What is a mole?
Atoms and molecules react one at a time, but nobody can count them one at a time. The mole is chemistry's counting unit — a dozen, scaled up to 6.022×1023 things (Avogadro's number, NA), defined exactly since the 2019 SI revision. Its magic trick: one atom of carbon weighs 12.011 atomic mass units, and one mole of carbon atoms weighs 12.011 grams — the same digits, units switched. So molar mass (g/mol) converts instantly between the mass on your balance and the number of particles reacting, which is the entire business of stoichiometry.
The one rule to remember: a mole counts particles, not mass. One mole of every substance contains the same number of molecules — but their weights are as different as the substances themselves.
The periodic table is a mass catalog
Every element's cell in the periodic table carries its average atomic mass; sum them per formula unit and you have the molar mass. The sample, Ca3(PO4)2 (calcium phosphate), parses to 3 Ca + 2 P + 8 O = 3(40.078) + 2(30.974) + 8(15.999) = 310.174 g/mol, and the panel itemizes each element's gram contribution alongside. Parentheses multiply whatever is inside, and the dot in CuSO4·5H2O stacks five waters of crystallization on top — both handled by the same parser. Counting the waters matters: CuSO4·5H2O comes to ≈ 249.7 g/mol, not ≈ 159.6.
Percent composition
Divide each element's mass contribution by the molar mass and you get its mass percent — the number a nutrition label or a fertilizer bag prints (“P2O5 source, 20% P”). Water is the classic sample: H contributes 2(1.008) = 2.016 g and O contributes 15.999 g per 18.015 g, so water is 11.19% hydrogen and 88.81% oxygen by mass — a reminder that “mostly hydrogen” by atom count is very different from by weight.
Empirical vs molecular formula
An empirical formula is the smallest whole-number ratio of atoms (CH2O); a molecular formula is the actual count in the molecule (C6H12O6, glucose — six copies of the same ratio). Combustion analysis hands you mass percentages; converting them goes through moles: the sample's 40.00% C, 6.71% H, 53.29% O becomes 3.330 : 6.657 : 3.331 mol, which divides down to a clean 1 : 2 : 1 — CH2O, empirical mass 30.026 g/mol. To climb from empirical to molecular you need the molar mass: n = 180.16 ÷ 30.026 = 6.000, so the molecule is (CH2O)6. Many substances (water, ammonia, CO2) already stand at n = 1, where the two formulas coincide.
Grams, moles, particles
The Mole/Gram/Particle panel walks the full triangle in one shot: the sample converts 18.015 g of water into exactly 1.000000 mol and 6.022×1023 molecules — and, since each H2O has three atoms, 1.807×1024 atoms. This triangle is the engine behind every stoichiometry problem on the Equation Balancer page and every molarity on the Solutions page.
Common misconceptions
- A mole of anything weighs about the same. A mole counts particles; one mole of H2 is 2 g, one mole of gold is 197.0 g — same count, vastly different mass.
- Percentages convert to subscripts directly. They must pass through division by atomic mass (moles) first — hydrogen's 6.71% contributes more atoms than oxygen's 53.29% precisely because H atoms are so light.
- Molecular formula is always a bigger version of the empirical. Only when n > 1. For H2O the two are identical, and the molecular panel's n = 1.000 case is routine.
- Atomic masses are exact integers times amu. The listed values are abundance-weighted averages over isotopes — chlorine's 35.45 g/mol is the blend of 35-Cl and 37-Cl.
Related tools: Periodic Table (the atomic masses this page sums), Equation Balancer (stoichiometry built on the mole), and Solutions (moles per liter).
