Chapter 6 · Chemical Composition
6.2Counting Nails by the Kilogram
8 min · two checks
Predict
If every nail has the same mass, how do you count nails by weighing the keg?
The idea
- Explain the mole by analogy with counting identical objects by mass.
- State Avogadro’s number and what it counts.
Suppose one nail has a mass of 5.0 g. A 2.0 kg box holds 2000 g / 5.0 g = 400 nails. You never opened the box. The method works only because the nails are identical. Atoms of an element are identical enough — we use the average atomic mass — so the same division works. The awkward part is that an atom’s mass in grams is tiny, so the convenient “box size” is huge.
Avogadro’s number, 6.022 × 10²³, is how many atoms are in exactly 12 g of carbon-12, and it is the number of particles in one mole of anything: atoms, molecules, ions, or electrons. One mole of nails would be absurd; one mole of atoms is a few tens of grams. Say “particles per mole,” not “a number with no unit,” when you convert.
Keep these
- Count = total mass / mass of one item, when items match.
- 1 mol = 6.022 × 10²³ particles.
- Use average atomic mass so the natural isotope mix is already included.