How to Calculate the Number of Atoms in a Sample

By Mara Pesacreta; Updated April 24, 2017
Figure the number of protons, neutrons and electrons present in an atom.

An atom is a particle that is composed of protons, neutrons, and electrons. The protons and neutrons reside in the nucleus, which is at the center of the atom, while the electrons reside in the electron cloud, which is outside of the nucleus. Protons have a positive charge, neutrons are neutral and electrons have a negative charge. Understanding the structure of the atom is important because atoms compose the elements of the periodic table. When working with a sample of an element or compound, you can use unit conversions to determine the number of atoms in the sample.

Record the weight of the sample. If the weight of the sample is provided, then write it down. If it is not provided, then weigh the sample on the gram scale. For example, you may find that the aluminum sample weighs 6.00 grams.

Find the element on the periodic table and determine its molar mass. The molar mass is the number of grams per mole. For example, the molar mass of aluminum is 26.982 g/mol.

Memorize Avagadro's number. Avagadro's number represents the number of atoms in one mole. This number is 6.022 X 10^23.

Set up the proportions for the conversion of the weight of the sample, to the number of atoms in the sample. In the first ratio, put 6.00 grams in the numerator and 1 in the denominator. In the second ratio, put 1 mole in the numerator and 26.982 grams in the denominator. In the third ratio, put 6.022 x 10^23 atoms in the numerator and 1 mole in the denominator.

Cross out the units in the ratios that are the same. For example, you can cross out the units grams and moles because they both appear in the numerator and the denominator of two of the ratios. This leaves you with the unit that you want, atoms.

Multiply the ratios. You should receive an answer of 1.33 x 10^23 atoms.

About the Author

Mara Pesacreta has been writing for over seven years. She has been published on various websites and currently attends the Polytechnic Institute of New York University.