Avogadro's Number is named after the Italian scientist Amadeo Avogadro, who first estimated the number of atoms or molecules per unit volume of a gas was a constant.

The value for Avogadro's Number (NA) was first determined by J. J. Loschmidt in 1865.

The modern value is 6.022 x 1023 particles per mole, where mole is the metric base unit for amount.

In other words, one mole of any substance contains 6.022 x 1023 particles (i.e. atoms, molecules).

To put this number in perspective, here it is written out: 602,200,000,000,000,000,000,000.


A Mole of Pennies

One mole of pennies would be 602,200,000,000,000,000,000,000 pennies, or $6.022 x 1021.

There are roughly 7 billion humans on earth, so if each person were to get an equal share of a mole of pennies, they would become instant multi-billionaires: each person would get $8.603 x 1011, or $860.3 billion.

If each person lives to the ripe old age of 80 years, they would have to spend $29 million a day for their entire lives to drain their bank account.

Talk about inflation!

Unfortunately, the entire surface of the earth would be buried to a depth of 230 meters in pennies.

A Mole of Water Molecules

What kind of container would hold a mole of water molecules? Remember, that's 602,200,000,000,000,000,000,000 molecules of water!

Well, one mole of rain drops (each having a volume of 0.10 mL, say) would fill almost 5,000 Lake Superiors.

One rain drop of this size would contain 3,300,000,000,000,000,000,000 water molecules.

So, one mole of water molecules would occupy about 18 mL of volume, or just over three and a half teaspoons.


A mole of copper atoms
According to the periodic table, one mole of copper (that's 6.022 x 1023 atoms of copper) weighs 63.546 grams.

Suppose you have a penny that was made of pure copper (one made before 1982, for example). This penny weighs about 3.0 grams.

To find the number of moles of copper in this penny, divide 3 grams by the atomic mass of a copper atom, which is 63.546 g/mol:

3.0 grams of copper / 63.546 g/mol = 0.047 mole of copper.

Now to determine the number of copper atoms in the penny, multiply the moles of copper by Avogadro's Number:

0.047 mole of copper x 6.022 x 1023 atoms of copper/mol = 2.8 x 1022 atoms of copper

So one penny contains about 28,000,000,000,000,000,000,000 copper atoms. No joke.

mole-pennies.jpeg
One mole of copper. Source: Fundamental Photgraphs, Richard Megna.

A copper atom has a radius of 128 picometers, which is 1.28 x 10-10 meter. So if you line up all the atoms of copper in one penny, they will form a line 1.8 trillion meters long. That's way past the orbit of Saturn from here!