Mass Percent Composition

Practice Problem #1:
Caffeine contains:   49.5% carbon
  5.2% hydrogen
28.8% nitrogen
16.5% oxygen
The molar mass of caffeine is approximately 194 grams per mole.
a) What is the empirical (simplest) formula of the caffeine?

b) What is the chemical formula of caffeine?

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.

1) Get from percentages into units of mass (grams)

Using the percentages given: With 100 grams of the compound:
49.5% carbon 49.5 grams carbon
5.2% hydrogen 5.2 grams hydrogen
28.8% nitrogen 28.8 grams nitrogen
16.5% oxygen 16.5 grams oxygen
------------------------ ------------------------
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, hydrogen, nitrogen and oxygen:

C
carbon
12.01 grams/mole
H
hydrogen
1.01 grams/mole
N
nitrogen
14.01 grams/mole
O
oxygen
16.00 grams/mole		 

Carbon:
                        1 mole carbon
   49.5 grams carbon x ------------------ = 4.12 moles carbon
                        12.01 grams carbon


Hydrogen:
                        1 mole hydrogen
   5.2 grams hydrogen x ------------------ =  5.15 moles hydrogen
                        1.01 grams hydrogen

Nitrogen:
                        1 mole nitrogen
   28.8 grams oxygen x ------------------ =  2.06 moles nitrogen
                        14.01 grams nitrogen

Oxygen:
                        1 mole oxygen
   16.5 grams oxygen x ------------------ = 1.03 moles oxygen
                        16.00 grams oxygen

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: 1.03

So divide all the numbers by 1.03: 


Carbon:

   4.12 moles carbon   / 1.03 =  4.0 moles carbon

Hydrogen:

   5.15 moles hydrogen / 1.03 =  5.0 moles hydrogen

Nitrogen:

   2.06 moles nitrogen   / 1.03 =  2.0 moles nitrogen

Oxygen:

   1.03 moles oxygen   / 1.03 =  1.0 moles oxygen

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:
          C4H5N2O

We have no "halves" of moles, so that formula is fine.

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
   4 moles carbon x  ------------------ =  48.04 grams carbon
                      1 mole carbon

Hydrogen
                        1.01 grams hydrogen
   5 moles hydrogen x  ------------------- = 5.05 grams hydrogen
                        1 mole hydrogen

Nitrogen
                        14.01 grams hydrogen
   2 moles hydrogen x  ------------------- = 28.02 grams nitrogen
                        1 mole nitrogen

Oxygen
                    16.00 grams oxygen
   1 mole oxygen x  ------------------ = 16.00 grams oxygen
                    1 mole oxygen
Add up the masses of carbon, hydrogen and oxygen to get the molar mass of C4H5N2O:
         48.04 + 5.05 + 28.02 + 16.00 = 97.11 grams/mole

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

The molar mass of caffeine is approximately 194 grams per mole.

Whoops! We have a compound with a mass of 97.11 grams/mole.

This means that C4H5N2O is the empirical formula of the compound.

empirical formula = simplest formula

Let's divide the molar mass of caffeine by the molar mass of C4H5N2O:
          194 grams caffeine / 97.11 grams C4H5N2O = 2.0

OK, so we know that the molar mass of caffeine is TWICE as much as the molar mass of C4H5N2O.

Multiply all those subscripts by 2:
C8H10N4O2

The molar mass of C8H10N4O2 is 194.22 grams/mole. That's pretty close to the number specified by the problem.

So here are our answers:

a) What is the empirical (simplest) formula of the compound?
The empirical (simplest) formula is:

      C4H5N2O

b) What is the chemical formula of caffeine?
The chemical formula of caffeine is:

      C8H10N4O2

Back to Mass Percent Composition Tutorial Page

Back to Chemistry Tutorials Home Page

1