By Rosann Kozlowski
Updated Mar 24, 2022
Want to know how many atoms are in a given quantity of a substance? By combining a few key pieces of information—molar mass, sample mass, and Avogadro’s number—you can determine the exact atom count. This guide walks you through the process with a practical copper example.
Consult a periodic table to find the atomic mass of each element in your compound. For a pure element like copper, the atomic mass appears directly below its symbol. The atomic mass of copper is 63.55 g/mol, meaning one mole of copper atoms weighs 63.55 grams.
For compounds, sum the atomic masses of all constituent atoms. The resulting value is the molar mass, expressed in grams per mole.
Use the molar mass to translate the known mass of your sample into moles. The calculation follows a simple unit‑cancelling ratio:
32.80 g Cu × 1 mol Cu / 63.55 g Cu = 0.52 mol Cu
In this example, 32.80 grams of copper correspond to 0.52 moles.
Avogadro’s number—6.022 × 1023—is the count of entities in one mole of any substance. Multiply the mole quantity by this constant to find the atom count:
0.52 mol Cu × 6.022 × 1023 atoms/mol = 3.13 × 1023 atoms
Thus, 32.80 grams of copper contain approximately 3.13 × 1023 atoms.
Steps 2 and 3 can be combined into one line:
32.80 g Cu × 1 mol Cu / 63.55 g Cu × 6.022 × 1023 atoms/mol = 3.13 × 1023 atoms
For quick calculations, you can use online tools such as the Omni Calculator, though you still need to know the molar mass to input correctly.
Avogadro’s number is named after Italian scientist Amedeo Avogadro (1776‑1856), who proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Although he did not define the exact value of 6.022 × 1023, his foundational work earned the constant his name. Avogadro’s theory was first published in 1811 and only gained widespread acceptance half a century later.
