The three conversions
Almost every mole question is one of these, and moles are always in the middle.
moles = grams ÷ molar mass
grams = moles × molar mass
particles = moles × 6.022 × 10²³
moles = particles ÷ 6.022 × 10²³
You never go straight from grams to particles. You go grams → moles → particles, one step at a time, which is why the mole is worth having at all.
Mass to moles, and back again
Going from grams to moles, divide by the molar mass.
How many moles are in 34.4 g of water? Water’s molar mass is 18.02 g/mol, so
34.4 g ÷ 18.02 g/mol = 1.91 mol
Going from moles to grams, multiply.
What is the mass of 6.80 mol of water?
6.80 mol × 18.02 g/mol = 122.5 g
The unit tells you which way round to go. Grams divided by grams-per-mole leaves moles; moles times grams-per-mole leaves grams. If your answer comes out in the wrong unit you have divided when you should have multiplied.
Moles to particles
Multiply by Avogadro’s number, 6.022 × 10²³, to turn a count of moles into a count of individual particles. Divide to come back.
How many molecules are in 2.0 mol?
2.0 × 6.022 × 10²³ = 1.20 × 10²⁴ molecules
Notice that this step does not care what the substance is. Two moles of water and two moles of sugar contain exactly the same number of molecules. They weigh very different amounts, because that is the other conversion.
For an ionic compound like NaCl there are no molecules, so the particles are called formula units instead. The arithmetic is identical.
Molar mass, and why the units are g/mol
Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol). You find it by adding up the atomic masses of every atom in the formula, straight off the periodic table.
For water:
2 × 1.008 (the two hydrogens) + 15.999 (the oxygen) = 18.02 g/mol
So one mole of water weighs about 18 grams, which is roughly a tablespoon.
The two units are deliberately lined up. An atom’s mass on the periodic table is in atomic mass units (u), and its molar mass in g/mol is the same number: carbon is 12.011 u per atom and 12.011 g/mol per mole. That is not a coincidence, it is what Avogadro’s number was chosen to make true, and it is the reason you can read a molar mass straight off the table without converting anything.
Common molar masses
| Substance | Formula | Adding up the atomic masses | Molar mass |
|---|---|---|---|
| Water | H₂O | 2 × 1.008 + 1 × 15.999 | 18.02 g/mol |
| Carbon dioxide | CO₂ | 1 × 12.011 + 2 × 15.999 | 44.01 g/mol |
| Oxygen gas | O₂ | 2 × 15.999 | 32.00 g/mol |
| Sodium chloride (salt) | NaCl | 1 × 22.990 + 1 × 35.450 | 58.44 g/mol |
| Calcium carbonate | CaCO₃ | 1 × 40.078 + 1 × 12.011 + 3 × 15.999 | 100.09 g/mol |
| Glucose | C₆H₁₂O₆ | 6 × 12.011 + 12 × 1.008 + 6 × 15.999 | 180.16 g/mol |
| Sucrose (table sugar) | C₁₂H₂₂O₁₁ | 12 × 12.011 + 22 × 1.008 + 11 × 15.999 | 342.30 g/mol |
| Sulfuric acid | H₂SO₄ | 2 × 1.008 + 1 × 32.060 + 4 × 15.999 | 98.07 g/mol |
| Ammonia | NH₃ | 1 × 14.007 + 3 × 1.008 | 17.03 g/mol |
| Methane | CH₄ | 1 × 12.011 + 4 × 1.008 | 16.04 g/mol |
| Sodium hydroxide | NaOH | 1 × 22.990 + 1 × 15.999 + 1 × 1.008 | 40.00 g/mol |
| Iron(III) oxide (rust) | Fe₂O₃ | 2 × 55.845 + 3 × 15.999 | 159.69 g/mol |
| Magnesium oxide | MgO | 1 × 24.305 + 1 × 15.999 | 40.30 g/mol |
| Hydrochloric acid | HCl | 1 × 1.008 + 1 × 35.450 | 36.46 g/mol |
The calculator above will do any formula you type, including brackets like Ca(OH)₂ and hydrates like CuSO₄·5H₂O, where the water of crystallisation counts toward the mass.
What does 2H₂O mean?
A number in front of a formula and a number inside it do completely different jobs.
- The subscript in H₂O is part of the substance. It says a water molecule contains two hydrogen atoms. Change it and you have a different chemical.
- The coefficient in 2H₂O is an amount. It says two moles of water. The substance is unchanged.
So the molar mass of 2H₂O is still 18.02 g/mol, because molar mass is a property of water and does not depend on how much you have. What the 2 changes is the mass on the balance: 2 × 18.02 = 36.03 g. Coefficients are how balanced equations count reactants, which is where this distinction starts to matter.
Why chemists count in moles at all
Atoms are far too small and far too numerous to count one at a time: a single drop of water holds well over a billion trillion molecules. So chemists use a counting unit, exactly the way a baker uses a dozen.
What makes the mole more useful than a dozen is its size. It is defined as 6.02214076 × 10²³ particles, a number chosen so that a mole of any substance weighs, in grams, the same number as one of its particles weighs in atomic mass units. That is the whole trick: it turns a balance, which measures mass, into an instrument that counts atoms.
One mole of carbon-12 weighs exactly 12 grams and contains Avogadro’s number of atoms. Read more about where those atomic masses come from on the atomic mass page.
Where the mole leads next
Moles are the working unit of the rest of chemistry. A balanced equation is a recipe in moles, so stoichiometry is mostly this page’s conversions applied twice: grams of one substance into moles, across the equation, then back into grams of another. It is free to embed on your own site or LMS with the snippet below.