Avogadro’s number

Avogadro’s number NA is the number of atoms in 12 grams of carbon-12. It’s about 6.02 × 1023. (Update: Avogadro’s number is now exactly NA = 6.02214076 × 1023 mol−1 by definition. More details here.)

Here are a few fun coincidences with Avogadro’s number.

  1. NA is approximately 24! (i.e., 24 factorial.)
  2. The mass of the earth is approximately 10 NA kilograms.
  3. The number of stars in the observable universe is 0.5 NA.

The first observation comes from here. I forget where I first heard the second. The third comes from Andrew Dalke in the comments below, verified by WolframAlpha.

For more constants that approximately equal factorials, see the next post.

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6 thoughts on “Avogadro’s number

  1. Wolfram Alpha informs me that Avogadro’s number and 24! differ by approximately 18 sextillion, assuming I counted my commas correctly. That represents just about 3%.

    I don’t know if any of this is particularly interesting, but I felt compelled to look it up and hoped that I might save others the effort.

  2. Nathan: Avogadro’s number and 24! are closer on a log scale: 54.75 versus 54.78.

    Andrew: Great! I hadn’t seen that one. It means that the number of stars in the universe equals is roughly the same order of magnitude as the number of atoms in something you could hold in your hand. See also Kevin Kelly’s quote here.

  3. The best demonstration of the size of Avogadro’s number is the assertion that in any glass of water there is likely to be a molecule that passed the kidneys of King Charles II.
    I’ve no idea if it’s true!!

  4. A movement is afoot to declare Avogadro’s number to be exactly 2^79, which is only 0.4% off the value we use now.

    It’s embarrassing to have a standardized value that is a count nobody knows the low bits of. The value has been bobbing around more than 0.4% in living memory, so nobody should have got too attached to the one we use at the moment.

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