Magnificent moles

You may well ask, what is the point of an SI unit that measures “amount”? Surely if we want to know an amount then we simply count whatever it is that we need to quantify. That’s fine until we get to VERY large numbers. How large? We’re talking here about numbers that are massively bigger than the age of the Universe in seconds.

The Universe has existed for about 13.8 billion years (see https://map.gsfc.nasa.gov/universe/uni_age.html) and each year comprises about 31.5 million seconds, so the Universe has existed for about 435 million, billion seconds (or 435 quadrillion seconds to use the generally accepted way of expressing large numbers).

This number is so large that we can’t possibly imagine how big it is. Douglas Adams, writing in The Hitchhiker’s Guide to the Galaxy, put it like this; “Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.” Admittedly, we don’t actually know how big the Universe is, but I still think the quote is helpful when thinking about things on a very large scale.

Back to our SI unit of amount, called the mole. One mole is equal to a number that is (roughly) 6 followed by 23 zeroes (6 x10^23). This compares with 435 followed by just 15 zeroes for the age of the Universe. In other words, the mole is a number that is about one million times bigger than the age of the Universe in seconds.

Despite being a massively, massive number, the mole is equal to something as small as the number of molecules in about half an eggcup of water (or the number of atoms in about a dessert spoon of water).

The mole is therefore vital to convert unimaginably large numbers into everyday contexts.

Interestingly, the mole was originally a concept rather than an actual number. In 1811, Amedeo Avogradro suggested that equal volumes of different gases contain the same number of particles.

This idea came from the realisation that the pressure of a gas depends on its temperature (the average energy of each particle) and the number of collisions occurring with the walls of the container each second. So if the pressure is the same for different gases at the same temperature, then equal volumes of different gases must contain equal numbers of particles. (The connection between temperature and pressure was covered recently in the post about Kinetic Theory, which can be read here.)

To give a value to Avogadro’s number, we turn to electrolysis and look at the quantity of electricity needed to deposit a mass of metal that is equal to the element’s atomic mass. It turns out that the quantity of electrical charge needed is a low multiple of a certain number. The multiple depends on the element’s valency (the charge on the metal’s ion) and the base number is known as the Faraday, which is equal to about 96500 C (coulombs).

The final step involves using the charge on one electron, which was first determined by Robert Millikan in his famous series of oil-drop experiments. This work, which took seven years to complete and came a full century after Avogadro first proposed his idea, contributed to Millikan winning the Nobel Prize for Physics in 1923.

If we divide the charge on one electron into the charge needed to deposit one atomic mass of a metal in electrolysis, then (assuming a +1 charge on the atom) the number we get will be equal to the number of (monovalent) atoms in one atomic mass of the element.

The charge on one electron is equal to 1.6 x 10^-19 C, and if we divide that into 96500 C we get a value of 6.03 x 10^23. The actual value for the mole is roughly 6.022 x 10^23 (see https://www.npl.co.uk/si-units/mole).

It turns out that there is even more to the mole than its origin in gases and its measurement in electrolysis, but I’ll leave that to a future post.