Percent Composition

Suppose you have twelve eggs in a basket and want to know what percentage of them are brown. The basket contains 4 brown eggs, so you would need to divide the number of brown eggs by the total number of eggs, times one hundred. This would tell you that 33% of the eggs are brown.

Similarly, when dealing with chemical compounds, we can calculate the percent composition of elements that are part of a compound! So, let's explore the world of percent composition.

• First, we will talk about the definition of percent composition.
• Then, we will look at the formula to calculate percent composition.
• After, we will look at the percent compositions of water (H₂O) and sodium chloride (NaCl).
• Then, we will explore percent composition by mass.
• Lastly, we will learn how to use a compound's percent composition to find the empirical formula.

Percent Composition Definition

First, let's look at the definition of percent composition.

Percent composition is considered an extensive property, meaning that it is independent of sample size. For instance, if you have a truckload of table salt (NaCl), or a tiny amount of it, the percent composition of NaCl will always be the same!

Figure 1 shows the percent composition of iron (III) oxide (Fe₂O₃) and iron (II) oxide (FeO). Fe₂O₃ is composed of 69.9% iron and 30.1% oxygen, whereas FeO is made up of 77.7% iron and 22.3 % oxygen.

Percent Composition Formula

Knowing how to calculate percent composition is extremely important for chemists because it helps them figure out which compounds are the best sources of an element!

To find the percent composition of an element, we can use the formula below.

$$ {}\text{% Composition of element in compound} = \frac{n\text{ } \times \text{ molar mass of element in sample of compound}}{\text{ molar mass of sample of compound}} \times 100\text{%} $$

where,

• \( n \) is the number of atoms of the element in 1 mol of the compound.
• The molar mass is the mass in grams of one mole of the element or compound.

Percent Composition of Water

Now that we know what percent composition is, and the formula used to calculate it, let's look at the percent composition of hydrogen (H) and oxygen (O) in water (\( H_{2}O \)).

First, we need to calculate the molar mass of water. Based on the Periodic Table, there are 1.0079 grams of hydrogen in one mole, and 16.00 grams of oxygen per mole of oxygen. So, the molar mass of water would be:

$$ \text{1 mol of } H_{2}O = 2\text{ } (\text{ 1.0079 g/mol }) + (\text{ 16.00 g/mol }) = 18.0158 \text{ g/mol} $$

Now, let's calculate the percent composition of oxygen (O).

$$ \text{% Composition of Oxygen (O)} = \frac{1\text{ } \times \text{ 16.00 g/mol O}}{\text{ 18.0158 g/mol}} \times 100\text{%} = \color {orchid} 88.81\text{ % O} $$

Lastly, we do the same for hydrogen. Notice that in 1 mol of water, there are 2 atoms of H, so n will be equal to 2.

$$ \text{% Composition of Hydrogen (H)} = \frac{2\text{ } \times \text{ 1.0079 g/mol H}}{\text{ 18.0158 g/mol}} \times 100\text{%} = \color {orchid} 11.19\text{ % H} $$

Percent Composition of NaCl

The percent composition of NaCl can be calculated in the same way we did for water. Always start by calculating the molar mass of the compound (unless it has already been given to you).

In the case of NaCl, we molar mass is:

$$ \text{1 mol of NaCl = 1 mol of Na + 1 mol of Cl} $$

$$ \text{1 mol of NaCl = 1 (22.990 g/mol) + 1 (35.45 g/mol) = 58.44 g/mol NaCl} $$

Now, we can calculate the percent composition of sodium (Na) and Chlorine (Cl).

$$ \text{% Composition of Sodium(Na)} = \frac{1\text{ } \times \text{ 22.990 g/mol O}}{\text{ 58.44 g/mol}} \times 100\text{%} = \color {orchid} 39.34\text{ % Na} $$

$$ \text{% Composition of Chlorine (Cl)} = \frac{1\text{ } \times \text{ 35.45 g/mol O}}{\text{ 58.44 g/mol}} \times 100\text{%} = \color {orchid} 60.66 \text{ % Cl} $$

Percent Composition by Mass

Percent composition can also be calculated using the mass of the element and compound using the following formula:

$$ {}\text{% Composition by mass} = \frac{\text{ } \text{ mass of element}}{\text{ mass of compound}} \times 100\text{%} $$

As an example, let's solve a problem!

Percent Composition of a Compound

Dealing with percent composition is basically dealing with calculations to find the percentage of each element in a compound. However, percent composition can also be used to determine the empirical formula of a compound when experimentally measured percent composition values are available.

For example, let's say that you have 100 grams of a certain compound that is 80.0% Carbon (C) and 20% hydrogen (H) by mass. How can we use this information to find out the compound's empirical formula?

If we have 100 g of this compound and 80% of its mass is attributed to carbon, then we can say that we have 80 grams of carbon (C). Similarly, 20% of hydrogen in its composition would mean 20 grams of hydrogen (H).

Now, we need to figure out a mole-to-mole ratio by converting grams to moles.

• \( \text{moles of C = 80 g C }\times \frac{\text{1 mol C}}{\text{12.011 g C}} = 6.67 \text{ moles of C} \)
• \( \text{moles of C = 20 g H }\times \frac{\text{1 mol C}}{\text{1.008 g C}} = 20 \text{ moles of H} \)

$$ \text{C}_{6.67}\text{ H}_{20} $$

Notice that the moles did not all come out as integers. So, when this happens, we need to divide both numbers by a common factor, or the lowest number which is 6.67 in this case.

$$C: \frac{6.67}{6.67}$$

$$ H: \frac{20}{6.67} $$

This would give us the empirical formula of the compound:

$$ \text{C}_{1}\text{ H}_{3} \text{ or } \color{Orchid} \text{C}\text{H}_{3} $$

Percent Composition of the Earth

Let's finish off by looking at the Earth's composition. The major constituents of the Earth's atmosphere are 78.084% Nitrogen (N₂), and 20.948% oxygen (O₂). The remaining percentage composition by volume of the atmosphere include various other gases such as water vapor, argon, carbon dioxide, neon, helium, methane, xenon, etc.

The Earth's core is composed of 88.8% iron, 5.8% nickel, and 0.27% cobalt, while its mantle primarily consists of 47.9% silicon dioxide, 34.1% magnesium oxide and 8.9% iron (II) oxide.

Now, I hope that you feel more confident in your understanding of percent composition!