Today, October 23, is Mole Day — the unofficial holiday when we celebrate Amedeo Avogadro and his contributions to molecular theory. In 1811, Avogadro hypothesized that given two volumetrically identical samples of gas at an equal temperature and pressure contained the same number of particles. In other words, an equal volume of hydrogen and nitrogen at the same temperature and pressure contains the same number of molecules. This rule allowed for a method of calculating the quantity of gas in a given container.
The unit of measurement associated with Avogadro is the mole. A mole is defined as the base unit of “substance,” defined as 6.022*10^23 particles (defined as atoms, molecules, ions, or electrons). The definition was tweaked in 2018 — a mole was previously defined as the number of atoms in 12 grams of carbon-12.
Avogadro’s number was set at 6.022*1023 to make certain that the mass of one “mole” of material in grams would be approximately numerically equal to the average mass of one molecule of the material in daltons. Wikipedia gives the following example: “one mole of water contains 6.022*1023 molecules, whose total mass is about 18.015 grams – and the mean mass of one molecule of water is about 18.015 daltons.” Concentrations are substances are often expressed in terms of molarity, reflected in a measure of moles of dissolved substance per unit of solution (commonly abbreviated mol/liter).
Mole day is celebrated on October 23, from 6:02 AM to 6:02 PM, though some heretics celebrate on June 2, June 22, or February 6 (6/2, 6/22, and 6/02 in countries where the day is written before the month). I’ve got to give a shout-out to my high school chemistry teacher, Mr. Nance, in all of this. He was absurdly fond of moles and mole day, and it wasn’t unusual to find questions on our tests that challenged us to find the molarity of a mole of moles suspended in a given volume of solution. Other fun tasks included calculating the various dimensions and physical properties of a “mole of moles.” The video below compares the size of a mole of moles to other objects in the solar system.
Randall Munroe took up this question in an XKCD “What If,” with rather gruesome results. Keep in mind that having 6.022*1023 of something is really rather a lot of it. When you pile up a mole of moles, what you end up with is a moon comprised entirely of moles.
What do you know about the core of the Earth? Probably at least two things: 1). It’s made of iron. 2). It’s molten. Moles are less dense than iron, but it turns out that when you’ve got 6.022*10^23 of something, it doesn’t really matter what it’s made of. What you end up with is a small planetoid, roughly half the mass of the moon with 1/16 of its gravity. The outer surface of the planet would freeze, while its fur forms an insulating layer. Below the mole-crust lies the mole-mantle, where anaerobic bacteria populations would still survive. These would slowly break the moles down into kerogen. Some of that kerogen might even form a layer of oil between the mole-mantle and the mole-core. As the planet cools, decompositional gases and molten (pun-intended) mole-oil might explode to the surface in the first-ever documented incidence of a molcano. As Munroe notes, a mole of moles also contains enough calories to feed the entire population of Earth for approximately 30 billion years, as long as you don’t mind eating organically mined, cosmically irradiated insectivore.
An oft-overlooked problem with our mole-moon is precisely where it ends up. Should it encroach upon Earth’s Roche limit, Very Bad Things would result. The Roche limit refers to the closest point from the center of a planet that a satellite can approach without being pulled apart by the planet’s gravitational field. Earth’s Roche limit is ~11,470 miles above the surface. If the mole-moon gets closer than that, it’s going to come apart. I don’t really know how to estimate the result of slamming a trillion trillion (approximately) worth of moles into a planetary surface, but it’s probably bad.
If any of you are wondering about the quality of my chemistry education, let me reassure you, the story problem questions in Mr. Nance’s class didn’t get this detailed. My answers occasionally did. This has more to do with the fact that I was a pretty terrible chemistry student and had a faint hope he might be one of those teachers who awarded points on the basis of ingenuity and cleverness as opposed to being any damn good at actual chemistry.