Today is 10/23, which is another math holiday in the tradition of Pi Day. On this hallowed day, we celebrate Amedeo Avogadro and his constant, appropriately called the Avogadro constant:

N A = 6.022140857(74)x1023

(The exponent at the end is what gives us 10/23, though some scientists do celebrate on 6/2.)

The units on this egregiously large number are abbreviated as mol-1, meaning that it takes this many things to make a mole.

What is a mole, you ask? Well, it’s…it’s just 6.022140857(74)x1023 of anything. It’s a unit of counting, like tens or hundreds or googols. Technically it’s for chemistry purposes, so it should be used for molecules, atoms, or elementary particles of some kind. In practice, though, it can be used for any countable object, whether it’s molecules or moles. (It works equally well for naked mole rats, too.)

It seems pretty silly to come up with a random number to count with, so you might suspect there’s some reason behind this one. In fact, there is! The Avogadro constant is the number of carbon atoms that are in 12 grams of carbon-12 (carbon with 6 neutrons, as opposed to carbon-14, which has 8 neutrons).

That’s pretty amazing when you stop to think about it—after all, keep in mind that a million is 106, and then realize that this number is nearly a million million million times that. For reference, a quick search tells me 12 g of 12C is about a teaspoon. That’s an unimaginable number of atoms in a space that fits easily in the palm of your hand.

To try to wrap our little human heads around the concept of the mole, we can look at some examples of what a mole means in non-atomic situations. Here’s a cool Instructables post illustrating the awesome size (metaphorically speaking) of the mole.

Also, I’ve taken the liberty of sharing with you a video that still haunts me in the best way from high school chemistry. You will never forget this number now. You’re welcome.

Speaking of remembering Avogadro’s constant, guess who never actually knew it in the first place? That’s right, Avogadro didn’t actually measure his number himself, since the ability to measure numbers of atoms was a little lacking in the early 1800s. However, he did come up with a relevant law: under the same pressure and temperature, different gases will have the same volume if they have the same number of molecules.

How is that useful? Think about splitting water into hydrogen and oxygen if you don’t know the ratio of H to O (ha ha) in water. If you measure the resulting hydrogen gas volume as twice the oxygen gas volume, you suddenly have a lot more information about the ratio of molecules. Without a way to directly measure the atoms involved, this was huge for chemistry.

Because of this law (Avogadro’s Law, naturally), the scientists who did finally measure the constant decided to name it after him. This didn’t happen until around 1910, when the charge of a single electron was first measured, so that we could compare the charge of a whole mole of electrons (represented by the Faraday constant) to a single one and figure out just how many charges we were looking at.

Today, the Avogadro constant is mostly used in chemistry, but it’s used to describe some other quantities in science. These sometimes have different, somewhat whimsical names—for example, a mole of differential equations has been called a leibniz by one of my professors. The energy in a mole of photons is one einstein.

We owe a lot to Avogadro and his constant devotion to chemistry. In fact, I don’t think it’s making a mountain out of a molehill to say that we wouldn’t be where we are today without him.

We certainly wouldn’t be celebrating Mole Day, at least.

Celebrate the holiday by checking out more about the Avogadro constant and the ongoing efforts to measure it more accurately! Also, this Wired article has a fun explanation of an experiment to measure the constant, and this ThoughtCo. article briefly explains how to convert from moles to grams. Revel in your nerdy knowledge!

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