Tenth Grade · Science · week 19

The mole and Avogadro's number

Convert between moles and number of particles using Avogadro's number, and explain why chemists need the mole as a counting unit.

Atoms and molecules are far too small and far too numerous to count one at a time, so chemists count them in bulk using a special counting unit called the mole -- exactly like a "dozen" always means 12, no matter what you are counting, a mole always means 6.022 x 10^23 of whatever you are counting. That number, 6.022 x 10^23, is Avogadro's number, and it was chosen specifically so that one mole of atoms would have a mass in grams equal to that element's atomic mass in amu -- a connection that makes the mole the bridge between counting particles and weighing them on a balance.

Converting between moles and particles uses Avogadro's number as a conversion factor, exactly like the metric conversions from earlier this year: moles x (6.022 x 10^23 particles / 1 mole) gives particles, and particles x (1 mole / 6.022 x 10^23 particles) gives moles.

📋 For the teacher
Teach it (10–15 min):
  • Compare Avogadro's number to a dozen directly and repeatedly this week: a dozen eggs is 12 eggs, a mole of eggs would be 6.022 x 10^23 eggs (impossibly, comically many) -- the absurd scale of the comparison actually helps the size of the number sink in.
  • Make sure moles-to-particles and particles-to-moles both get equal practice; students often get comfortable multiplying by Avogadro's number but freeze the first time they need to divide by it instead.
  • Keep a visible reminder that the mole is fundamentally a COUNTING unit, just like "dozen" or "pair" -- it will start connecting to mass and volume in the next two weeks, but this week is purely about counting.
  • Have them practice reading 6.022 x 10^23 out loud ("six point zero two two times ten to the twenty-third") until scientific notation this large feels ordinary rather than intimidating.
Talk about it:
  • Why did chemists invent the mole instead of just using a smaller everyday counting unit?
  • What is Avogadro's number, and what does it count?
  • How is converting moles to particles similar to the metric conversions from earlier this year?

Mastery looks like: They correctly convert between moles and number of particles using Avogadro's number in either direction, with correct sig figs.

Common stumbles: Multiplying by Avogadro's number when the problem actually requires dividing (going from particles back to moles); losing track of the power of 10 when multiplying two numbers in scientific notation.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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