The mole

One of the essential skills you must have as a good chemist is to be able to calculate how much of a particular reactant you will need to use to make a certain amount of your desired product or how much of a certain product you will be able to make from your starting reactants. The problem here is that it is not possible to count out or weigh individual atoms into a flask; since the atoms are by themselves far too small to weigh or count so counting atoms is a complete non-starter. What is needed is a quantity or number that will let you compare equal numbers of particles and use this number to calculate how much of the reactants to use or how much product you can expect to make in a any chemical reaction.

Chemists are not the only people faced with this problem; consider paper! You don't buy individual sheets of paper; you buy paper in reams. A ream contains 500 sheets of paper. A ream of A3 paper will be bigger than a ream of A4 paper because A3 paper is bigger than A4 paper- obviously! But a ream of A3 paper will still contains 500 sheets of paper. The ream is a standardised unit used by paper suppliers because it contains a standard number of sheets; 500 sheets. So if an order comes in for 10 000 sheets of paper would you rather count out 10 000 sheets of paper or quickly count out 20 reams?

Chemists like paper suppliers need a standard unit which they can use to measure out equal numbers of reacting particles, whether they are atoms, molecules or ions. Now chemists don't use reams instead they use a unit called the mole. The word mole may seem an odd choice of a word, since most people think of moles as furry little critters that dig up your lawn! However the word mole is actually derived from a Latin word meaning mass or pile, so think of the mole as the unit of mass used by chemists. 1 mole of a substance is the mass of 6.022 x 10²³ particles, that is Avogadro's number of particles. So like the example above with paper, would you rather measure out 1 mole of a substance or count out 6.022 x 10²³ atoms?

Measuring the mass of atoms

Chemists use a relative atomic mass scale to measure the mass of atoms (relative simply means compared to). In 1961 the isotope of carbon (¹²C) was picked as the standard from which the masses of all other atoms would be compared. On the carbon-12 scale the ¹²C isotope is given an atomic mass of exactly 12 units. This means that 12 grams of ¹²C contains 1 mole of carbon atoms. That is 6.022 x10²³ atoms.

On this scale the mass of magnesium is 24, since magnesium atoms are twice as "heavy" as carbon atoms. So we would say the relative atomic mass of magnesium is 24. This means that magnesium atoms have twice the mass of carbon atoms. The relative atomic mass of magnesium is therefore 24; we use the symbol A_r for relative atomic mass. So if we weigh out 24g of magnesium we will have the same number of atoms as we have in 12g of ¹²C; that is 1 mole of magnesium atoms. The only difference is the magnesium atoms are twice as massive as carbon atoms.

Similarly carbon atoms are 12 times as heavy as hydrogen atoms, so it follows that 12g of carbon and 1g of hydrogen contain the same number of atoms, that is 1 mole of atoms. The relative atomic mass expressed in grams for all elements will contain 1 mole of atoms.

The mole and Avogadro

1 mole of carbon or 12 grams of carbon is quite a large pile of carbon and obviously atoms are very very small, so there is going to be quite a large number of atoms in that pile of carbon. In fact it's an unbelievable huge number of carbon atoms, there are: 600 000 000 000 000 000 000 000 atoms of carbon in the charcoal block opposite! That is 6.022 x 10²³ atoms. That's a lot! This number is often called Avogadro's number; after the Italian scientist Amedeo Avogadro. Imagine having to count them! Well that is why we don't, we weigh them. That is the beauty of the mole. By simply weighing out 12g of carbon we know exactly how many atoms we have. If you weigh out 1.2g of carbon; that is 1/10th of a mole or 0.1 moles then you can easily work out how many atoms of carbon you have:

1.2g of carbon = 0.1 x 6x10²³ = 6x10²² atoms

It follows then that:

• 1 mole or 24g of magnesium contains 6 x 10²³ atoms of magnesium
or
• 1 mole or 32g of sulfur also contains 6 x 10²³ atoms of sulfur
or
• 1 mole or 48g of titanium also contains 6 x 10²³ atoms of titanium.

Key points

• Chemists need to know how many atoms are reacting in order to calculate the amount of products they can make. However atoms are too small to count so chemists weigh them instead.
• All measurements have a standard or reference point, whether it is the kilogram or the metre. The standard chemists use to measure the masses of atoms against is the carbon-12 isotope (¹²C). It is assumed to have a mass of exactly 12 units. The masses of all other atoms are obtained by comparing their mass against ¹²C
• 1 mole of any substance contains Avogadro's number of particles, that is 6.022x10²³ (which is often just simplified to 6 x 10²³) particles.

Check your understanding - Questions on the mole

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