Why chemists count in moles
Atoms and molecules are far too small to count one by one, so chemists group them in moles. One mole is 6.02214076 × 10²³ entities, Avogadro’s number. The trick is that one mole of any substance weighs its molar mass in grams: 18.015 g for water, 44.01 g for carbon dioxide. So a balance becomes a way to count molecules.
The formulas
- Moles n = mass ÷ molar mass
- Mass m = moles × molar mass
- Number of entities = moles × 6.022 × 10²³
- Gas volume = moles × molar volume: 22.414 L at 0 °C and 1 atm, about 24.05 L at 20 °C and 1 atm
Worked example
How many moles and molecules are in 100 g of water?
- Molar mass of H2O: 2 × 1.008 + 16.00 = 18.015 g/mol.
- Moles: 100 ÷ 18.015 = 5.55 mol.
- Molecules: 5.55 × 6.022 × 10²³ = 3.34 × 10²⁴.
- As steam at 0 °C and 1 atm, that much water would fill about 124 L (in practice water condenses, but the figure shows the scale).
Molar masses of common substances
| Substance | Formula | Molar mass (g/mol) |
|---|---|---|
| Water | H2O | 18.015 |
| Carbon dioxide | CO2 | 44.009 |
| Oxygen | O2 | 31.998 |
| Table salt | NaCl | 58.44 |
| Glucose | C6H12O6 | 180.16 |
| Table sugar | C12H22O11 | 342.30 |
| Ethanol | C2H5OH | 46.07 |
| Chalk, limestone | CaCO3 | 100.09 |
Finding a molar mass
Add up the atomic masses from the periodic table, each multiplied by the number of atoms in the formula. For glucose, C6H12O6: 6 × 12.011 + 12 × 1.008 + 6 × 15.999 = 180.16 g/mol. For hydrates, include the water molecules.
Where the conversion is used
- Stoichiometry: balanced equations work in moles, so convert grams to moles before comparing reactants.
- Solutions: molarity is moles per liter.
- Gases: the ideal gas law uses moles.
- Everyday scale: a teaspoon of sugar (about 4 g) is 0.012 mol, still 7 × 10²¹ molecules.
Common mistakes
- Using the atomic mass of an element instead of the molecule: O2 is 32.00 g/mol, not 16.00.
- Forgetting to convert milligrams or kilograms to grams.
- Rounding molar masses too early, which adds up in multi-step problems.