Reactions happen between particles, but you cannot count particles — you can only weigh them. The mole is the bridge, and n = m ⁄ M is how you cross it. Almost every chemistry calculation you meet is this one wearing a different hat.
What each letter means
| Symbol | Meaning | Unit |
|---|---|---|
| n | Amount of substance — how many moles | mol |
| m | Mass, the thing you actually measure | g |
| M | Molar mass — the mass of one mole of that substance | g/mol |
A mole is 6.022 × 10²³ particles. The number is enormous and arbitrary-looking, but it is chosen so that one mole of a substance weighs, in grams, the same number as its relative formula mass. Carbon has a relative atomic mass of 12, so one mole of carbon is 12 g. That is the entire convenience of the system.
Watch the units cancel and you will rarely go wrong: g ÷ (g/mol) leaves mol. If your units do not cancel to what you expected, the arithmetic will not save you.
Working out a molar mass
Add up the relative atomic masses of every atom in the formula, counting each one as many times as it appears.
Water, H₂O: two hydrogens at 1.01 and one oxygen at 16.00 gives 2(1.01) + 16.00 = 18.02 g/mol.
Sulfuric acid, H₂SO₄: 2(1.01) + 32.06 + 4(16.00) = 98.08 g/mol.
Calcium hydroxide, Ca(OH)₂: the subscript applies to everything in the bracket, so it is 40.08 + 2(16.00 + 1.01) = 74.10 g/mol. Forgetting to multiply both atoms inside the bracket is the usual slip here.
Hydrated salts include their water. Copper(II) sulfate pentahydrate, CuSO₄·5H₂O, has the mass of five waters added on: 159.61 + 5(18.02) = 249.71 g/mol.
A worked example
How many moles are there in 25.0 g of calcium carbonate, CaCO₃?
Molar mass first. Ca is 40.08, C is 12.01, and three oxygens at 16.00:
M = 40.08 + 12.01 + 3(16.00) = 100.09 g/mol
Then the moles.
n = m ⁄ M = 25.0 g ⁄ 100.09 g/mol = 0.250 mol
Sanity check: the molar mass is about 100, and 25 is about a quarter of it, so a quarter of a mole is exactly what we should expect. Making that estimate before reaching for a calculator catches most order-of-magnitude errors.
Backwards now: what mass of calcium carbonate contains 0.400 mol?
m = n × M = 0.400 × 100.09 = 40.0 g
Where marks get lost
Mass in kilograms. M is in grams per mole, so m must be in grams. A 2.5 kg sample is 2500 g. This is worth a thousandfold error if missed.
Missing a bracket in the formula. Mg(NO₃)₂ contains two nitrogens and six oxygens, not one and three. Expand the brackets on paper before adding anything up.
Using the atomic mass when the element is diatomic. One mole of oxygen gas, O₂, is 32.00 g, not 16.00 g. The same catches people with H₂, N₂ and the halogens.
Rounding the atomic masses too early. Using 16 for oxygen is normally fine; using 1 for hydrogen in a compound with many hydrogens is not, and will drift your answer outside the accepted range.
Confusing molar mass with molecular mass. They are numerically the same, but molar mass carries the unit g/mol and molecular mass is a plain ratio with no unit. Examiners do notice.
Questions students actually ask
What exactly is a mole?
A counting unit, like a dozen but much larger: 6.022 × 10²³ particles. Chemists use it because that number of particles of any substance weighs, in grams, the same as its relative formula mass — which turns weighing into counting.
How do I find the molar mass of a compound?
Add the relative atomic masses of all the atoms in the formula, multiplying each by how many times it appears. Watch brackets and any water of crystallisation, which both count.
Is molar mass the same as molecular mass?
Numerically yes, but they are different quantities. Molecular mass is a ratio with no units; molar mass is measured in grams per mole. Use molar mass in this formula.
Why do I need moles at all — why not just use mass?
Because reactions happen particle by particle, not gram by gram. A balanced equation tells you two moles of hydrogen react with one of oxygen; it says nothing directly about masses, and the mass ratio is not 2:1.
How do I get from moles to the actual number of particles?
Multiply by Avogadro’s number, 6.022 × 10²³. So 0.25 mol contains about 1.5 × 10²³ particles. Divide by it to go the other way.
Related formulas
The dilution formula · The ideal gas law · Arithmetic progression
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