Source: Oxygen, Water Molecule, Sodium Chloride, Wikimedia Commons

When converting between particles and moles, you will use the equality 1 mole = 6.02 x 10^{23} particles. This number is given in the section titled Constants and Conversions on the Chemistry STAAR reference material.

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

1 mole over 6.02 × 10^{23} particles1 mole6.02 × 10^{23} particles or
6.02 × 10^{23} particles over 1 mole6.02 × 10^{23} 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.

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.)

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.

Mark through the units to double check that they all cancel and that you are left with the units you want.

Multiply the numbers in the numerators, and then multiply the numbers in the denominators.

Divide the numerator by the denominator. Be sure to add your units to your final answer.

Practice Problem 1

How many moles of magnesium are in 3.01 x 10^{22} atoms of magnesium?

Practice Problem 2

How many molecules are there in 4.00 moles of glucose, C_{6}H_{12}O_{6}?

Now You Try!

Practice Problem 3

How many molecules are found in 3.2 moles of CH_{4}?