It’s a big day for chemistry (and math!) enthusiasts—October 23 is National Mole Day! Before images of burrowing, subterranean rodents with limited vision come to mind, allow us to offer a brief explanation of this very big number.

In chemistry, a mole is a unit of measurement that describes a quantity of anything! While you could *conceivably* have a mole of water molecules, a mole of chocolates, or a mole of whales—anything countable, really—a mole is a very, very large quantity. One mole is equal to **6.022 **×** 10 ^{23}** particles of the substance you’re counting. That’s a lot of

*stuff*, which is why the mole is used by chemists exclusively in reference to things that are very small, such as the number of molecules of chemical compounds or the number of atoms of a given element.

6.022 x 10^{23} is referred to as Avogadro’s Number, named for 19^{th} century Italian chemist Amedeo Avogadro, whose theories laid the groundwork for atomic theory.

For a fun, quick lesson on the mole and its history, check out this awesome video (via TED-Ed):

Here’s a quick example of how chemists use the mole in calculations.

*How many molecules are there in 36 grams of H _{2}O?*

Solution: To get from grams to molecules, first we have to go from grams to moles. Then we convert from moles to grams.

A mole is equal to the mass of 6.022 × 10^{23} particles of a given element. Hydrogen has a molar mass of 1 gram per mole (1 amu) and oxygen has a molar mass of 16 grams per mole. That said, H_{2}O has a molar mass of (1 × 2) + (16 × 1) = 18 grams per mole.

So, 36 grams of H_{2}O × (1 mole ÷ 18 grams) = 2 moles of H_{2}O

To go from moles to molecules, we multiply by Avogadro's number, 6.022 × 10^{23}.

So, 2 moles of H_{2}O × 6.022 × 10^{23} = 1.204 × 10^{23} = 1.204 × 10^{24}. (High school chemistry students—don’t forget your significant figures!)

Therefore, there are 1.204 × 10^{24} molecules of H_{2}O in a 36-gram sample!

Now try this: How many grams of CH_{4} are in a sample containing 1.8066 × 10^{24} molecules of CH^{4}? Email your answer to ilovemath@mathnasium.com for a chance to win a Mathnasium prize pack!

Learn more about how chemists use the mole in calculations here (via General Chemistry Online). Also, these mole day jokes made us giggle (via chemistry.about.com).

How are you celebrating National Mole Day?