# Mole Day

Mole Day is a nerd holiday celebrated on October 23 between 6:02 a.m. and 6:02 p.m. in honor of Avogadro’s number, $6.02\times 10^{23}$. In 10th grade, my chemistry class was assigned a project for mole day. The project was pretty open-ended. There was a long list of things we could make, and it include things like a comic, a short film, and website. The only real requirement was that the product had to be related to moles in some way. I decided to make a “website,” but I interpreted that option very literally in order to allow myself a lot of freedom.

This was what I made. I’ve also remade the project below because I was not very good at JavaScript in 10th grade.1 This remake also depicts a mole more precisely. The number of triangles in the old version is $3^{50} \approx 7.18\times 10^{23}$.2 It also has much smoother animation, and it’s mobile friendly (though, it’s better on desktop).

Unfortunately, your browser does not support HTML canvases.

Interestingly, this demo might make a mole seem bigger than it actually is. The triangles are arranged flat on a plane rather than packed together in space, unlike most atoms in the real world. A mole of carbon atoms arranged in a sheet one atom thick would have an area of 10 000 m2, or almost an entire soccer field, but a mole of carbon atoms arranged in a ball would have a volume of 1.2 cm3, which is less than a teaspoon.[^stats] Also, the Sierpiński triangle has density zero. If a mole of carbon atoms was arranged like the triangles were in the demo, the entire triangle would have sides 160 km long and have an area of 11 000 km2, larger than Delaware. Of course, the triangle would be mostly empty space, but this does mean that at the end of the demo, the individual white triangles become about a million times smaller than actual atoms.

1. I’m not very good now, either, but better than in 10th grade.

2. The fact that $6.02\times 10^{23}$ is so close to a power of 3 is the reason I chose use the Sierpiński triangle over some other easily-generated fractal. [^stats]: I’m making the following assumptions: a carbon atom is a sphere with radius 70 pm. These spheres will pack with density 0.907 on a plane and 0.740 in space. A soccer field is 125 m by 85 m.