A “mole” is just a number. There are many wordy definitions of a mole to be found on the Internet, such as Wikipedia’s definition:
The mole is defined as the amount of substance of a system that contains as many “elementary entities” (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (12C). A mole has 6.0221415 × 1023 atoms or molecules of the pure substance being measured. A mole will possess mass approximately equal to the substance’s molecular/atomic weight in grams. Because of this, one can measure the number of moles in a pure substance by weighing it and comparing the result to its molecular/atomic weight.
In reality, of course, no substance is truly “pure,” as found in the technical definition of a mole, but that’s the basic idea. For example, a mole of hydrogen atoms will have a mass of 1.00794, even though the atomic weight of hydrogen is 1, exactly. The reason for this is that hydrogen exists in nature in a couple of isotopes, which have different masses. Because the actual atomic weight is so much closer to 1 than it is to 2, for instance, means that hydrogen atoms with a mass of 1 amu (atomic mass units) are much more common in the natural world than hydrogen atoms with a mass of 2 amu.
This means that a “mole” (or 6.022 × 1023 atoms) of hydrogen in nature will have a mass of approximately 1.00794 g. A mole of “pure” hydrogen atoms (having a mass of 1 amu) would have a mass of 1 g, exactly, though, by definition and on the balance. So it is with all elements: a mole of that atom would have a mass of the atomic weight in grams. For example, a mole of gold atoms would have a mass of about 196.97 g.
That’s a lot of atoms, and a mole is an extremely big number. However, in terms of our world, it’s really not that big. For example, a strand of human hair has about a million carbon atoms across its diameter. That is, one strand of the girl’s hair (indicated by the red arrows) has a diameter of about a million atoms of carbon. Since a mole is a lot bigger, a strand of human hair has a diameter of about one quintillionth of a mole.
According to the US Mint, the composition of the penny changed in 1962, when tin was removed from the coin. (There wasn’t so much tin in it anyway, but the last traces were removed permanently in 1962.)
Beginning in 1962, the composition of the penny was 95 percent copper and 5 percent zinc. And during the 1982 minting run, the US Mint switched over to a composition that was 97.5 percent zinc and 2.5 percent copper.
From the Periodic Table of the Elements (link), we see that the atomic weight of copper (atomic number 29) is 63.546, and the atomic weight of zinc (atomic number 30) is 65.38.
Question 1. How many pennies from 1965 would it take to make a mole of atoms?
In 1965, the composition of the penny was 95:5 = copper:zinc. That means, if we had 100 g of pennies, we would have 95 g of copper and 5 g of zinc. More importantly, if we had a mole of penny atoms, 95 percent of them would be copper (about 5.72 × 1023 atoms), and 5 percent of them (about 3.01 × 1022 atoms).
And even more importantly toward answering our question, a mole of atoms that is composed of 95 percent copper atoms and 5 percent zinc atoms would have a mass of (95%)(63.546) g + (5%)(65.38) g. That comes to about 63.64 g. If we had a bag that had a mass of 63.64 g, we would have about a mole of penny atoms (copper and zinc combined).
A penny from 1965 would have a mass of about 3.11 g. Therefore, 63.64 g of pennies would comprise about 63.64 / 3.11 pennies, or about 20.46 pennies. Therefore if you have 21 cents in pennies dated between 1962 and mid-1982, you have more than a mole’s worth of metal atoms.
Question 2. How many pennies from 1990 would it take to make a mole of atoms?
A mole of atoms in the pennies from 1990 would have a mass of (97.5%)(65.38) g + (2.5%)(63.546) g = 65.334 g. The composition change caused the mass of a penny to go down to about 2.5 g. Therefore, we would need a few more pennies to have a mass of 65.334 if we are using the 1990 pennies:
65.334 g / ( 2.5 g per penny ) = 26.13 pennies to have one mole of metal atoms. By the way, this is not what they mean by the “shrinking value of the dollar.”