Mole Conversions

Moles are a counting unit that make it easier for chemists to work with large numbers.

Just as we say that one dozen eggs is equal to twelve eggs, we can say that one mole of atoms is equal to 6.02 times ten to the 23rd atoms.

6.02 times ten to the 23rd is called Avogadro’s number.

An essential skill in chemistry is being able to convert between mass, moles, and number of atoms.

Suppose we start with two moles of helium, and we want to figure out how many grams of helium we have.

To convert between grams and moles, we need to use the molar mass.

The molar mass is the mass of one mole of an element and is found on the periodic table.

If we look this number up for helium, we find that helium has a molar mass of 4.0 grams per mole.

So one mole of helium has a mass of 4.0 grams.

We can use the molar mass as a conversion factor.

Two moles of helium times four grams of helium per mole of helium is equal to eight grams of helium.

Notice how “moles of helium” cancels out.

Let’s consider a related problem, in which we are given 8.0 grams of helium and we want to calculate the number of moles of helium.

For this problem, we want to divide by the molar mass.

So 8.0 grams of helium divided by 4.0 grams per mole gives us 2.0 moles of helium.

Notice how the grams cancel out to give us moles as our unit.

We can also do this problem by multiplying by one over the molar mass which gives us 8.0 grams of helium times one mole of helium per 4.0 grams of helium.

Once again, grams cancel out to give moles.

So the answer is 2.0 moles of helium.

So to recap, to convert moles to grams, we multiplied by the molar mass.

To convert grams to moles, we divided by the molar mass.

Here’s a table to help us keep track of how to do the different conversions.

We can also use the number of moles to calculate the number of atoms that are present.

For example, let's say we have 0.500 moles of silver, and we want to know how many atoms of silver we have.

Once again, we need a conversion factor.

From Avogadro’s number, we know that one mole of silver atoms is equal to 6.02 times 10 to the 23rd silver atoms.

So if we multiply 0.500 moles of silver by the conversion factor of 6.02 times 10 to the 23rd atoms of silver per one mole of silver, mols of silver cancel, and we get 3.01 times 10 to the 23rd atoms of silver.

Now let’s consider a related problem: we start with a known number of atoms, and we want to find out how many moles we have.

For example, let’s say we start out with 3.01 x 1023 atoms of silver.

This time we need to divide by Avogadro’s number.

3.01 x 1023 atoms of silver divided by 6.02 x 1023 atoms of silver per mole of silver gives 0.500 moles of silver.

Notice how the atoms of silver cancel out to give moles of silver as our units.

So, to convert moles to atoms, we multiply by Avogadro’s number.