The Mole and Avogadro's Number, Explained
A mole is a counting unit equal to 6.022 x 1023 particles, and that huge number is called Avogadro's number. One mole of anything contains exactly that many pieces. Those pieces can be atoms, molecules, ions, or electrons. The mole lets chemists count particles that are far too small to see or weigh one at a time, which is why it turns up in nearly every calculation they make.
What is a mole in chemistry?
A mole is the SI unit for the amount of a substance. It always stands for 6.022 x 1023 particles. The particles can be atoms, molecules, ions, or formula units. You must say what you are counting. One mole of water means 6.022 x 1023 water molecules. One mole of oxygen atoms means 6.022 x 1023 oxygen atoms.
The word mole is short for the older term gram-molecule. Think of it as chemistry's version of a dozen or a pair. A pair is 2 and a dozen is 12, but a mole is a staggering 6.022 x 1023. The number is large because atoms are tiny. You need a huge count of them to make an amount you can hold and weigh.
The abbreviation for mole is "mol." You will see it in nearly every chemistry calculation. It appears in units like grams per mole and moles per liter.
What is Avogadro's number?
Avogadro's number is 6.022 x 1023. Written more precisely, it is 6.02214076 x 1023. This exact value has defined the mole since the SI system was revised in 2019. Before that, the mole was tied to a physical sample of carbon-12. Now the number itself is fixed by definition, so it never changes.
The number is named after the Italian scientist Amedeo Avogadro. He did not calculate it himself. He proposed the idea that equal volumes of gases hold equal numbers of particles. Later scientists measured the value and named it in his honor.
To picture how big 6.022 x 1023 is, try a comparison. One mole of marbles would cover the entire Earth many miles deep. Yet one mole of carbon atoms weighs only about 12 grams. That gap shows how small a single atom really is.
Written out in full
Avogadro's number equals about 602,200,000,000,000,000,000,000. That is 602 sextillion. Scientists never write it this way in practice. Scientific notation keeps it short and easy to use.
Why chemists count in moles
Chemists use the mole because they cannot count atoms directly. Atoms are far too small and too numerous to count one by one. Instead, chemists weigh a sample. Then they convert that mass into a number of moles. The mole acts as a bridge between grams you can measure and particles you cannot see.
This bridge matters for reactions. A balanced equation tells you the ratio of particles that react. For example, two hydrogen molecules react with one oxygen molecule. You cannot pick out single molecules in the lab. But you can measure out two moles of hydrogen and one mole of oxygen. The ratio stays the same at the mole scale as at the particle scale. This idea sits at the heart of stoichiometry.
The mole and molar mass
The mole connects to mass through molar mass. The molar mass of a substance in grams per mole equals its atomic or molecular mass in atomic mass units. This is the key link. It means one mole of any element weighs its atomic mass in grams. One mole of carbon weighs 12.01 grams because carbon's atomic mass is 12.01.
To find the molar mass of a compound, add up the molar masses of every atom in it. Water is H2O. It has two hydrogen atoms and one oxygen atom. Hydrogen is 1.008 g/mol. Oxygen is 16.00 g/mol. So water is (2 x 1.008) + 16.00, which equals 18.02 g/mol.
The table below shows one mole of several common substances.
| Substance | Formula | Molar mass (g/mol) | Particles in 1 mole |
|---|---|---|---|
| Carbon | C | 12.01 | 6.022 x 1023 atoms |
| Water | H2O | 18.02 | 6.022 x 1023 molecules |
| Oxygen gas | O2 | 32.00 | 6.022 x 1023 molecules |
| Table salt | NaCl | 58.44 | 6.022 x 1023 formula units |
Notice that each substance has a different mass but the same number of particles. That is the whole point of the mole. It fixes the count and lets the mass vary.
How do you convert grams, moles, and atoms?
You convert between grams, moles, and particles using two tools. The first tool is molar mass, which links grams and moles. The second tool is Avogadro's number, which links moles and particles. You always pass through moles in the middle. Grams connect to moles, and moles connect to particles.
Here is the path in simple terms. To go from grams to moles, divide by the molar mass. To go from moles to particles, multiply by 6.022 x 1023. To reverse the trip, do the opposite operations in reverse order.
Worked example one: atoms in 2 moles of carbon
Question: How many carbon atoms are in 2 moles of carbon?
This one only needs Avogadro's number. You already know the number of moles.
- Start with 2 mol of carbon.
- Multiply by 6.022 x 1023 atoms per mole.
- 2 x (6.022 x 1023) = 1.2044 x 1024 atoms.
So 2 moles of carbon holds about 1.2 x 1024 atoms. Doubling the moles doubled the atoms. The relationship is direct and simple.
Worked example two: molecules in 36.0 grams of water
Question: How many water molecules are in 36.0 grams of water?
This trip needs both tools. You start in grams and finish in molecules.
- Step 1. Find the molar mass of water. It is 18.02 g/mol.
- Step 2. Convert grams to moles. Divide 36.0 g by 18.02 g/mol. That gives about 2.00 mol.
- Step 3. Convert moles to molecules. Multiply 2.00 mol by 6.022 x 1023. That gives 1.204 x 1024 molecules.
So 36.0 grams of water contains about 1.2 x 1024 molecules. Each molecule also holds 2 hydrogen atoms and 1 oxygen atom. So the sample holds three times as many atoms as molecules.
How is the mole different from molarity?
The mole and molarity sound alike but mean different things. A mole is a fixed count of particles. Molarity is a concentration. It tells you how many moles of a substance are dissolved in one liter of solution. Its unit is moles per liter, written mol/L or M.
Here is a quick example. A 1 M salt solution has 1 mole of salt in every liter. If you pour out half a liter, you have 0.5 mole of salt. The mole counts particles. Molarity tells you how crowded those particles are in a solution. Keep the two ideas separate and your calculations will stay clear.
Frequently asked questions
Is a mole the same as Avogadro's number?
They are closely tied but not identical. Avogadro's number is the value 6.022 x 1023. A mole is the amount of substance that contains that many particles. In short, Avogadro's number is the count, and a mole is the unit built from that count. One mole always equals 6.022 x 1023 particles.
Why is Avogadro's number so large?
Avogadro's number is large because atoms are extremely small. A single atom weighs almost nothing. You need a vast number of atoms to reach a mass you can weigh on a balance. The value 6.022 x 1023 was chosen so that one mole of a substance weighs its atomic mass in grams.
How many atoms are in one mole?
One mole of an element contains 6.022 x 1023 atoms. This is true for any element. One mole of gold, one mole of helium, and one mole of iron each hold the same number of atoms. Only their masses differ, because each element has a different atomic mass.
Why is the unit called a mole?
The name has nothing to do with the animal. Mole is a short form of the older term gram-molecule, which chemists used in the 1800s. Over time they trimmed the long name down to mole. You now see the abbreviation mol in nearly every chemistry calculation, from grams per mole to moles per liter.
How do you convert moles to grams?
To convert moles to grams, multiply the number of moles by the molar mass. For example, 3 moles of water times 18.02 g/mol equals 54.06 grams. To reverse it, divide grams by molar mass to get moles. Molar mass is the tool that links moles and grams in both directions.