Infographic on the mole. One mole is the amount of substance that contains exactly 6.022 x 10^23 atoms, molecules or ions. This number is also known as Avogadro's number. Using moles makes it easier to talk about amounts of substances involved in reactions by relating the mass of a substance to its atomic or molecular mass. Amount of substance (moles) = mass (grams) divided by the mass of 1 mole (grams per mole). One mole contains a different mass for different substances.
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Today, 23rd October is Mole Day – which might put you in mind of small, furry, burrowing animals. However, they don’t even seem to have a commemorative day of any kind; we’re actually talking about the mole in chemistry, a concept that makes it easier to talk about the amounts of substances involved in chemical reactions. This is a fundamental concept and one that all chemists utilise.

The problem that chemists have with atoms and molecules is that they’re a little on the small side, which makes counting them essentially impossible. To put the size of atoms into perspective, if we scaled up the size of a helium atom so it was the size of one of the full stops in this article, scaling up an average gerbil’s size by the same factor would give you one terrifying, Earth-sized gerbil. When carrying out chemical reactions, we often want to get some idea of how much of the product we can expect to get from a reaction, but the enormous numbers of atoms or molecules involved in even a small sample would make these calculations incredibly unwieldy.

This is where the mole comes in. It’s defined as the amount of substance that contains exactly 6.02214076 × 1023 atoms, molecules or ions. French scientist Jean Perrin proposed naming this number after Amedeo Avogadro, the Italian scientist widely credited with being the first to realise that the volume of a gas, at a given temperature and pressure, is directly proportional to the number of atoms or molecules, regardless of the gas’s identity. Hence, we know 6.022 x 1023 as ‘Avogadro’s number’.

Avogadro’s number was, up until 2019, defined as being the number of atoms present in 12 grams of carbon-12. It’s now defined simply as being 6.022 140 76 × 1023 elementary entities. One mole of any substance, then, contains exactly this number of atoms or molecules. Obviously, dependent on the mass of the atoms or molecules, the total mass of one mole of a substance can vary – one mole of water weighs very marginally over 18 grams, whilst one mole of the salt you have in your kitchen, sodium chloride, weighs 58.4 grams.

This can seem confusing for chemistry students at first, but it makes sense if you think about it. Different substances will have atoms, molecules or ions which have different masses. Gold atoms have a greater mass than iron atoms, so the mass contained in one mole of gold atoms is greater.

As an analogy, it’s useful to think of using moles to express the amount of substance as being analogous to weighing coin rolls to estimate the number of coins they contain. In this analogy,  the value of the coins is like mass – it’s different for different coins, in the same way the masses of atoms of different elements differ. The number of coins is like the number of atoms, and the rolls of coins are like moles of atoms.

That’s what a mole is – but why do we need it? Well, for starters, it makes expressing amounts of chemicals a lot easier. We don’t have to represent the number of molecules of a substance we have and use the large numbers that would entail, and we can instead use moles in our calculations to simplify them. We can find the amount in moles of any mass of any substance, simply by dividing the mass we have of the substance by the ‘molar mass’ – that is, the total of the atomic masses of the atoms that make up the substance. Additionally, using moles can help us easily predict the masses of products we can obtain from reactions.

In summary, then, the mole is a vital tool for chemists – probably the reason there’s a day to commemorate it, whilst its furrier namesakes go the whole year unappreciated.

[Note: this post was updated on 23 October 2020 to ensure it is up to date with the recent redefinition of the mole. It was also updated to ensure that the terms and analogies used were consistent in their depiction of the mole as an amount of substance, and to avoid usage of the incorrect phrase ‘number of moles’. I’m very grateful to Juris Meija (@MeijaJuris) for his help with this.]

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