# Counting Units

Students are shown other numerical groupings to introduce the concept of the mole. Included are: a pair of socks, an egg carton for a dozen eggs, a six-pack of canned soft drinks, a box containing a gross of "golf" pencils, and a ream of paper.

Many students typically have problems wrestling with the concept of the mole when it is first introduced. Even if they have a good grasp of what a unit is, they sense that the mole is different. It isn't really a unit at all, but a counting group because the species we are dealing with (atoms, particles, molecules, ions, radicals, etc.) are , in theory, discrete, not continuous. Therefore we are, theoretically, counting, not measuring.

Some of your brighter students may argue that since we are learning that matter itself is composed of discrete particles, aren't all other units also really countings also? While acknowledging the validity of this viewpoint, we can point out that, whereas the other units focus on the continuous nature of matter as it appears on the macroscopic scale, the mole focuses on the discrete nature of matter on the microscopic scale that is posited by the atomic theory. You might want to tie this to the discrete nature of energy and quanta that the students will be learning about when they study spectra and the electronic structure of the atom.

One difference between the counting "units" introduced in this demonstration and the mole is that, whereas the pair, dozen, six-pack, etc. are exact, mole amounts are approximated to certain numbers of significant digits. This is because the mole is so very large and cannot actually be counted directly in most cases, but is rather inferred from actual measurements (mass, volume, etc.).

A real world corollary of this is when one orders large numbers of small, cheap items, such as small washers, from supply houses. They rarely ever actually count the items. Instead, they weigh out a given amount, and since they know how much each item weighs, they can approximate how many items are there. They are frequently off by a few items, but when there are that many, nobody really cares if the count is off a little.

- a pair of socks
- an egg carton for a dozen eggs
- a six-pack of canned soft drinks
- a box containing a gross of "golf" pencils
- a ream of paper.

Use the examples to illustrate that the numerical "unit" doesn't tell us what it is that we are "counting," nor does it tell us how big it is or how much it weighs.

None, really. Don't poke yourself in the eye with a "golf" pencil, I guess!

Gather materials.