Most compounds are made up of different kinds of atoms. For instance, water is made of of
hydrogen atoms and oxygen atoms. One water molecule, H2O, is made up of 3 atoms: 1 oxygen
atom and 2 hydrogen atoms. But would we say that water is ⅓ oxygen and ⅔ hydrogen?
No, not if we’re talking about % composition by mass. That’s because hydrogen and oxygen
atoms weigh different amounts - they have different gram atomic masses, as you can see
from the periodic table.
the Percent composition of a compound is the percent of the total mass of the compound
that is due to each component. The atoms of each element weigh
different amounts, so we need to look at the periodic table to find the percent composition
by mass. We’ll calculate the mass of a mole of the compound, as well as the mass due to
each element in the compound. If you add up the % compositions for all the elements in
a compound, it should sum to 100%. Let’s do this for water.
First, we find the molar mass of water from the periodic table by summing up the gram
atomic masses from each element. 2x (1.008 g/mol) (that’s the hydrogens) + 1x (15.999
g/mol) (that’s the oxygen) = 18.015 g/mol. Now what percent of the total molar mass of
water is due to hydrogen? The hydrogen % composition is the mass due to hydrogen divided by the
total molar mass, times 100%. In each water molecule, there are 2 atoms of hydrogen. So
the total mass of hydrogen in a mole of water is 2(1.008) = 2.016 grams. What percent of
the total molar mass of water is that? Divide it by the molar mass of water, and multiply
by 100%. 2.016/18.015 x 100% = 11.19%.
The rest of the mass must be due to oxygen, right? 100% - 11.19% = 88.81% of the mass
of water is due to oxygen. But let’s check, just to make sure. There is one atom of oxygen
in each water molecule, so that is 1 x 15.999 = 15.999 grams of oxygen in each mole of water.
To find the % of water’s molar mass due to oxygen, we’ll divide that by the total
molar mass and multiply by 100%. 15.999/18.015 x 100% = 88.81%, on the nose. The percentages
DO add up to 100% (11.19 + 88.81 = 100%), so we didn’t mess up anywhere.
For a more complicated example, let’s look at GLUCOSE. We usually think of glucose as
a single thing - it’s one sugar, a monosaccharide - and it is ONE molecule. But it’s made
up of three kinds of atoms: carbon, hydrogen, and oxygen. Its formula is C6H12O6. So one
molecule of glucose has 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen.
What is the % composition by mass of glucose? That is to say, what % of its mass is from
carbon, what % of its mass is hydrogen, and what % of its mass is oxygen?
Step 1: To find the molar mass of glucose, C6H12O6,
sum up the gram atomic masses of the individual atoms. Again, we get that from the Periodic
Table. There are 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen, so, the
molar mass of glucose equals: (6 x 12.011 g/mol) + (12 x 1.008 g/mol) +
(6 x 15.999 g/mol ) = 180.156 g/mol.
Step 2: Find the % Mass of each element in Glucose
We will take the mass of each element in 1 mole of glucose, divide it by the molar mass
of glucose, then multiply by 100%.
First, % mass from carbon: The mass of Carbon in 1 mole of glucose divided
by the molar mass of glucose (the mass of 1 mole of glucose) times 100% is
6(12.011)g / 180.156g x 100%. = 72.066g/ 180.156g x 100%
= 0.400 x 100% = 40.0% So Glucose is 40% carbon, by mass.
Next, the % mass from hydrogen The mass of Hydrogen in 1 mole of glucose
divided by the molar mass of glucose times 100% is
12(1.008) g / 180.156g x 100% = 12.096g/180.156g x 100%
= 0.067 x 100% = 6.7% Glucose is 6.7% hydrogen, by mass.
And finally, the % mass from oxygen: The mass of oxygen in 1 mole of glucose divided
by the molar mass of glucose, times 100% is 6(15.999)g / 180.156g x 100%
= 95.994g /180.156g x 100% = 0.533 x 100%
= 53.3% Glucose is 53.3% oxygen, by mass.
Let’s check to make sure these three % compositions add to 100%:
40% + 6.7% + 53.3% = 100%.