In chemistry, a **mole** is an SI base unit for quantity. Despite the name, it has nothing to do with the small brown/gray garden pest or the tasty chocolate sauce on Mexican food. The mole unit describes the amount or number of things.

### Mole Definition and Units

**As of the 2019 definition, the mole is exactly 6.022×10^{23}.**

1 mole = 6.022 x 10^{23}.

This number is Avogadro’s number. The mole has no units. It just describes the number of something.

1 mole of atoms = 6.022 x 10^{23} atoms

1 mole of water = 6.022 x 10^{23} water molecules

1 mole of moles = 6.022 x 10^{23} moles.

### Purpose of the Mole

The purpose of the mole is making very large numbers easier to worth with. After all, it is much easier to write 1 mole than 6.022 x 10^{23}. The mole unit is a convenient means to convert between atoms and molecules and mass of those atoms or molecules. Moles are important enough to chemists that they celebrate Mole Day on October 23 (10-23).

### Example Mole Calculations

Here are some example chemistry problems using the mole:

#### Mole Example Problem #1

Find the mass of a single atom.

**Question:** What is the mass of single atom of nitrogen?

**Solution:** The atomic mass of an element is the the mass in grams of one mole of that element. When we look at the periodic table, we see the atomic mass of nitrogen is 14.001 grams/mole.

This means 1 mole of nitrogen atoms has a mass of 14.001 grams.

1 mole of N atoms = 6.022 x 10^{23} N atoms = 14.001 grams.

Divide both sides of the equation by 6.022 x 10^{23} N atoms to get the mass of one nitrogen atom.

1 N atom = 2.325 x 10^{-23} g.

**Answer:** One nitrogen atom has a mass of 2.325 x 10^{-23} grams.

#### Mole Example Problem #2

Find the mass of a known number of molecules.

**Question:** What is the mass in grams of 5 billion water molecules?

**Solution:****Step 1:** Find the mass of one mole of water.

Water is H_{2}O. Therefore, to find the mass of one mole of water, we need to know the mass of hydrogen and the mass of oxygen.

On our periodic table we see the mass of one mole of hydrogen is 1.001 g and the mass of one mole of oxygen is 16.00 g.

One mole of water has 2 moles of hydrogen and 1 mole of oxygen.

Mass of one mole of water = 2 (mass of hydrogen) + 1 mass of oxygen

Mass of one mole of water = 2(1.001 g) + 16.00 g = 18.002 g

**Step 2:** Find the mass of 5 billion (5 x 10^{9}) water molecules.

For this part, we use Avogadro’s number in a ratio.Solve for x grams

x grams = 1.49 x 10^{-13} grams

**Answer:** 5 billion water molecules has a mass of 1.49 x 10^{-13} grams.

#### Example Problem #3

Find the number of molecules in a given mass.

**Question**: How many water molecules in 15 grams of ice?

**Solution:****Step 1:** Find the mass of one mole of water.

We did this step in the second example. One mole of water is 18.002 grams.

**Step 2:** Use Avogadro’s number in a ratio.Solve for x H_{2}O molecules

x H_{2}O molecules = 5.018 x 10^{23} H_{2}O molecules

**Answer:** There are 5.018 x 10^{23} water molecules in 15 grams of ice.

### References

- Andreas, Birk; et al. (2011). “Determination of the Avogadro Constant by Counting the Atoms in a 28Si Crystal”.
*Physical Review Letters*. 106 (3): 30801. doi:10.1103/PhysRevLett.106.030801 - Bureau International des Poids et Mesures (2019).
*The International System of Units (SI)*(9th ed.). - de Bièvre, Paul; Peiser, H. Steffen (1992). “‘Atomic Weight’ — The Name, Its History, Definition, and Units”.
*Pure and Applied Chemistry*. 64 (10): 1535–43. doi:10.1351/pac199264101535 - Himmelblau, David (1996).
*Basic Principles and Calculations in Chemical Engineering*(6 ed.). ISBN 978-0-13-305798-0. - Yunus A. Çengel; Boles, Michael A. (2002).
*Thermodynamics: An Engineering Approach*(8th ed.). TN: McGraw Hill. ISBN 9780073398174.