TL;DR:
A mole is a fixed number of things,
6.022 × 10²³, just as a dozen is 12.Molar mass, in grams per mole, equals the atomic or formula mass read from the periodic table.
Moles = grams ÷ molar mass. For water,
18.02 g/mol, so 18.0 g is 1.00 mol.
You cannot count molecules one at a time, and you cannot weigh a single one on a kitchen scale. Chemists solved this with a counting unit called the mole. It is no more mysterious than a dozen, only much larger.
A dozen is a number, not a weight
A dozen means 12 of anything. A dozen eggs and a dozen bowling balls both have 12 items, but they weigh very different amounts. The count is the same, the mass is not.
A mole works the same way. One mole is 6.022 × 10²³ of anything: atoms, molecules, ions. That number is Avogadro's number. It was chosen so that the mass of one mole, in grams, matches the mass of one particle in atomic mass units. A mole of bowling balls would have a mass far beyond anything, but a mole of atoms fits in your hand.
Molar mass from the periodic table
The molar mass is the mass of one mole, in grams per mole (g/mol). For an element, it is the atomic mass printed on the periodic table. Carbon is about 12.01 g/mol, hydrogen about 1.008 and oxygen about 16.00.
For a compound, add the molar masses of all the atoms in the formula. Water, H₂O, has two hydrogens and one oxygen: 2 × 1.008 + 16.00 = 18.016, so about 18.02 g/mol.
Worked example: 18 g of water is one mole
Formula mass of water:
2 × 1.008 + 16.00 = 18.02 g/mol.Convert grams to moles:
n = m / M = 18.0 g ÷ 18.02 g/mol ≈ 1.00 mol.Count the molecules:
1.00 mol × 6.022 × 10²³ per mol = 6.022 × 10²³ molecules.Count the atoms. Each molecule has 3 atoms, so
3 × 6.022 × 10²³ = 1.807 × 10²⁴ atoms.
Try other amounts with the same relation. Half as much water, 9.0 g, is 9.0 ÷ 18.02 ≈ 0.50 mol. A 100 g glass of water is 100 ÷ 18.02 ≈ 5.55 mol. And going the other way, 2.00 mol of water has mass 2.00 × 18.02 = 36.0 g.
Here is a check on size. Water has a density of about 1.00 g/mL, so 18 g is about 18 mL, roughly a tablespoon. So a tablespoon of water holds 6.022 × 10²³ molecules. That is a huge number, which is why the unit is so useful.
Another compound: carbon dioxide
For CO₂, 12.01 + 2 × 16.00 = 44.01 g/mol. So 44.0 g of CO₂ is 1.00 mol, and 22.0 g is 22.0 ÷ 44.01 = 0.500 mol. The same moles-to-grams recipe works for every substance.
The conversion triangle
There are three linked quantities, and one formula moves between them.
Grams to moles: divide by molar mass,
n = m / M.Moles to grams: multiply by molar mass,
m = n × M.Moles to particles: multiply by
6.022 × 10²³.Particles to moles: divide by
6.022 × 10²³.
Writing the units with each step helps. 18.0 g × (1 mol / 18.02 g) leaves mol, because grams cancel, as in units and dimensional analysis.
Weighing chemicals: In a lab, never taste or sniff chemicals to identify them. Wear goggles when weighing, use a clean spatula, and read the safety data sheet for anything unfamiliar. Do not experiment with chemicals at home.
A dozen helps with scale too. Because a mole is 6.022 × 10²³ and a dozen is 12, one mole is 6.022 × 10²³ ÷ 12 ≈ 5.0 × 10²² dozens. Atoms are so small that a mole of them still fits in your hand.
The reason grams and atomic masses line up is simple. If one carbon atom has a mass of about 12 atomic mass units, then a mole of carbon atoms has a mass of about 12 grams, since the mole was defined to make exactly that conversion between the atomic scale and the lab scale.
How to check your answer
Round trip. Convert grams to moles and back and compare with the start.
Size. A mass bigger than the molar mass is more than 1 mol, and smaller is less than 1 mol.
Units. The unit left must be mol, not g or g/mol.
Formula mass. Count the atoms in the formula again and add.
Mistakes that cost marks
Multiplying by molar mass when you should divide.
Forgetting to count both hydrogens in H₂O when adding up the mass.
Mixing up molecules and atoms: a mole of water molecules is three moles of atoms.
Using the atomic number instead of the atomic mass.
Thinking a mole is a mass. It is a count.
Where you will use it next
Moles are the bridge between balanced equations and real amounts. Start with balancing chemical equations by counting atoms, then continue to stoichiometry step by step.
Frequently asked questions
Why is the number 6.022 × 10²³ and not something rounder?
The mole was originally defined so that 12 g of carbon-12 is one mole. Today the SI fixes the number exactly at 6.02214076 × 10²³, chosen to agree with that older definition, so it is not a round number.
Is the mole used for anything but atoms?
It counts any particles, including molecules, ions and electrons. It is the standard amount unit in chemistry.
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