This is a worked example problem showing how to calculate mass percent composition. Percent composition indicates the relative amounts of each element in a compound. For each element, the mass percent formula is:

**% mass = (mass of element in 1 mole of the compound) / (molar mass of the compound) x 100%**

or

**mass percent = (mass of solute / mass of solution) x 100%**

The units of mass are typically grams. Mass percent is also known as percent by weight or w/w%. The molar mass is the sum of the masses of all the atoms in one mole of the compound. The sum all the mass percentages should add up to 100%. Watch for rounding errors in the last significant figure to make sure all the percentages add up.

### Key Takeaways

- Mass percent composition describes the relative quantities of elements in a chemical compound.
- Mass percent composition is also known percent by weight. It is abbreviated as w/w%.
- For a solution, mass percent equals the mass of an element in one mole of the compound divided by the molar mass of the compound, multiplied by 100%.

## Mass Percent Composition Problem

Bicarbonate of soda (sodium hydrogen carbonate) is used in many commercial preparations. Its formula is NaHCO_{3}. Find the mass percentages (mass %) of Na, H, C, and O in sodium hydrogen carbonate.

**Solution**

First, look up the atomic masses for the elements from the Periodic Table. The atomic masses are found to be:

- Na is 22.99
- H is 1.01
- C is 12.01
- O is 16.00

Next, determine how many grams of each element are present in one mole of NaHCO_{3}:

- 22.99 g (1 mol) of Na
- 1.01 g (1 mol) of H
- 12.01 g (1 mol) of C
- 48.00 g (3 mole x 16.00 gram per mole) of O

The mass of one mole of NaHCO_{3} is:

22.99 g + 1.01 g + 12.01 g + 48.00 g = 84.01 g

And the mass percentages of the elements are

- mass % Na = 22.99 g / 84.01 g x 100 = 27.36 %
- mass % H = 1.01 g / 84.01 g x 100 = 1.20 %
- mass % C = 12.01 g / 84.01 g x 100 = 14.30 %
- mass % O = 48.00 g / 84.01 g x 100 = 57.14 %

**Answer**

- mass % Na = 27.36 %
- mass % H = 1.20 %
- mass % C = 14.30 %
- mass % O = 57.14 %

When doing mass percent calculations, it's always a good idea to check to make sure your mass percents add up to 100% (helps catch math errors):

27.36 + 14.30 + 1.20 + 57.14 = 100.00

## Percent Composition of Water

Another simple example is finding the mass percent composition of the elements in water, H_{2}O.

First, find the molar mass of water by adding up the atomic masses of the elements. Use values from the periodic table:

- H is 1.01 grams per mole
- O is 16.00 grams per mole

Get the molar mass by adding up all the masses of elements in the compound. The subscript after the hydrogen (H) indicates there are two atoms of hydrogen. There is no subscript after oxygen (O), which means only one atom is present.

- molar mass = (2 x 1.01) + 16.00
- molar mass = 18.02

Now, divide the mass of each element by the total mass to get the mass percentages:

mass % H = (2 x 1.01) / 18.02 x 100%

mass % H = 11.19%

mass % O = 16.00 / 18.02

mass % O = 88.81%

The mass percentages of hydrogen and oxygen add up to 100%.

## Mass Percent of Carbon Dioxide

What are the mass percentages of carbon and oxygen in carbon dioxide, CO_{2}?

### Mass Percent Solution

**Step 1:** Find the mass of the individual atoms.

Look up the atomic masses for carbon and oxygen from the Periodic Table. It's a good idea at this point to settle on the number of significant figures you'll be using. The atomic masses are found to be:

- C is 12.01 g/mol
- O is 16.00 g/mol

**Step 2:** Find the number of grams of each component make up one mole of CO_{2.}

One mole of CO_{2} contains 1 mole of carbon atoms and 2 moles of oxygen atoms.

- 12.01 g (1 mol) of C
- 32.00 g (2 mol x 16.00 gram per mole) of O

The mass of one mole of CO_{2} is:

- 12.01 g + 32.00 g = 44.01 g

**Step 3:** Find the mass percent of each atom.

mass % = (mass of component/mass of total) x 100

And the mass percentages of the elements are

For carbon:

- mass % C = (mass of 1 mol of carbon/mass of 1 mol of CO
_{2}) x 100 - mass % C = (12.01 g / 44.01 g) x 100
- mass % C = 27.29 %

For oxygen:

- mass % O = (mass of 1 mol of oxygen/mass of 1 mol of CO
_{2}) x 100 - mass % O = (32.00 g / 44.01 g) x 100
- mass % O = 72.71 %

**Answer**

- mass % C = 27.29 %
- mass % O = 72.71 %

Again, make sure your mass percents add up to 100%. This will help catch any math errors.

- 27.29 + 72.71 = 100.00

The answers add up to 100% which is what was expected.

## Tips for Success Calculating Mass Percent

- You won't always be given the total mass of a mixture or solution. Often, you'll need to add up the masses. This might not be obvious! You may be given mole fractions or moles and then need to convert to a mass unit.
- Watch your significant figures!
- Always make sure the sum of the mass percentages of all components adds up to 100%. If it doesn't, you need to go back and find your mistake.