Percentage by Mass of an Element in a Compound

Introduction

How much iron can be extracted from a tonne of iron ore? Which fertiliser supplies the most nitrogen per bag? Both questions ask what fraction of a compound's mass comes from one element. Because every sample of a compound has the same fixed composition, you can answer them from the formula alone, using relative atomic masses and the relative formula mass. This page shows how to calculate the percentage by mass of an element.

Core explanation

The formula. The percentage by mass of an element in a compound is:

% by mass = (Ar × number of atoms of the element in the formula) ÷ Mr × 100

The top of the fraction is the mass contributed by that element in one formula unit; the bottom is the total mass of the formula unit.

A simple example: water. Mr(H₂O) = 18. Oxygen contributes 1 × 16 = 16. % O = 16 ÷ 18 × 100 = 88.9%. Hydrogen contributes 2 × 1 = 2, so % H = 2 ÷ 18 × 100 = 11.1%. Together they make 100%. Most of the mass of water comes from oxygen, even though there are twice as many hydrogen atoms, because each oxygen atom is sixteen times heavier.

Why it works for any sample. The law of constant composition tells us that a pure compound always contains its elements in the same proportions by mass. Whether you have one drop of water or a swimming pool, 88.9% of the mass is oxygen. So the percentage worked out for one formula unit applies to any amount.

Using percentage composition. Once you know the percentage, you can find the mass of an element in any sample:

mass of element = percentage ÷ 100 × mass of sample

For example, 50 g of water contains 88.9 ÷ 100 × 50 = 44.4 g of oxygen.

Comparing compounds. Percentages allow fair comparisons. Iron forms two common oxides:

Compound Mr % Fe --- --- --- FeO 72 56 ÷ 72 × 100 = 77.8% Fe₂O₃ 160 112 ÷ 160 × 100 = 70.0%

FeO contains a higher proportion of iron by mass, although Fe₂O₃ is the more common ore.

Checking your answer. Work out the percentage of every element and add them. The total should be 100% (or very close, allowing for rounding). This is an excellent way to catch mistakes.

Step-by-step reasoning

To find the percentage of nitrogen in ammonium nitrate, NH₄NO₃:

1. Mr = (2 × 14) + (4 × 1) + (3 × 16) = 80. 2. Mass of nitrogen in the formula = 2 × 14 = 28. 3. % N = 28 ÷ 80 × 100. 4. % N = 35%.

Visual explanation

Draw a bar 100 squares long to represent the mass of carbon dioxide, CO₂ (Mr 44). Shade 27 squares for carbon (12 ÷ 44 ≈ 27%) and the remaining 73 for oxygen. The bar shows at a glance that most of the mass comes from oxygen.

Real-world analogy

A fruit salad weighing 1 kg might contain 300 g of melon. Melon then makes up 30% of the salad by mass. If you make a bigger bowl using the same recipe, melon is still 30%. A compound's formula is a fixed recipe, so its percentage composition never changes.

Real-world example

Fertiliser bags list the percentage of nitrogen they supply. Urea, CO(NH₂)₂, with Mr 60, contains 28 ÷ 60 × 100 ≈ 46.7% nitrogen, while ammonium nitrate contains 35%. That is why urea is popular: it delivers more nitrogen per kilogram transported and spread.

Why?

Why multiply the Ar by the number of atoms? Because every atom of the element contributes to the mass. In Fe₂O₃ there are two iron atoms, so iron contributes 2 × 56 = 112 to the formula mass of 160. Using only one atom would halve the answer.

Common misconception

"The element with the most atoms has the largest percentage by mass." Not necessarily. Water has two hydrogen atoms and one oxygen atom, yet oxygen makes up nearly 89% of its mass. Percentage by mass depends on atomic masses as well as numbers of atoms.

Worked example

Question: Calculate the percentage by mass of calcium in calcium carbonate, CaCO₃.

Reasoning: Mr = 40 + 12 + (3 × 16) = 100. Calcium contributes 40. % Ca = 40 ÷ 100 × 100.

Answer: 40% calcium by mass.

Quick check

1. What is the percentage by mass of carbon in methane, CH₄ (Mr 16)? Answer: 12 ÷ 16 × 100 = 75%.

Exam focus

Examiners expect three clear steps: calculate Mr, find the mass of the element in the formula, then divide and multiply by 100. Remember to multiply Ar by the number of atoms, and give answers to a sensible number of significant figures, usually three.

Advanced insight

The calculation can also be reversed. If an analysis shows the percentage by mass of each element in an unknown compound, chemists divide each percentage by the Ar to find the simplest ratio of atoms — the empirical formula. This is how the compositions of newly discovered substances are worked out.

Summary

The percentage by mass of an element in a compound equals the Ar of the element multiplied by its number of atoms, divided by Mr, multiplied by 100. Because compounds have constant composition, the percentage applies to any sample and can be used to find the mass of an element in it. The percentages of all elements add up to 100.

Practice questions

1. Calculate the percentage by mass of sodium in sodium chloride, NaCl (Mr 58.5). Answer: 23 ÷ 58.5 × 100 = 39.3%. 2. Calculate the percentage by mass of oxygen in carbon dioxide, CO₂. Answer: Mr = 44; oxygen contributes 32; 32 ÷ 44 × 100 = 72.7%. 3. Calculate the percentage by mass of copper in copper(II) oxide, CuO. Answer: Mr = 63.5 + 16 = 79.5; 63.5 ÷ 79.5 × 100 = 79.9%. 4. What mass of calcium is present in 25 g of calcium carbonate? Answer: Calcium is 40% by mass, so 40 ÷ 100 × 25 = 10 g. 5. Which contains the greater percentage of sulfur by mass, SO₂ or SO₃? Answer: SO₂, because 32 ÷ 64 × 100 = 50%, compared with 32 ÷ 80 × 100 = 40% for SO₃.