I was bouncing around tumblr late last night and came across the term "a mole of bees" besides the fact i doubt there is a mole of any living thing on earth, how much space would this take up?
Well, it actually depends. The definition of mole is:
The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number.
The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.
See: Definition of mole (The International System of Units, page 134).
The problematic part is that last one: “any other particle or specified group of particles”.
So… what’s the elementary unit for bees?
Option 1: Elementary particles for bees is a single bee
I think this is the option you had in mind.
If that’s the case, then a mole of bees is 6.02214076 × 1023 bees.
For their size, they vary a lot, so let’s take the minimum and maximum sizes: 2 mm / 39 mm. Let’s assume they are cylindrical to a ratio of 0.25/1, meaning that we would have a minimal bee of 2 mm long and 0.5 mm in girth as a minimum bee, and a maximum bee of 39 mm long with 9.75 mm in girth.
Since we know how to calculate the volume for cylinders (V = r2 × π × h), we can now run some calculations.
Volume of our minimal bee: πr2 h = π · (0.25 mm)2 · 2 mm ≈ 0.3927 mm3
Volume of our maximum bee: π r2 h = π · (4.875 mm)2 · 39 mm ≈ 2,911.8146 mm3
Volume of mole of minimal bees: 0.3927 mm3 · 6.02214076 × 1023 ≈ 2.36 × 1023 mm3 ≈ 236,000 km3
Volume of mole of maximum bees: 2,911.8146 mm3 · 6.02214076 × 1023 ≈ 1.75 × 1027 mm3 ≈ 1,790,000,000 km3
This means that we could fill 55 Grand Canyons with a mole of our minimal bees, or 450,000 Grand Canyons with maximal bees!
Option 2: Elementary particles for bees are organic molecules
This one is a lot more boring. I don’t have good numbers because I could not find any analysis on the chemical composition of the bee body. But because the Avogadro’s constant is meant to equal the number of molecules with their atomic weight, we can make these deductions:
If a bee was made of a single “particle” of Hydrogen (atomic weight ≈ 1), then a mole of bees would be about 1 gram.
If a bee “particle” was made of two atoms of Hydrogen (atomic weight ≈ 1 + 1), then 2 grams.
If two Hydrogens and one Carbon atom (atomic weight ≈ 1 + 1 + 12), then 14 grams.
Let’s say that the “average” bee particle is then 3 H, 2 C, 0.5 N, 1.8 O. (These are totally made up numbers!) In a case like this, the average atomic weight of a bee “particle” would be 50.4, making a mole of bees 50.4 grams.
At that point, you can imagine that a mole of bees would probably be about a fistful of bees.
