Calculating Empirical Formulas

The percent composition can be used to calculate the empirical formula, but it will require us to covert between mass and moles, since percent composition is done in grams and formulas are written to represent mole or atom ratios.

Here is a sample problem:

A compound consists of 80% carbon and 20% hydrogen. What is the empirical formula?

 

Our first step is to get rid of the percents. A percent alone is unusable, since it is just a ratio. So, for instance, if 15% of the students taught by your chemistry teacher are left-handed, I still have no idea how many lefties or righties are being taught because I don’t know the total number of students.

To get past that stumbling block in our problem, we make a simple assumption—that we have 100 g of the substance. That way 80% carbon turns into 80g of carbon. We could of course choose any amount but 100g makes the math easy.

So, we can now translate that question into:

A 100 g sample of a compound consists of 80g of carbon and 20g of hydrogen. What is the empirical formula?

Now we’ll convert the grams to moles:

That means that the compound contains 6.66 mols of C for every 19.84 mols of H. This is the correct mole ratio, but it isn’t pretty. To make it a simple ratio, we simply divide both mole amounts by the smallest number (in this case 6.66 moles)

At this point we get to do a little playing with the significant figures. 2.98 is trying very hard to be 3, so the mole ratio is 1C:3H. Therefore the empirical formula is:

CH₃

Let's look at a more complex example.