Avogadro's number is one of the most important constants used in chemistry. It is the number of particles in a single mole of a material, based on the number of atoms in exactly 12 grams of the isotope carbon-12. Although this number is a constant, it contains too many significant figures to work with, so we use a rounded value of 6.022 x 10^{23}. So, you know how many atoms are in a mole. Here's how to use the information to determine the mass of a single atom.

### Key Takeaways: Using Avogadro's Number to Calculate Atomic Mass

- Avogadro's number is the number of particles in one mole of anything. In this context, it is the number of atoms in one mole of an element.
- It's easy to find the mass of a single atom using Avogadro's number. Simply divide the relative atomic mass of the element by Avogadro's number to get the answer in grams.
- The same process works for finding the mass of one molecule. In this case, add up all the atomic masses in the chemical formula and divide by Avogadro's number.

## Avogadro's Number Example Problem: Mass of a Single Atom

**Question:** Calculate the mass in grams of a single carbon (C) atom.

**Solution**

To calculate the mass of a single atom, first look up the atomic mass of carbon from the periodic table. This number, 12.01, is the mass in grams of one mole of carbon. One mole of carbon is 6.022 x 10^{23} atoms of carbon (Avogadro's number). This relation is then used to 'convert' a carbon atom to grams by the ratio:

mass of 1 atom / 1 atom = mass of a mole of atoms / 6.022 x 10^{23} atoms

Plug in the atomic mass of carbon to solve for the mass of 1 atom:

mass of 1 atom = mass of a mole of atoms / 6.022 x 10^{23}

mass of 1 C atom = 12.01 g / 6.022 x 10^{23} C atoms

mass of 1 C atom = 1.994 x 10^{-23} g

**Answer**

The mass of a single carbon atom is 1.994 x 10^{-23} g.

The mass of a single atom is an extremely small number! This is why chemists use Avogadro's number. It makes working with atoms easier because we work with moles rather than individual atoms.

## Applying the Formula to Solve for Other Atoms and Molecules

Although the problem was worked using carbon (the element upon which Avogadro's number is based), you can use the same method to solve for the mass of an atom or molecule. If you're finding the mass of an atom of a different element, just use that element's atomic mass.

If you want to use the relation to solve for the mass of a single molecule, there's an extra step. You need to add up the masses of all of the atoms in that one molecule and use them instead.

Let's say, for example, you want to know the mass of a single atom of water. From the formula (H_{2}O), you know there are two hydrogen atoms and one oxygen atom. You use the periodic table to look up the mass of each atom (H is 1.01 and O is 16.00). Forming a water molecule gives you a mass of:

1.01 + 1.01 + 16.00 = 18.02 grams per mole of water

and you solve with:

mass of 1 molecule = mass of one mole of molecules / 6.022 x 10^{23}

mass of 1 water molecule = 18.02 grams per mole / 6.022 x 10^{23} molecules per mole

mass of 1 water molecule = 2.992 x 10^{-23} grams

## Sources

- Born, Max (1969):
*Atomic Physics*(8th ed.). Dover edition, reprinted by Courier in 2013. ISBN 9780486318585 - Bureau International des Poids et Mesures (2019).
*The International System of Units (SI)*(9th ed.). English version. - 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 - International Union of Pure and Applied Chemistry (1993).
*Quantities, Units and Symbols in Physical Chemistry*(2nd ed.). Oxford: Blackwell Science. ISBN 0-632-03583-8. - National Institute of Standards and Technology (NIST). "Avogadro constant". Fundamental Physical Constants.