Moles and molar mass, made simple

The mole is a counting unit, nothing more mysterious than a dozen. A dozen means 12 things. A mole means 6.022 × 10²³ things, a number chosen so that the mass of one mole of a substance in grams matches the atomic or molecular mass in the periodic table. That neat coincidence is why chemists love it.

Why we need it

Atoms are far too small to count one by one or weigh individually. Moles let you weigh out a pile of a substance and know how many particles you have. One mole of carbon-12 weighs 12 g. One mole of water weighs about 18 g. Same number of particles, different mass, because each water molecule is heavier than a carbon atom.

Finding molar mass

Add up the atomic masses of every atom in the formula. For carbon dioxide, CO₂: 12.011 + 2 × 15.999 = 44.009 g/mol. When brackets appear, multiply what is inside them: in Mg(OH)₂ there are two oxygens and two hydrogens.

The conversion triangle

To get...	Do this
moles from mass	mass ÷ molar mass
mass from moles	moles × molar mass
particles from moles	moles × 6.022 × 10²³
moles from a solution	concentration (mol/L) × volume (L)

A worked example

How many molecules are in 9.0 g of water? Molar mass is 18.015 g/mol, so moles = 9.0 ÷ 18.015 = 0.4996 mol. Particles = 0.4996 × 6.022 × 10²³ ≈ 3.0 × 10²³ molecules. Since 9.0 g is half a mole, the answer is half of Avogadro's number, and the sum agrees.

Where students slip

Using the molar mass of a single atom for a molecule (oxygen gas is O₂, so its molar mass is about 32, not 16), forgetting to multiply by the subscript, and mixing up grams with kilograms. Write the unit on every line and the mistakes tend to show themselves.