How to Calculate Mass Percent Composition

Below 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 of all the mass percentages should add up to 100%. When working through problems, watch for rounding errors in the last significant figure to make sure all the percentages add up.

Mass Percent Composition Problem

Bicarbonate of soda (sodium hydrogen carbonate) is used in many commercial preparations. Its formula is NaHCO₃. Find the mass percentages (mass %) of Na, H, C, and O in sodium hydrogen carbonate.

Solution

Step 1: First, look up the atomic masses of the elements on the Periodic Table. You will see that the atomic masses are:

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

Step 2: Next, determine how many grams of each element are present in one mole of NaHCO₃:

• 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 NaHCO₃ is:

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

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 is always a good idea 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 problem is finding the mass percent composition of the elements in water, H₂O.

Step 1: First, get 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

Step 2: Calculate 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

Step 3: 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, CO₂?

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 CO₂ 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 CO₂ 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

The mass percentages of the elements are:

For carbon:

• mass % C = (mass of 1 mol of carbon/mass of 1 mol of CO₂) 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 CO₂) 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 percentages add up to 100%. This will help catch any math errors.

• 27.29 + 72.71 = 100.00

The answers add up to 100%, which was expected.

Tips for Success Calculating Mass Percent

• You will not always be given the total mass of a mixture or solution. Often, you will need to add up the masses. This might not be obvious. You may be given mole fractions or moles and then need to convert them 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 does not, you need to go back and find your mistake.