# How Big is a Mole

Moles, of course, are furry critters with poor vision that dig up gardens and golf courses. They’re smaller than your average cat. For students of chemistry, however, the mole is a magic (and often mysterious) number.

The mole is nothing more than a counting number. It is equal to Avogadro’s number of anything. Avogadro’s number is (approximately) 6.02214199 X 10^23 or 602214199000000000000000. Usually we round that off a bit and say 6.022 X 10^23, or even 6 X 10^23 if we’re being really lazy and just need a rough estimate. This is, of course, bad math and horrible for significant figures, and I’m sure I’ll hear about it from serious chemists everywhere, but such is life.

In practice, the mole is used only when working with chemicals, but it can be applied to anything you like. The problem is that most things are so large that having such a large number of them is entirely impractical. I’ll give a few examples of each though, because it’s always fun to see. We’ll walk through a few, and then put them all into a table at the end so if you don’t need the “how” and just want the results, scroll way down.

Water:
Water has a molar mass of 18.02 grams per mole that is to say, one mole of water molecules has a mass of 18.02 grams. Under normal conditions, water has a density of one gram per milliliter, so one mole of water is 18.02 milliliters, or 1.22 tablespoons.

Gasses:
Under normal conditions, one mole of a gas takes up 22.414 liters of space. Don’t like metric? That’s 5.92 gallons, or about the size of your everyday beach ball (inflated).

Salt:
Salt (sodium chloride) has a molar mass of 58.44 grams per mole. The typical canister of Morton Salt weighs 26 ounces, or 737 grams. That comes out to 12.6 moles, so if you were to take about 1/13 of the container (remember, some settling occurs), you’d have close to a mole of salt.
The official density of salt is 1.154 g/cm^3 (http://www.saltinstitute.org/15.html), so assuming you have exactly the same particle size they did, one mole of salt will be 50.6 cubic centimeters, or 3.36 tablespoons. For better results, weigh out your 58.44 grams. (That’s good advice for any solid.)

Sugar:
Table sugar is sucrose C12H22O11 and has a molar mass of 342.34 grams per mole. Working on the assumption that we’re talking about bagged white sugar, we can use the density (found at http://www.sugartech.co.za/density/index.php) of 700 kg/m^3 for a volume estimate. That comes out to just about half a liter (0.489 L) for one mole of sugar, and since a half liter is very nearly half a quart, one mole of sugar is roughly one pint, or two cups, of sugar (by volume). Again though, going by mass will be more accurate.

Vinegar / 3% Acetic Acid:
Vinegar is acetic acid dissolved in water, usually to the tune of a 3% solution. (If yours is something else, just multiply our result by three and divide by the percent in yours.) The density of vinegar is very close to that of water, so we’ll stay with 1 g/mL as our density. Acetic acid (CH3COOH) has a molar mass of 60.06 grams per mole. To get those 60 grams, we’d need 2000 grams of the vinegar, or about two liters.

Stamps:
This will vary, depending on the size of your stamps, but at the moment I have a book of 20 US, \$0.41 forever stamps which I’ll use as a model. It measures roughly 15.7cm by 4.4cm, for an area of 69.08 square centimeters. That was 20 stamps remember. We want one mole of stamps, so we’d need 3.011 X 10^22 booklets, for a total area of 2.08 X 10^24 square centimeters, or 8.03 X 10^13 square miles, which is still enormous, seeing as the Earth’s surface area is only 196940400 square miles. This means our mole of stamps would cover the Earth well over eighty thousand times — or the entire surface of the sun a mere 68 times.

Big Fat Turkeys:
At the time of this writing, Thanksgiving is approaching, so I have turkey on the brain. We can estimate that a nice plump turkey is about one cubic foot in volume, and so one mole of turkeys would occupy 6 X 10^23 cubic feet. The Earth’s volume is roughly 1.08 X 10^21 cubic meters (and a cubic meter is about 35.3 cubic feet) or 3.81 X 10^22 cubic feet. As a result, one mole of our Big Fat Turkeys would take up almost as much room as Sixteen Earths or one fourth of Uranus. If this leads some of you to an inappropriate joke, I do apologize to your audience in advance.

-Mass and approx. Volume or Area of one mole-

Water………18.02 g, 18.02 mL, 1.22 tbsp
Gas (any)…..22.414 L, 5.92 Gal.
Salt……….58.44 g, 50.6 cc, 3.36 tbsp
Sugar………342.34 g, 0.489 L, 2 cups
3% Vinegar….2 L
Stamps……..1.606 X 10^14 square miles or ~80,000 Earth’s Surfaces
Turkeys…….~16 Earths or 1/4 Uranus