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Percentage Composition

Percentage composition by mass: calculate the element contribution, divide by the compound's total relative mass, then multiply by 100.

  • SEC G3 Pure Chemistry 2027
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Learning objectives

  • calculate the percentage mass of an element in a compound when given appropriate information

Percentage composition uses one consistent comparison: mass contributed by the requested element divided by the total formula mass, then multiplied by 100.

1. Definition

Percentage composition (percentage by mass) is the percentage of a compound’s mass that comes from a specific element.

2. Key Ideas

  • Use Aᵣ values to find Mᵣ (see Atomic & Molecular Mass).
  • Percentage by mass:
    • % by mass = (mass contribution)/(total Mᵣ) × 100
  • “Mass contribution” means: (subscript × Aᵣ) for that element.

3. Detailed Explanations

Quick Recall (one method)
  • Find total Mᵣ first.
  • Mass contribution of element X = (subscript of X) × Aᵣ(X).
  • % by mass = (mass contribution)/Mᵣ × 100.

A. The Core Formula (Always the Same)

For an element X in a compound:

% by mass of X = (mass of X in the formula)/(Mᵣ of the compound) × 100

Where:

  • mass of X in the formula = (number of X atoms in the formula) × Aᵣ(X)
The only line you need

“Percentage by mass = (mass contribution ÷ total Mᵣ) × 100.”

CO₂ composition by massBar chart showing percentage by mass for carbon and oxygen in CO₂ (carbon 27.3%, oxygen 72.7%).CO₂ composition by massElementPercentage by mass (%)
Carbon is 27.3% of the mass; oxygen is 72.7% (because there are 2 O atoms).
Data table
ElementCO₂
C27
O73

B. Reading Brackets Before Calculating

If the formula contains brackets, count the requested element across the complete formula before choosing the numerator. For example, (NH₄)₂SO₄ contains two nitrogen atoms and eight hydrogen atoms. The outside 2 multiplies every atom inside NH₄.

4. Common Mistakes

  • Forgetting to multiply by 100 (leaving a decimal instead of a percentage).
  • Using Aᵣ of an element as the total Mᵣ (wrong; you must calculate the compound’s Mᵣ).
  • Not multiplying by subscripts (e.g., using 16 for oxygen in CO₂ instead of 2 × 16).
  • Using the mass of a bracketed group when the question asks for one element only.

5. Exam Tips

Always show the Mr line

Examiners expect to see Mᵣ calculated (or clearly stated) before the percentage step.

Round properly

Keep unrounded values in your calculator and round only the final answer to a precision justified by the data or specified by the question. Always include the % sign.

6. Worked Examples

Modelled example 1

Element in a Simple Compound (CO2)

Core

Problem

Find the percentage by mass of carbon in carbon dioxide, CO₂. Given Aᵣ(C) = 12, Aᵣ(O) = 16.
Study the worked solution

  1. Calculate the whole formula mass

    Method

    Add the mass contributions from one carbon and two oxygen atoms.

    Reason

    The denominator must represent the complete CO₂ formula.

    Working

    Mᵣ(CO₂) = 12 + 2(16) = 44.

  2. Identify the carbon contribution

    Method

    Use 12 as the mass due to carbon.

    Reason

    Each formula contains one carbon atom.

    Working

    Carbon contribution = 1(12) = 12.

  3. Convert the fraction to a percentage

    Method

    Divide the carbon contribution by the whole and multiply by 100.

    Reason

    Percentage by mass is part mass divided by total mass.

    Working

    %C = (12/44) × 100 = 27.3%.

Guided practice 2

Element in a Bracketed Formula ((NH4)2SO4)

About 7 min

Problem

Find the percentage by mass of nitrogen in ammonium sulfate, (NH₄)₂SO₄. Given Aᵣ(N) = 14, Aᵣ(H) = 1, Aᵣ(S) = 32, Aᵣ(O) = 16.

Apply the bracket multiplier

Hints

Hint 1: expand the bracket
The outer 2 multiplies both N and H: N₂H₈.
Hint 2: form part over whole
Use nitrogen mass 28 over total formula mass 132, then multiply by 100.
View solution step by step

  1. Expand and calculate formula mass

    Method

    Apply the outer 2 to N and H before adding all contributions.

    Reason

    The bracket means two complete NH₄ groups.

    Working

    Mᵣ = 2(14) + 8(1) + 32 + 4(16) = 132.

  2. Find nitrogen mass

    Method

    Multiply two nitrogen atoms by Aᵣ(N).

    Reason

    Only the nitrogen contribution belongs in the numerator.

    Working

    Mass of N = 2(14) = 28.

  3. Calculate percentage

    Method

    Divide part by whole and multiply by 100.

    Reason

    This converts the nitrogen mass fraction into a percentage.

    Working

    %N = (28/132) × 100 = 21.2%.

Common misconception 3

Error Analysis (Fix the Setup)

Find and correct the mistake

Learner response

A student writes %O in CO₂ = (16/44) × 100. Explain what is wrong and correct it.

Locate the first incorrect quantity

Error

View solution step by step

  1. Locate the missing multiplier

    Method

    Replace 16 with 2(16) in the numerator.

    Reason

    The formula CO₂ contains two oxygen atoms.

    Working

    Oxygen contribution = 2(16) = 32.

  2. Correct the percentage

    Method

    Use the full oxygen contribution over the unchanged total mass.

    Reason

    Mᵣ(CO₂) = 44 was already correct.

    Working

    %O = (32/44) × 100 = 72.7%.

Examiner practice 4

Compare Two Fertilisers (Nitrogen %)

6 marks

Examination question

Which fertiliser is richer in nitrogen by mass: ammonium nitrate, NH₄NO₃, or urea, CO(NH₂)₂? Given Aᵣ(N) = 14, Aᵣ(H) = 1, Aᵣ(C) = 12, Aᵣ(O) = 16. [6 marks]

Calculate both percentages before comparing

View solution step by step

  1. Calculate ammonium nitrate formula mass

    1 mark

    Method

    Sum all atom contributions in NH₄NO₃.

    Reason

    The complete formula mass is the denominator for nitrogen percentage.

    Working

    Mᵣ(NH₄NO₃) = 14 + 4(1) + 14 + 3(16) = 80.

  2. Calculate ammonium nitrate nitrogen percentage

    1 mark

    Method

    Use the mass of both nitrogen atoms over formula mass.

    Reason

    NH₄NO₃ contains two nitrogen atoms in total.

    Working

    %N = [2(14)/80] × 100 = 35.0%.

  3. Calculate urea formula mass

    1 mark

    Method

    Apply the outer 2 to the complete NH₂ group.

    Reason

    The bracket multiplier counts two nitrogen atoms and four hydrogen atoms.

    Working

    Mᵣ(CO(NH₂)₂) = 12 + 16 + 2[14 + 2(1)] = 60.

  4. Calculate urea nitrogen percentage

    1 mark

    Method

    Divide the two-nitrogen contribution by 60.

    Reason

    Percentage compares nitrogen mass with the whole urea formula mass.

    Working

    %N = [2(14)/60] × 100 = 46.7%.

  5. Compare like quantities

    2 marks

    Method

    Compare the two nitrogen percentages and name the richer fertiliser.

    Reason

    Both values describe nitrogen mass per 100 g, so they are directly comparable.

    Working

    46.7% > 35.0%, so urea is richer in nitrogen by mass.

Challenge 5

Element percentage in an unfamiliar formula

Minimal support

Formula transfer

An oxide has formula X₂O₃, where Aᵣ(X) = 27. Calculate the percentage by mass of oxygen. Use Aᵣ(O) = 16.

Find part and whole from the formula

Hints

Hint 1: calculate the whole
Use two X atoms and three oxygen atoms in the denominator.
Hint 2: calculate the requested part
Only the three oxygen atoms belong in the numerator.
View solution step by step

  1. Calculate the whole formula mass

    Method

    Add the two X and three O contributions.

    Reason

    The denominator represents the complete X₂O₃ formula.

    Working

    Relative formula mass = 2(27) + 3(16) = 102.

  2. Calculate oxygen percentage

    Method

    Divide the oxygen contribution by the whole and multiply by 100.

    Reason

    Three oxygen atoms contribute 3(16) = 48.

    Working

    %O = (48/102) × 100 = 47.1%.

7. Mind Stretchers

Mind stretcher 1: “% of Elements Must Add to 100” CheckExtension

Question: A compound has 40.0% carbon and 6.67% hydrogen by mass. What percentage is oxygen? Explain why your method is valid.

Show Answer

Percentages of all elements in a pure compound must add to 100%.

%O = 100 - 40.0 - 6.67; = 53.33%

Mind stretcher 2: Work Back From % (Data Interpretation)Extension

Question: A fertiliser contains 21.2% nitrogen by mass. Which is more consistent: NH₄NO₃ or (NH₄)₂SO₄? Show one calculation.

Show Answer

(NH₄)₂SO₄ has:

Mᵣ = 132; Mass of N = 28; %N = 28/132 × 100 = 21.2%

So 21.2% matches (NH₄)₂SO₄, not NH₄NO₃.

8. Quiz

Quiz time

Ready to check your understanding? Try the interactive quiz, then review any questions you missed.

Go to quiz