The mole is

• a unit of measurement;
• also called Avogadro’s number; and
• represents 6.02 × 1023 things.

These things can be items such as Source: Oxygen, Water Molecule, Sodium Chloride, Wikimedia Commons

When converting between particles and moles, you will use the equality 1 mole = 6.02 x 1023 particles. This number is given in the section titled Constants and Conversions on the Chemistry STAAR reference material. Source: STAAR Reference Material, Texas Education Agency

This equality can be written as a set of two conversion factors. They are as follows:

1 mole over 6.02 × 1023 particles 1 mole 6.02 × 1023 particles     or     6.02 × 1023 particles over 1 mole 6.02 × 1023 particles 1 mole

Remember that the words ions, atoms, molecules, or formula units can be substituted in place of the word particles.

Let’s practice a few mole-particle conversions. You will use the steps for dimensional analysis to help solve these problems.

1. Write the given information as a fraction by placing it over 1. (Placing it over 1 makes it a fraction but does not change its value.)
2. Write a conversion factor that has the unit you want to remove in the denominator and the unit you want to end up with in the numerator. After you fill in your units, add the numbers. (Usually one of the numbers is a 1, but it can be in either the denominator or the numerator.) Note: In some cases you may need to repeat this step a number of times in order to get the unit you want to end up with in the numerator.
3. Mark through the units to double check that they all cancel and that you are left with the units you want.
4. Multiply the numbers in the numerators, and then multiply the numbers in the denominators.

### Practice Problem 1

How many moles of magnesium are in 3.01 x 1022 atoms of magnesium?

### Practice Problem 2

How many molecules are there in 4.00 moles of glucose, C6H12O6?

Now You Try!

### Practice Problem 3

How many molecules are found in 3.2 moles of CH4?

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