day! It’s the 23rd of October and, at least where I am right now, it’s still between 6:02 am and 6:02 pm, so that means it’s time for chemists to celebrate! Of course, I’m in the U.K., so the date thing doesn’t quite work — for me this is 23/10, not 10/23 — but since there are only 12 months in a year (even in 2020) the British system is a bit unsatisfactory, so I’ll go with the American date format for the day.

There are literally loads of atoms in everything

What’s a mole? Well, to paraphrase Douglas Adams: atoms are small. You just won’t believe how vastly, hugely, mind-bogglingly small they are. I mean, you may think the latest incarnation of the walnut whip is small, but that’s just peanuts to atoms. Or even walnuts.

There are literally loads and loads of atoms in everything. There are so many of the blasted things that the numbers are a real pain to deal with. A teaspoon of table sugar, for example, has about 7,400,000,000,000,000,000,000 sucrose molecules in it, and since each sucrose molecule contains 45 atoms, that’s a whopping 330,000,000,000,000,000,000,000 atoms. And that’s not even a heaped teaspoon.

Even if we used standard form and wrote that last number as, for example, 3.3 x 10²³ it’s a bit of a pain. And chemists are far too busy to write things out in full — why do you think they came up with all these symbols in the first place? — so what we do is we pick a convenient amount, which turns out to be 6.022 x 10²³, and call that a “mole”. It’s just like calling twelve eggs “a dozen” only, you know, bigger.

I’m not going to explain the origin of the actual number further than this. There’s an awesome graphic here from Compound Interest and, if you want to know more, just click through.

What I am going to do are some… interesting mole calculations. People usually do grains of sand or coins or something. But those are so boooorrring. It’s nearly Halloween, right? I say we go gruesome.

Let’s start with blood!

A healthy adult has about 35 trillion red blood cells in their body at any given moment. (Vampires, presumably, have even more… although… do vampires make their own blood supply? Interesting question…).

35 trillion is a big number, right? A trillion is a million million (on the short scale, which everyone uses, don’t start), 1,000,000,000,000, or 10¹², so 35 trillion is 3.5 x 10¹³.

But that’s only 0.000000000058 of a mole! Even if we count everyone on the planet, we only get to 0.45 of a mole. Yes, that’s right. Even if we drained the blood out of every, single human on the planet, we’d only about half a mole of red blood cells.

Ooh, how about bacteria? We have a lot of those on us, right? In fact, we have more microbes in and on our bodies than human cells! (Well, we can argue about the definition of “human” here, I suppose, but… let’s not.) Apparently there are around 3.8 x 10¹³ bacteria in our colons which means… damn. This is the blood cells thing all over again, isn’t it? If we took all the humans on the planet, sucked out their gut bacteria (don’t ask) and collected it all together (really, don’t) we’d have, yes, a little under half a mole of microbes.

Don’t tell the tooth fairy’s boss. She really IS scary.

Okay, this is all very well, but it’s not helping us get an idea of scale, is it? All right. Let’s try human teeth. Why not? I mugged the tooth fairy for this one (she’s much tougher than she looks), and it’s about 8 mm long. Adult teeth are a bit larger, of course, but the fairy has less of those. Let’s assume 1 cm to make things easier. That’s 0.01 m. If we had a mole of human teeth they would stack up to… 6.02 x 10²¹ metres, or 6.02 x 10¹⁸ km, or (we need to ramp this up a bit) about 640,000 light years. That would reach a little dwarf galaxy in the constellation of Canes Venatici, somewhere in the general neighbourhood of the Milky Way. Or, alternatively, to Neptune and back…. some 670 million times. Gosh.

What about… hair? A fine human hair is about 0.05 mm across, which means a mole of (fine) hair would be 3.01 x 10¹⁹ metres thick. The diameter of the Earth is 12,700,000 metres so that’s about… 2,400,000,000,000 times wider than the Earth. Even Rapunzel might struggle with that much hair.

There are about half a mole of red blood cells in all the humans on the planet.

Hang on, let’s go back to those red blood cells for a minute… okay, if there’s about half a mole of red blood cells in all the humans on the planet, and we assume a single red blood cell is 7.8 μm (0.0000078 m) if we put all those red blood cells in a line it would be…2.3 x 10¹⁵ kilometres long. The circumference of the sun is about 4,400,000 kilometres so…

… with all the people on the planet, we could make half a billion rings of blood around the sun, one cell thick.

There’s a thought.

In summary, the mole is a flipping big number. Too big, really, to count anything other than atoms (or molecules, or ions). But it is useful for that.

Happy Mole Day!

Look, these numbers are big, right. I’m going to be amazed if there isn’t some sort of order of magnitude mistake. Just… let me know.

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