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A single drop of water contains more individual molecules than there are stars in the observable universe. How do chemists count these invisible particles when weighing a sample on a digital scale?

The Mole and Avogadro's Constant

To connect the submicroscopic world of atoms to grams in the lab, chemists use a counting unit called the mole.
One mole of any substance contains exactly 6.022×10236.022 \times 10^{23} particles, a value known as Avogadro's constant (NAN_A). In 1811, Italian scientist Amedeo Avogadro hypothesized that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, laying the groundwork for this universal constant.
The relative formula mass (MrM_r) is the sum of the relative atomic masses (ArA_r) of all atoms shown in a chemical formula. When you measure out the MrM_r of a substance in grams, you have exactly one mole of that substance.
What happens when an exam asks you not just for the number of molecules, but for the specific number of individual ions or atoms inside a sample?

Counting Atoms and Ions in Compounds

To find the number of individual ions or atoms in a given mass, calculate the moles of compound first, then multiply by the number of specific atoms per formula unit before using Avogadro's constant.
Let's solve a classic Grade 8/9 question: Calculate the total number of oxide ions (O2−\text{O}^{2-}) present in 10.20 g10.20\text{ g} of aluminum oxide, Al2O3\text{Al}_2\text{O}_3 (Ar:Al=27.0,O=16.0A_r: \text{Al} = 27.0, \text{O} = 16.0).
First, determine the relative formula mass: Mr(Al2O3)=(2×27.0)+(3×16.0)=102.0 g/molM_r(\text{Al}_2\text{O}_3) = (2 \times 27.0) + (3 \times 16.0) = 102.0\text{ g/mol}
Next, find the moles of Al2O3\text{Al}_2\text{O}_3: n=massMr=10.20 g102.0 g/mol=0.100 moln = \frac{\text{mass}}{M_r} = \frac{10.20\text{ g}}{102.0\text{ g/mol}} = 0.100\text{ mol}
Because each formula unit of Al2O3\text{Al}_2\text{O}_3 contains 33 oxide ions, 0.100 mol0.100\text{ mol} of Al2O3\text{Al}_2\text{O}_3 delivers 0.300 mol0.300\text{ mol} of O2−\text{O}^{2-} ions.