How Much Would a Mole of Moles Weigh?

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Question:

How much would a mole of moles weigh? (asked by Anonymous)

Answer:

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.

Definitions

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.

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One comment on “How Much Would a Mole of Moles Weigh?

  1. I think you’ve made a mistake in your second calculation – the minimum that a mole of *anything* weighs is 1g, unless you’re looking at particles smaller than a proton. Most of the atoms in a mole are oxygen, with carbon making up somewhere in the region of 18% (assuming it’s not too different from a human – I haven’t found a breakdown of the constituents of a mole by element) so the mass of a mole of mole-atoms would be somewhere in the region of 15g – equal to the mean of the atomic masses of its constituent atoms.

    Fun fact: given that a small mole is around 18% carbon and has a mass of around 60g or so, one mole contains very close to one mole of carbon atoms!

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