Celebrating National Mole Day with Wolfram|Alpha

Today is National Mole Day. Unlike most of Wolfram|Alpha’s team I’m not a scientist, so if you’re curious to learn what the day is about, so am I—we can learn together! Thankfully, Wolfram|Alpha is a great tool for learning pretty much anything.

So, is Mole Day about this?

Hmm. Maybe not. Oh, it’s probably something like this?

You know what I should have tried? I should have just queried “What is a mole?”

A mole (symbolized as “mol,” like how kilograms are “kg”) is one of the seven fundamental measuring units of the International System of Units (SI). Just like meters determine length, kilograms mass, seconds time, amperes electrical currents, kelvins thermodynamic temperature, and candelas luminous intensity, moles are used to determine the amount of a substance. A mole contains 6.02 x 10^23 of particles or objects  that make up that substance, whether they’re atoms or molecules. So you can see why Mole Day is celebrated from 6:02am to 6:02pm on October 23, or 10/23 in US date notation. It’s thematically similar to Pi Day (March 14).

6.02 x 10^23 is a big number. Also known as Avogadro’s number, it is named after the Italian savant Amedeo Avogadro and his accomplishments in physics, as he is the first to have proposed that the volume of a gas is directly proportional to the number of molecules or atoms within it. It doesn’t even matter what kind of gas we’re talking about, either. It applies to all of them.

So 6.02 x 10^23 is just insanely, mind-bogglingly huge. I would guess that one mole of oxygen would be really heavy.

Actually it’s not. I have it on good authority that atoms and molecules are very small, and understandably do not weigh very much. The weight of one mole of oxygen is 16 grams (12 grams less than a one-ounce bag of potato chips you’d buy at a vending machine).

Let’s play around with this for a bit. I think I’m getting the hang of this. Let’s compare how many grains of sand there are on Earth compared to Avogadro’s number.

Now let’s query Avogadro’s number divided by the number of stars in the observable universe.

Two? Really? Golly. That’s a lot of stars. So Avogadro’s number is, if nothing else, a really, really big number. All this computing is making me thirsty, so how about we query two moles of water?

Two moles of water is 36 ml. For reference, an average can of soda—12 fluid ounces—is 355 ml. So two moles of water is pretty much a mouthful.

Of course, moles are  rather useful in physics and chemistry equations, not to mention medicine. Here are some queries my coworkers advised me to show off.

Perhaps not unexpectedly, the mole features prominently in Avogadro’s law.

The mole is also used in the definition of many physical quantities, such as:

As a fundamental constant of nature, the Avogadro number is intimately related to other well-known constants, such as the Faraday constant and the molar gas constant. The Avogadro number is also used in the definition of the unified atomic mass unit.

One could be forgiven for thinking that there’s nothing new happening with the mole and the Avogadro number, which was first used 150 years ago. But actually, the precise definition is still a matter of active discussion. At present it’s a measured value, and every few years a more precise value is measured. Within the next few years, the Avogadro number might become an exact quantity within the so-called “new” International System of Units.

A similar situation occurred with the speed of light, which for hundreds of years was a measured value, until it became an exact value in 1983, which implicitly defined the meter.

One possibility is the number 84,446,888^3, suggested by Fox and Hill.

Once the mole is defined through an exact Avogadro number, the actual celebration time on 10/23 of each year will be defined up to a fraction of a second, which my coworkers tell me will make the day even more festive.

Mole Day is a great day to reflect on just how profoundly awesome science is. You can learn more if you refer to the day’s organizers, check out a very nice overview of the mole based on the Avogadro constant or a magazine literally called The Mole, or read some scientific literature, but I suggest you experiment with moles yourself using Wolfram|Alpha.