# A Mole of Moles

Like most freshmen at Vanderbilt, I took Chemistry 102a during my first semester. On the first day of class, we (ostensibly, seeing as I slept through it) discussed the concept of a mole. A mole is a unit of measurement, generally used to describe the number of atoms or molecules of something, of which there are usually a lot. One mole comes out to 602,214,129,000,000,000,000,000, known as Avogadro’s Number, or roughly one trillion trillion. Incidentally a decent approximation of the number of grains of sand on the earth, one trillion trillion is by all reasonable measures an unfathomably large number for us. An amusing XKCD page deals with the question, “What would happen if you were to gather a mole of moles in one place?” Assuming one mole (the animal) weighs about 75 grams, a mole (the unit) of moles (the animal) comes out to roughly 10^22 Kg, which is slightly more than half the mass of the moon. If placed on the surface of the earth, the mole of moles would span the entire globe with an average thickness of 80 kilometers (the upper edge of our atmosphere), exterminating all life on earth in the process. Released into space, gravity would compress the moles into a planet-like sphere replete with a molten core of moles and volcanic-like surface activity. The following diagram shows the mole of moles to scale with the earth and moon:

“There might be a billion habitable planets in our galaxy. If we colonized them, we’d certainly bring mice and rats with us. If just one in a hundred were populated with small mammals in numbers similar to Earth’s, after a few million years—not long, in evolutionary time—the total number which have ever lived would surpass Avogadro’s number.” – XKCD

The universe is unfathomable massive. It’s funny to think that even on earth, a location so puny and insignificant when compared with essentially anything else in the universe, we still deal with numbers more massive than the number of planets in the universe. With estimates around 1,000,000,000,000,000,000,000,000, or 10^24, planets, it’s absurd that a similar number of moles would take up a space the size of the moon. Crazier still, one mole of water weighs in at 18.0152 grams, or about a tablespoon and a fifth.