The mole & molar mass
The idea
Atoms are far too small to count one at a time, so chemistry uses a bulk counting unit: the mole, which is 6.022 × 10²³ particles (Avogadro's number), the same way a dozen is 12. The unit is sized so the bridge to the lab bench is effortless: one mole of a substance has a mass in grams numerically equal to its formula mass in amu. Carbon's atoms average 12.0 amu, so one mole of carbon weighs 12.0 g — that number, 12.0 g/mol, is its molar mass.
To get a compound's molar mass, add up the molar masses of every atom in the formula, multiplying through any subscripts and parentheses. Then conversions become one-step arithmetic: divide grams by molar mass to get moles, multiply moles by molar mass to get grams, and multiply moles by 6.022 × 10²³ to count particles.
Keep the idea straight: a mole is a count, not a mass. A mole of feathers and a mole of lead contain identical numbers of particles but wildly different masses, just as a dozen eggs and a dozen bowling balls weigh nothing alike. Mass per mole differs between substances precisely because their particles differ in mass.
Worked example
How many moles are in 18.5 g of calcium hydroxide, Ca(OH)₂, and roughly how many formula units is that? Use Ca = 40.1, O = 16.0, H = 1.0 g/mol.
- Compute the molar mass, remembering the subscript 2 outside the parentheses doubles everything inside: 40.1 + 2 × (16.0 + 1.0) = 40.1 + 34.0 = 74.1 g/mol.
- Convert mass to moles by dividing by molar mass: 18.5 g ÷ 74.1 g/mol = 0.250 mol. The division makes sense dimensionally — grams divided by grams-per-mole leaves moles.
- Count the particles: 0.250 mol × 6.022 × 10²³ formula units/mol ≈ 1.51 × 10²³ formula units of Ca(OH)₂.
- Sanity-check the size: 18.5 g is almost exactly one quarter of 74.1 g, so getting one quarter of a mole confirms the arithmetic.
Answer. 18.5 g of Ca(OH)₂ is 0.250 mol, or about 1.51 × 10²³ formula units.
Check your understanding
- Why is the molar mass in g/mol numerically the same as the formula mass in amu — what makes that no coincidence?
- Why do chemists insist on converting to moles instead of comparing substances gram for gram?
- If you had 18.5 g of a compound with twice the molar mass, what would happen to the mole count and the particle count?
- How would you explain to a friend what Avogadro's number actually counts and why it is so enormous?
Build the foundations first
The mole & molar mass builds on these concepts. If any feel shaky, start there.