Percent Composition

Every formula hides a recipe

In 1.5.6 you calculated that urea is 46.7% nitrogen by mass, which matches the “46% N” printed on fertilizer bags. List the mass percent of every element in a compound and you get a recipe by mass. It works the other way too: when chemists analyze an unknown substance, this recipe is often the first thing they measure, and the formula comes from it (next lesson).

The list of mass percents of all the elements in a compound is its percent composition百分组成. With molar masses, calculate the percent of each element X for one mole of the compound:

\%\ \text{X} = \frac{\text{g of X in 1 mol}}{\text{molar mass}} \times 100\%

The mass of an element in 1 mol of compound is its molar mass times its subscript in the formula. This gives the same numbers as 1.5.6’s “atomic mass × number of atoms ÷ formula mass,” now read in g/mol.

The percents add up to 100% (give or take a few hundredths from rounding). You could find the last element by subtracting from 100%, but calculating each one and adding them up is a better check.
Percent composition depends only on the formula, not on the sample size: a drop of water and a lake of water are both 11.19% hydrogen by mass.
Water of hydration can be treated as a single unit. In 2.5.5, CuSO₄·5H₂O turned out to be 36.1% water by mass.

Percent composition from experimental data

If you don’t know the formula, calculate the percent directly from measured masses:

\%\ \text{X} = \frac{\text{g of X}}{\text{g of sample}} \times 100\%

Compare the measured value with the values calculated for each possible formula to identify the compound. Chinese textbooks usually talk about one element at a time (元素的质量分数, “mass fraction of an element”); “percent composition” for the full list is the usual US term.

This lesson uses the atomic masses on the AP periodic table, such as H 1.008, C 12.01, N 14.01, O 16.00, Mg 24.31, Al 26.98, Si 28.09, S 32.06, Cl 35.45, Fe 55.85, and Cu 63.55.

Pick a substance or type a formula to see its percent composition, then compare some nitrogen fertilizers below it:

Try it: percent composition calculator

Compare: which nitrogen fertilizer has the most nitrogen? (% N by mass)

NH₃ammonia82.2%

CO(NH₂)₂urea46.7%

NH₄NO₃ammonium nitrate35.0%

NH₄Clammonium chloride26.2%

(NH₄)₂SO₄ammonium sulfate21.2%

NH₄HCO₃ammonium bicarbonate17.7%

These are values for the pure compounds. Real fertilizer has impurities, so the % N on the bag is a little lower.

Example 1: the percent composition of glucose

Find the percent composition of glucose, C₆H₁₂O₆.

Step-by-step solution

Mass of each element in one mole.
$\begin{aligned} \text{C: } & \ 6(12.01) = 72.06 \\ \text{H: } & \ 12(1.008) = 12.096 \\ \text{O: } & \ 6(16.00) = 96.00 \end{aligned}$
Molar mass: 72.06 + 12.096 + 96.00 = 180.16 g/mol.
Percent of each element. Element’s mass ÷ molar mass × 100%:
$\begin{aligned} \%\,\text{C} &= 72.06 / 180.16 \\ &= \boxed{40.00\%} \\ \%\,\text{H} &= 12.096 / 180.16 \\ &= \boxed{6.714\%} \\ \%\,\text{O} &= 96.00 / 180.16 \\ &= \boxed{53.29\%} \end{aligned}$
Check. 40.00% + 6.714% + 53.29% = 100.00%.
A common mistake. Dividing one atom’s mass (12.01 for carbon) by the molar mass, forgetting to multiply by the number of atoms.

Example 2: which iron oxide is it?

Iron forms three common oxides: black FeO, red-brown Fe₂O₃, and black, magnetic Fe₃O₄. When 3.20 g of one of them is completely reduced with carbon monoxide, 2.24 g of iron remains. Which oxide was it?

Step-by-step solution

The idea. Find the measured percent iron, then compare it with each oxide’s theoretical value.
Measured value.
$\begin{aligned} \%\,\text{Fe} &= \frac{2.24}{3.20} \times 100\% \\ &= 70.0\% \end{aligned}$
Theoretical values.

Oxide M (g/mol) % Fe
FeO 71.85 77.73%
Fe₂O₃ 159.70 69.94%
Fe₃O₄ 231.55 72.36%

For example, Fe₂O₃: 2(55.85) ÷ 159.70 × 100% = 69.94%.
Conclusion. 70.0% matches Fe₂O₃, so the sample was iron(III) oxide, the main component of rust.

Oxide	M (g/mol)	% Fe
FeO	71.85	77.73%
Fe₂O₃	159.70	69.94%
Fe₃O₄	231.55	72.36%

Practice: which value is closest to the mass percent of oxygen in each compound?

H₂O
CO₂
MgO
Fe₂O₃
SiO₂
Al₂O₃
SO₃
C₆H₁₂O₆

Common mistakes

Mistake 1: “Water is two-thirds hydrogen.” Two of the three atoms in a water molecule are hydrogen, so H is 2/3 by number of atoms. But H atoms are light, so H is only 2.016 ÷ 18.02 = 11.19% by mass. Percent composition is always by mass.

Mistake 2: “Al₂O₃ is 26.98 ÷ 101.96 aluminum.” The formula has two Al atoms, so the mass of aluminum is 2 × 26.98 = 53.96 and % Al = 53.96 ÷ 101.96 × 100% = 52.92%. Count every atom first, including subscripts outside parentheses and in water of hydration.

Mistake 3: “A bigger sample has a higher percent of each element.” A bigger sample has more grams of each element, but its total mass grows by the same factor, so the ratio stays the same. Percent composition depends only on the formula.

Quick check

How many grams of copper are in 50.0 g of CuO?

Which compound has the highest mass percent of oxygen?

Summary

Percent composition lists the mass percent of every element: % = mass of the element in 1 mol ÷ molar mass × 100%. The percents add up to about 100%.
From lab data, % = mass of element ÷ mass of sample × 100%. Comparing it with calculated values identifies the compound.
Percent composition is by mass, not by number of atoms, and it doesn’t depend on sample size.

On to AP (for later)

AP Chemistry Unit 1 uses percent composition to tell pure substances from mixtures. A pure substance has a fixed percent composition, while a mixture’s composition changes with the amounts of its parts. AP questions also give elemental analysis data and ask you to find the percent composition and then the empirical formula, which is the next lesson.

Percent Composition百分组成

Learning goals

Before you start

Every formula hides a recipe

Percent composition

Percent composition from experimental data

Example 1: the percent composition of glucose

Example 2: which iron oxide is it?

Common mistakes

Quick check

Summary

Feedback / Report a problem