What Is a Mole in Chemistry? Avogadro's Number Explained Simply
A simple guide to the mole: why chemists count atoms in batches of 6.022 x 10^23, how to read molar mass off the periodic table, and worked examples.
Ask a chemist how much of something they have and they will not always answer in grams. Often they answer in moles. The word has nothing to do with the animal or the skin blemish. It is a counting unit, like a dozen or a pair, but for a number so enormous that it only makes sense when you are counting atoms and molecules.
This article explains why chemists need such a unit, where the strange number behind it comes from, and how to use the periodic table to convert between moles and grams. If you can multiply and divide, you can do mole calculations.
The counting problem
Chemistry happens between individual atoms. When hydrogen burns in oxygen, two hydrogen molecules combine with one oxygen molecule to make two molecules of water. The recipe is about numbers of particles, not masses.
The trouble is that atoms are absurdly small. A single glass of water contains far more molecules than there are grains of sand on Earth, or stars in the observable universe. Nobody can count them one at a time. Yet a chemist mixing two substances needs to know that the particles are present in the right ratio, otherwise some of one reactant is wasted.
The solution is to weigh instead of count, and to use a conversion factor that turns a mass into a number of particles. That conversion factor is the mole.
The definition
One mole of anything contains 6.022 x 10^23 particles. Written out, that is 602,200,000,000,000,000,000,000, and it is called Avogadro's number, or the Avogadro constant, after the Italian scientist Amedeo Avogadro. He never calculated it himself; the constant was named in his honour in the early twentieth century because of his earlier insight that equal volumes of gas contain equal numbers of molecules.
The particles can be anything: atoms, molecules, ions or electrons. A mole of carbon atoms, a mole of water molecules and a mole of sodium ions all contain the same number of particles. What differs is how much they weigh.
Since 2019 the mole has been defined by fixing the Avogadro constant as exactly 6.02214076 x 10^23. Before that it was defined as the number of atoms in exactly 12 grams of carbon-12. Both definitions give the same number to any precision you are ever likely to need, but the new one no longer depends on weighing a lump of carbon.
How big is Avogadro's number?
It is genuinely hard to picture. A mole of seconds is more than a million times longer than the age of the universe. If every person alive counted one atom per second without stopping, it would take all of humanity working together millions of years to count a single mole. And yet that many water molecules fit in a spoon. The mole is enormous only because atoms are so tiny; it is exactly the right size to bridge the world of atoms and the world of things we can hold and weigh.
Why carbon-12 and 12 grams?
The number was not plucked from the air. It was chosen so that the mass of one mole of a substance in grams equals the relative mass of one of its particles. Carbon-12, the most common form of carbon, has six protons and six neutrons and was chosen as the reference point, given a relative atomic mass of exactly 12. A mole was then defined so that 12 grams of it contained one mole of atoms.
The payoff is huge. Because every other element is measured against carbon-12, the relative atomic mass printed on the periodic table doubles as the mass of one mole of that element in grams. This quantity is called the molar mass, and its unit is grams per mole, written g/mol.
Reading molar mass off the periodic table
Look at any element on the table and you will see two numbers. The whole number is the atomic number, the count of protons. The decimal number is the relative atomic mass, and that is the one you want. It is a decimal because most elements exist as a mix of isotopes, atoms with different numbers of neutrons, and the table shows the average.
Some values worth knowing, rounded to two decimal places: hydrogen 1.01, carbon 12.01, oxygen 16.00, sodium 22.99 and chlorine 35.45. To find the molar mass of a compound, add up the atoms in its formula.
- Water, H2O. Two hydrogens and one oxygen: (2 x 1.01) + 16.00 = 18.02 g/mol. One mole of water weighs about 18 grams, which is roughly a tablespoon.
- Carbon dioxide, CO2. One carbon and two oxygens: 12.01 + (2 x 16.00) = 44.01 g/mol.
- Sodium chloride, NaCl. One sodium and one chlorine: 22.99 + 35.45 = 58.44 g/mol. A mole of table salt is a little under 60 grams.
Notice that a mole of water molecules fits in a spoon while a mole of salt is a small heap, yet both contain the same number of particles. The mole counts; it does not weigh.
Moles to grams and back
The whole business comes down to one relationship. The number of moles equals the mass divided by the molar mass. Rearranged, mass equals moles multiplied by molar mass. A few examples show how it works.
- How many moles are in 36 grams of water? Divide the mass by the molar mass: 36 / 18.02 = 2.0 moles, near enough.
- What is the mass of 0.5 moles of carbon dioxide? Multiply: 0.5 x 44.01 = 22.0 grams.
- How many moles are in 117 grams of sodium chloride? Divide: 117 / 58.44 = 2.0 moles.
- How many molecules are in 2 moles of water? Multiply by Avogadro's number: 2 x 6.022 x 10^23 = 1.204 x 10^24 molecules.
Gases have one extra shortcut. At room temperature and ordinary atmospheric pressure, one mole of any gas takes up roughly 24 litres, regardless of which gas it is. That is why balloons of different gases can hold the same number of molecules even when the gases have very different masses.
Why chemists cannot do without it
A balanced chemical equation is a recipe written in moles. Take the burning of carbon to form carbon dioxide: C + O2 gives CO2. The equation says one atom of carbon reacts with one molecule of oxygen. Scale it up by Avogadro's number and it says one mole of carbon, about 12 grams, reacts with one mole of oxygen, about 32 grams, to give one mole of carbon dioxide, about 44 grams. The masses add up, as they must, and the chemist knows exactly how much of each reactant to weigh out.
Without the mole there would be no way to translate the tidy whole-number ratios in equations into quantities you can measure on a balance. Every laboratory, factory and pharmacy depends on that translation. Students aged 14 to 16 studying GCSE and equivalent courses meet it early, and it stays in use for the rest of a chemist's career.
Chemists even celebrate it. Mole Day falls on 23 October, from 6:02 in the morning until 6:02 in the evening, a date and time built from the digits of the number.
Common mistakes
- Using the atomic number instead of the atomic mass. Oxygen is element 8, but its molar mass is 16 g/mol. Always use the decimal number.
- Forgetting that some elements come as molecules. Oxygen gas is O2, so one mole of oxygen gas weighs 32 grams, not 16, and contains two moles of oxygen atoms.
- Treating the mole as a mass. A mole of hydrogen and a mole of gold contain the same number of atoms, but the gold weighs almost 200 times more.
- Mixing up units. Molar masses are in grams per mole. If a question gives kilograms, convert first.
- Rounding too early. Keep an extra decimal place through the calculation and round at the end.
Key takeaways
- A mole is a counting unit containing 6.022 x 10^23 particles, a number now fixed exactly by definition.
- The relative atomic mass on the periodic table is also the mass in grams of one mole of that element, called the molar mass.
- Add up the atoms in a formula to get a compound's molar mass: water is about 18 g/mol, carbon dioxide 44 g/mol and sodium chloride 58.44 g/mol.
- Moles equal mass divided by molar mass, and mass equals moles multiplied by molar mass.
- Balanced equations are written in moles, which is how chemists turn particle ratios into masses they can weigh out.
- Watch out for atomic number versus atomic mass, and for elements such as oxygen that exist as two-atom molecules.
