A mole of sodium chloride, NaCl, is the same amount, 6.022 × 10 23. Here, however, it is 6.022 ×10 23 molecules. With molarity, consider the moles of solute as finding the number of molecules in solution.
- I like fill-in-the-blank days. However, there is a problem with mole day. Mole day is, of course, 10/23. You know, a mole? One mole is 6.02 x 1023 Avogadro’s number.
- The number of mole mounds or surface ridges present is no indication of how may moles may be present. On average, one acre of land will support about two or three moles at one time. But areas next to large tracts or forested areas may be subject to continual invasions by moles because such areas may support many moles.
What would happen if you were to gather a mole (unit of measurement) of moles (the small furry critter) in one place?
—Sean Rice
Things get a bit gruesome.
First, some definitions. A mole is a unit. It’s not a typical unit,though. It’s really just a number—like “dozen” or “billion.” If you havea mole of something, it means you have 602,214,129,000,000,000,000,000of them (usually written ( 6.022times10^{23} )). It’s such a bignumber because it’s used for counting numbers of molecules, which thereare a lot of.
'One mole' is close to the number of atoms in a gram of hydrogen. It’salso, by chance, a decent ballpark guess for the number of grains ofsand on Earth.
A mole is also a type of burrowing mammal. There are a handful of typesof moles, and some of them are trulyhorrifying.
So what would a mole of moles—602,214,129,000,000,000,000,000animals—look like?
First, let’s start with wild ballpark approximations. This is an exampleof what might go through my head before I even pick up a calculator,when I’m just trying to get a sense of the quantities - the kind ofcalculation where 10, 1, and 0.1 are all close enough that we canconsider them equal:
I can pick up a mole (animal) and throw it.[citation needed] Anything I can throw weighs one pound. One pound is one kilogram. Thenumber 602,214,129,000,000,000,000,000 looks about twice as long as atrillion, which means it’s about a trillion trillion. I happen toremember that a trillion trillion kilograms is how much a planet weighs.
… if anyone asks, I did not tell you it was ok to do math like this.
That’s enough to tell us that we’re talking about pile of moles on thescale of planets. It’s a pretty rough estimate, though, since it couldbe off by a factor of thousands in either direction.
Let’s get some better numbers.
An eastern mole (Scalopus aquaticus) weighs about 75 grams, whichmeans a mole of moles weighs
Number Of Moles Formula
[(6.022times10^{23})times75mathrm{g}approx4.52times10^{22}mathrm{kg}]
Mole Number In Chemistry
That’s a little over half the mass of our moon.
Mammals are largely water. A kilogram of water takes up a liter ofvolume, so if the moles weigh ( 4.52times10^{22} ) kilograms,they take up about ( 4.52times10^{22} ) liters of volume. Youmight notice that we’re ignoring the pockets of space between the moles.In a moment, you’ll see why.
The cube root of ( 4.52times10^{22} ) liters is 3,562 kilometers,which means we’re talking about a sphere with a radius of 2,210kilometers, or a cube 2,213 miles on each edge. (That’s a neatcoincidence I’ve never noticed before—a cubic mile happens to be almostexactly ( frac{4}{3}pi ) cubic kilometers, so a sphere with aradius of X kilometers has the same volume as a cube that’s X miles oneach side.)
If these moles were released onto the Earth’s surface, they’d fill it upto 80 kilometers deep—just about to the (former) edge of space:
Mole Number Formula
This smothering ocean of high-pressure meat would wipe out most life onthe planet, which could—to reddit’s horror—threaten the integrity of theDNS system. So doing this on Earth is definitely not an option.
Instead, let’s gather the moles in interplanetary space. Gravitationalattraction would pull them into a sphere. Meat doesn’t compress verywell, so it would only undergo a little bit of gravitationalcontraction, and we’d end up with a mole planet a bit larger than themoon.
The moles would have a surface gravity about one-sixteenth as strong asEarth’s—similar to that of Pluto. The planet would start off uniformlylukewarm—probably a bit over room temperature—and the gravitationalcontraction would heat the deep interior by a handful of degrees.
But this is where it gets weird.
The mole planet is now a giant sphere of meat. It has a lot of latentenergy (there are enough calories in the mole planet to support theEarth’s current population for 30 billion years). Normally, when organicmatter decomposes, it releases much of that energy as heat. Butthroughout the majority of the planet’s interior, the pressure is over ahundred megapascals, which is enough to kill all bacteria and sterilizethe mole remains—leaving no microorganisms to break down the moletissues.
Closer to the surface, where the pressure is lower, there’s anotherobstacle to decomposition—the interior of a mole planet is low inoxygen. Without oxygen, the usual decomposition doesn’t happen, and theonly bacteria that can break down the moles are those which don’trequire oxygen. While inefficient, this anaerobic decomposition canunlock quite a bit of heat. If continued unchecked, it would heat theplanet to a boil.
But the decomposition is self-limiting. Few bacteria can survive attemperatures above about 60 °C, so as the temperature goes up, thebacteria die off, and the decomposition slows. Throughout the planet,the mole bodies gradually break down into kerogen, a mush of organicmatter which would—if the planet were hotter—eventually form oil.
The outer surface of the planet radiates heat into space and freezes.Because the moles form a literal fur coat, when frozen it insulates theinterior of the planet and slows the loss of heat to space. However, theflow of heat in the liquid interior is dominated by convection. Plumesof hot meat and bubbles of trapped gases like methane—along with the airfrom the lungs of the deceased moles—periodically rise through the molecrust and erupt volcanically from the surface, a geyser of deathblasting mole bodies free of the planet.
Eventually, after centuries or millennia of turmoil, the planet calmsand cools enough that it begins to freeze all the way through. The deepinterior is under such high pressure that as it cools, the watercrystallizes out into exotic forms ofice such as ice III and ice V,and eventually ice II and ice IX (norelation).
Mole Number Of Nacl
All told, this is a pretty bleak picture. Let’s try an alternateapproach.
I don’t have any reliable numbers for global mole population (or smallmammal biomass in general), but we’ll take a shot in the dark andestimate that there are at least a few dozen mice, rats, voles, andother small mammals for every human.
There might be a billion habitableplanetsin our galaxy. If we colonized them, we’d certainly bring mice and ratswith us. If just one in a hundred were populated with small mammals innumbers similar to Earth’s, after a few million years—not long, inevolutionary time—the total number which have ever lived would surpassAvogadro’s number.
Mole Number Formula
If you want a mole of moles, build a spaceship.