Mass Percent Composition

Do you feel like this:             stressed out

when you see this:

Ibuprofen contains:   75.7% carbon
  15.5% oxygen
8.8% hydrogen
The molar mass of the compound is approximately 206 grams per mole.
What is the chemical formula of the compound?

Don't scream. You can do this. Here's how:

The strategy:
1) Get from percentages into units of mass (grams).
2) Use information from the periodic table to convert grams into the number of moles.
3) Do a mole-to-mole comparison so we can get the ratio of carbon to oxygen to hydrogen.
4) Once we have a ratio of each of these, we can determine the formula for the compound.
5) Compare the molar mass of the formula to the given molar mass of the compound. If it's the same, we're done. If it's different, we'll have to adjust things.

Here goes:

1) Get from percentages into mass (grams):

The percentages of carbon, oxygen and hydrogen add up to 100%. (This method will always work. The individual percentages of each component, added together, must equal one-hundred percent!)

So let's assume we have 100 grams of the compound. That way, we'll be able to use the percentages that were given, and it will be easy to determine the number of grams. Here's what I mean:

Using the percentages given: With 100 grams of the compound:
75.5% carbon 75.5 grams carbon
15.5% oxygen 15.5 grams oxygen
8.8% hydrogen 8.8 grams hydrogen
------------------------ ------------------------
100% total 100 grams total

2) Use information from the periodic table to convert grams into the number of moles

Using the periodic table, we can get the following information about the molar masses of carbon, oxygen and hydrogen:

C
carbon
12.01 grams/mole
O
oxygen
16.00 grams/mole
H
hydrogen
1.01 grams/mole
[Note: We're going to use dimensional analysis to convert these numbers. If you don't know what I'm talking about, you might want to visit the Dimensional Analysis Tutorial.] 

Carbon:
                        1 mole carbon
   75.5 grams carbon x ------------------ = 6.29 moles carbon
                        12.01 grams carbon


Oxygen:
                        1 mole oxygen
   15.5 grams oxygen x ------------------ = 0.97 moles oxygen
                        16.00 grams oxygen


Hydrogen:
                        1 mole hydrogen
   8.8 grams hydrogen x ------------------ =  8.71 moles hydrogen
                        1.01 grams hydrogen

3) Do a mole-to-mole comparison so we can get the ratio of carbon to oxygen to hydrogen

Just divide by the smallest number.

In this case, we see that oxygen has the smallest number of moles: 0.97

So divide all the numbers by 0.97: 


Carbon:

   6.29 moles carbon   / 0.97 =  6.5 moles carbon

Oxygen:

   0.97 moles oxygen   / 0.97 =  1.0 moles oxygen

Hydrogen:

   8.71 moles hydrogen / 0.97 =  9.0 moles hydrogen

4) Once we have a ratio of each of these, we can determine the formula for the compound.

Try putting the number of moles as subscripts for each element:
          C6.5H9O1

Hm, if we had whole numbers, everything would be fine. But in this case, that 6.5 moles of oxygen just doesn't look right!

So let's multiply everything by 2, to get rid of that half-mole: 


Carbon:

   6.5 moles carbon  x 2 = 13 moles carbon

Oxygen:

   1.0 moles oxygen  x 2 = 2 moles oxygen

Hydrogen:

   9.0 moles hydrogen x 2 = 18 moles hydrogen
OK, that looks better. Now just use those numbers as your subscripts:
          C13H18O2

5) Compare the molar mass of the formula to the given molar mass of the compound. If it's the same, we're done. If it's different, we'll have to adjust things

Our chemical formula is:
          C13H18O2

Let's determine the molar mass.

[Note: If you're unsure how to calculate molar mass, check out the Moles and Molar Mass Tutorial.] 


Carbon:
                      12.01 grams carbon
   13 moles carbon x  ------------------ = 156 grams carbon
                      1 mole carbon

Hydrogen
                        1.01 grams hydrogen
   18 moles hydrogen x  ------------------- = 18.18 grams hydrogen
                        1 mole hydrogen

Oxygen
                     16.00 grams oxygen
   2 moles oxygen x  ------------------ = 32.00 grams oxygen
                     1 mole oxygen
Add up the masses of carbon, hydrogen and oxygen to get the molar mass of C13H18O2:
         156 + 18.18 + 32.00 = 206.2 grams/mole

Compare this to what was given at the very beginning of the problem:

The molar mass of the compound is approximately 206 grams per mole.

Guess what? We're done!

Yes, this took awhile. The process is long, but if you follow the steps, you'll eventually get to the correct answer:
1) Get from percentages into units of mass (grams).
2) Use information from the periodic table to convert grams into the number of moles.
3) Do a mole-to-mole comparison so we can get the ratio of carbon to oxygen to hydrogen.
4) Once we have a ratio of each of these, we can determine the formula for the compound.
5) Compare the molar mass of the formula to the given molar mass of the compound. If it's the same, we're done. If it's different, we'll have to adjust things.

Do some mass percent composition practice problems

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