How much would a mole of moles weigh? (asked by Anonymous)
There are two ways to interpret this question, both of which are equally silly. Maybe you mean a mole (unit of measurement) of moles (the subterranean mammal), or perhaps you mean, how much would a mole of mole molecules weigh? I’ll deal with each possibility in turn.
A mole is a number – 602,214,129,000,000,000,000,000 or 6.022×1023 – usually used as a unit of measurement for things like molecules, where you have an awful lot of them. A mole is (roughly) the number of atoms in a gram of hydrogen. It’s also (again, roughly) the number of grains of sand on Earth.
A mole is also a small, burrowing mammal in the family Talpidae. They are adapted to a subterranean lifestyle with large claws and small eyes.
1. Counting Moles
Ok so option one is that we want to know how much a mole (6×1023) of moles would weigh. Your average mole weighs around 50g – 100g, so 6.022 × 1023 × 75g ≈ 4.52 × 10 22kg. That’s roughly half the mass of the moon, or around 1% the mass of Earth. And, aggregated together in space, the moles would take up a planet-sized amount of space – filling a cube over 2000 miles wide and with a gravitational field similar to Pluto’s. Loose on the surface of the Earth, a mole of moles would be 80km deep – more or less filling our atmosphere. If the sea of moles didn’t crush / suffocate us all, they could provide enough food to feed us for 30 billion years. (Follow the rest of this thought experiment to it’s ridiculous conclusion over at what if?)
2. Dividing Moles
Option two is that we want to know the weight of 602,214,129,000,000,000,000,000 atoms of mole. A mole, weighing say, 100g, would have roughly 1 x 1026 atoms in it – that’s about 167 moles of atoms in each actual mole, so 1 mole of mole atoms would be approximately 1/167th of a mole – about 0.6g.
Featured image used under a creative commons license from Wikimedia Commons. Original image by Leptictidium