# Use Avogadro’s Number to Calculate the Mass of a Single Atom

Have you ever wondered about the mass of a single atom? It’s easy to calculate! All you need is the relative atomic mass (atomic weight) of the element and Avogadro’s number. Here is how you calculate the mass of a single atom and how you extend the same principle to find mass of a single molecule.

mass of single atom = atomic mass of element / Avogadro’s number

Usually, atomic mass refers to the relative atomic mass from the periodic table. If you are dealing with a certain isotope of an element, then the atomic mass is the number of protons and neutrons in that atom.

### Mass of a Single Atom Using Avogadro’s Number

Avogadro’s number is the number of particles in a mole of anything. It is exactly 6.02214076 ×1023, but let’s round it to 6.022 x 1023 for easy calculations.

One mole of atoms is Avogadro’s number of atoms, so if you know the mass of one mole, then one calculation gives you the mass of a single atom:

### Mass of a Single Silver Atom

For example, here is how to find the mass of a single silver atom using Avogadro’s number:

1. Look up the atomic mass of silver. It is 107.89 grams per mole (g/mol).
2. Use Avogadro’s number. It is approximately 6.022×1023.
3. Divide the atomic mass by Avogadro’s number. Notice the mole unit cancels out, leaving only atoms and grams.
• mass of silver atom = 107.89 g/mol / 6.022×1023 atoms/mol
• mass of silver atom = 1.792 x 10-22 grams

### Mass of a Single Carbon Atom

Example: Find the mass in grams of a single carbon (C) atom.

From the periodic table, the atomic mass of carbon is 12.01. This is the mass of one mole of carbon atoms.

• mass of single atom = mass of mole of atoms / Avogadro’s number
• mass of carbon atom = 12.01 g/mol / 6.022×1023 atoms/mol
• mass of single carbon atom = 1.994 x 10-23 g

### Finding the Mass of a Single Molecule

The same principle applies when finding the mass of a single molecule. The only difference is that you add up all the atomic masses of the atoms of the elements and then divide that value by Avogadro’s number.

mass of a single molecule = sum of atomic masses of atoms / Avogadro’s number

### Mass of a Single Water Molecule

For example, calculate the mass of a single water molecule. The formula for a water molecule is H2O. So, there are two hydrogen atoms and one water atom in a single molecule.

1. Find the mass of one mole of water molecules. Look up the atomic mass of hydrogen and oxygen. The atomic mass of hydrogen is 1.01 and the atomic mass of oxygen is 16.00.
2. Add up the atomic masses of the elements to find the mass of one mole of water. Since there are two hydrogen atoms and one oxygen atom:
1.01 + 1.01 + 16.00 = 18.02 grams per mole of water
3. Divide the mass of one mole of water by Avogadro’s number for the final answer.
• mass of 1 molecule = mass of one mole of molecules / 6.022 x 1023
• mass of 1 water molecule = 18.02 grams per mole / 6.022 x 1023 molecules per mole
• mass of 1 water molecule = 2.992 x 10-23 grams

Need more practice? Here is how to find the number of atoms and molecules in a single drop of water.

### References

• International Union of Pure and Applied Chemistry (1980). “Atomic Weights of the Elements 1979”. Pure Appl. Chem. 52 (10): 2349–84. doi:10.1351/pac198052102349
• National Institute of Standards and Technology (NIST). “Avogadro’s Constant.” Fundamental Physical Constants.