Moles, Avogadro's Number and Molar Mass
Dr. MJ Patterson

This module provides the first opportunity to use the technique of dimensional analysis to work with a chemical concept.  We will continue to use this approach to solve problems for the entire course.

Review of This Approach:

1. Write the quantity to be converted as a fraction divided by 1.
2. Write the conversion factor as a fraction so that the bottom units cancel with the units on the top of the original number in the previous step.

A mole is a chemical term for a particular number.  This idea of naming numbers is nothing new.  Twelve is called a dozen.  One hundred forty-four is called a gross.  It does not matter what the objects are.  In other words, 12 eggs are a dozen, and 12 doughnuts are a dozen.

A mole is the same idea as a dozen, but the number involved is a lot bigger than 12.  In fact, one mole is equal to 6.02 x 1023 items.  This number is also called Avogadro's Number, and is sometimes abbreviated NA.

In our formalism, we can write a conversion factor:

1 mole items = 6.02 x 1023 items

Memorize this conversion factor!  Avogadro's number should be etched into your permanent long term memory!

For this module, the items we are concerned about are atoms.  We will very quickly move on to include ions, molecules and other chemical entities in this approach.

Example 1:
How many atoms are found in 8.3 moles of potassium?

Solution 1:

1 mole = 6.02 x 1023 atoms

Start by writing the amount to be converted, or 8.3 moles of potassium, as a fraction over 1.  Then, multiply by the conversion factor written as a fraction.  Make sure the bottom of the conversion factor has the units of moles to cancel with the top of the first step.

 (8.3 mol K) (6.02 x 1023 atoms K) = 5.0 x 1024 atoms K (1) (1 mol K)

This same process works for any element, not just K.  The conversion factor does not specify which element, so it is general for all elements!

Example 2:
How many moles are in 9.75 x 1025 atoms of any element?

Solution 2:

1 mole = 6.02 x 1023 atoms

Start by writing the number of atoms over 1.  Then multiply by the conversion factor so that the units cancel.

 (9.75 x 1025 atoms) (1 mol) = 1.62 x 102 moles = 162 moles of any element (1) (6.02 x 1023 atoms)

Molar Mass

The second conversion factor introduced in this module was the molar mass, or how many grams one mole of an element weighs.  The molar mass is found on the periodic table.

Let's find the molar mass of lithium.  First find lithium on the periodic table.  It is in the first column, second row.  Note that there are two numbers with lithium.  The smaller whole number, 3, is the atomic number, or the number of protons in an atom of lithium.  The larger number, 6.94, is the molar mass averaged over all the naturally occurring isotopes.  It is this number that we want to use for the molar mass.

You can write the molar mass as a conversion factor:

1 mole Li = 6.94 g Li

This factor depends on which element we are using!  For carbon or iron, we would use a different value of the molar mass from the periodic table.

Example 3:
How many grams would 2.5 moles of calcium weigh?

Solution 3:
Use the molar mass of calcium.

1 mol Ca = 40.08 g Ca

 (2.5 mol Ca) (40.08 g Ca) = 100 g Ca (1) (1 mol Ca)

Example 4:
How many moles are in 225 g of iron?

Solution 4:
Again, use the molar mass of iron as a conversion factor, making sure units cancel.

 (225 g Fe) (1 mol Fe) = 4.03 mol Fe (1) (55.85 g Fe)

Two-Step Conversions

These two conversion factors can be hooked together to convert between grams and atoms.  First, convert to moles.  Then, convert to the other unit.

Example 5:
How many atoms are in 225 g of Fe?

Solution 5:
This starts just like Example 4.  We finish it by multiplying by the conversion factor 1 mole = 6.02 x 1023 atoms, set up so that moles will cancel.

 (225 g Fe) 1 mol Fe) (6.02 x 1023 atoms Fe) = 2.43 x 1024 atoms Fe (1) (55.85 g Fe) (1 mol Fe)