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D2.2 · Determine percent composition through inquiry

Learn to determine percent composition through inquiry through clear examples and targeted practice.

Ontario Grade 11 Chemistry

Quantities in Chemical Reactions

SCH3U D2.2 — Determine percent composition through inquiry

A pure compound has a consistent composition. A larger sample has more particles, but the particles contain the same elements in the same ratio. Percent composition describes what percentage of the compound’s mass comes from each element. You can investigate it using composition evidence, such as supplied measurements of the masses of elements in a sample. You can also compare that evidence with a value calculated from the compound’s formula. Keep observed or supplied evidence separate from calculated values.

What you will learn

Explain what percent composition tells you about a compound.
Use chemical formulas and atomic masses to calculate the percent by mass of each element.
Use supplied or collected composition evidence to determine and evaluate percent composition.
Check whether results are reasonable and whether percentages add to about 100%.

1. Bridge: atoms, formulas, and mass

A chemical formula shows which elements are in a substance and how many atoms of each are represented. In water, the formula is

\mathrm{H_2O}

. The small number 2 is a subscript. It means that two hydrogen atoms are represented for each oxygen atom. Oxygen has no written subscript, so its count is one.

Each element has an atomic mass listed on the periodic table. Atomic mass is the average mass assigned to an atom of that element. A formula lets you add the atomic masses represented by its atoms. This gives the formula mass.

Percent means “out of 100.” Percent composition by mass is the share of a compound’s total mass that comes from one element. It is not the share of the atoms. An element with fewer atoms can contribute a large share of the mass if its atoms are heavier.

For a formula-based calculation, multiply each element’s atomic mass by its atom count. Add the element contributions to find the total formula mass. Divide each contribution by the total and multiply by 100%. Use the same mass units in the numerator and denominator.

\%\text{ by mass}=\frac{m_{\text{element}}}{m_{\text{total}}}\times100\%

A subscript gives an atom count, not a percentage.
Formula mass is the sum of the atomic masses represented in a formula.
Percent composition by mass compares an element’s mass contribution with the total mass.

2. Inquiry: use composition evidence

An inquiry question should be answerable with evidence. For example: “What percentage of this sample’s mass is element A, and what percentage is element B?” To answer it, you need the mass of each element in the sample and the total sample mass. The evidence might be measurements collected during an investigation or a data set supplied for analysis.

Before calculating, identify exactly what the evidence represents. Record the measured or supplied mass for each element and the total sample mass. Check that all masses use the same units. If the total mass is not given, add the element masses, but do this only when the evidence accounts for all elements in the sample.

For each element, divide its mass by the total sample mass and multiply by 100%. This gives the evidence-based percent composition. Keep the measured values unchanged in your record. Do not adjust them to make the percentages total 100%.

Then check the result. The percentages should be positive and should add to about 100% if the evidence includes all elements. A difference from 100% may come from rounding or from incomplete or imprecise evidence. State what the evidence supports. Do not claim that a sample has a particular formula unless the evidence establishes that identity.

\%\text{ element by mass}=\frac{m_{\text{element}}}{m_{\text{sample}}}\times100\%

Use actual collected measurements or data that have been supplied.
Keep the mass units consistent and identify what the total includes.
Calculate each element’s share from its mass and the total sample mass.
Report discrepancies honestly; do not alter evidence to force a result.

3. Compare evidence with a formula-based value

When a sample’s formula is known, you can calculate the percent composition expected from that formula. Use the atomic masses provided on the course periodic table. Count each atom, find each element’s mass contribution, add the contributions, and calculate the percentages.

A comparison can help you judge whether the composition evidence is consistent with the stated formula. Put the evidence-based percentage beside the formula-based percentage for each element. Describe whether they are close or differ. A difference does not by itself prove why the values disagree.

Use suitable precision. Keep extra digits during intermediate calculations and round the final percentages to match the precision of the measurements or atomic masses used. Units cancel when a mass is divided by a mass in the same units. Check that the percentages add to about 100%; a small difference can result from rounding.

\%\text{ element} = \frac{nA}{M}\times100\%

A formula-based result and a measurement-based result come from different evidence.
Compare values without changing the supplied or measured data.
Round final results appropriately and check their total.

Worked example

Determine composition from supplied evidence

A data set for a 10.00 g sample of a two-element compound reports 2.70 g of element X and 7.30 g of element Y. Determine the percent composition by mass from the supplied evidence, then compare the result with a formula-based value of 27.0% X and 73.0% Y.

Identify the evidence
The supplied masses are 2.70 g of X and 7.30 g of Y. Their sum is 10.00 g, matching the stated sample mass, so the data account for the full sample.
$2.70\,\mathrm{g}+7.30\,\mathrm{g}=10.00\,\mathrm{g}$
Calculate the share of X
Divide the mass of X by the total sample mass. The gram units cancel, leaving a fraction of the sample’s mass. Multiply by 100% to express it as a percentage.
$\%X=\frac{2.70\,\mathrm{g}}{10.00\,\mathrm{g}}\times100\%=27.0\%$
Calculate the share of Y
Use the same total sample mass for Y. The supplied masses have three significant figures, so report the percentage to three significant figures.
$\%Y=\frac{7.30\,\mathrm{g}}{10.00\,\mathrm{g}}\times100\%=73.0\%$
Compare and check
The evidence-based percentages match the stated formula-based values. Their total is 100.0%, which is consistent with a data set that accounts for the whole sample.
$27.0\%+73.0\%=100.0\%$

Answer: The supplied evidence gives 27.0% X and 73.0% Y by mass. These values match the formula-based comparison values.

Check: The element masses add to the sample mass, and the percentages add to 100.0%. Both checks support the calculation.

Common mistakes and how to avoid them

Treating a subscript as a percentage or as a percent of the atoms.

Correction: A subscript gives an atom count. Percent composition compares mass contributions with total mass.

Dividing an element’s mass by the wrong total.

Correction: Use the total mass of the sample represented by the evidence, including all elements.

Changing measurements so the percentages add to 100%.

Correction: Keep the evidence unchanged. Report a difference and consider whether rounding or incomplete evidence could explain it.

Treating a planned measurement as if it had already been collected.

Correction: Label a proposed measurement as a plan. Use only data that were actually collected or supplied as evidence.

Assuming that matching percentages prove a formula.

Correction: State only what the comparison supports. Percent composition evidence alone does not necessarily establish a compound’s identity.

Lesson summary

A formula shows the atom counts used in a formula-based composition calculation.
Composition evidence can also come from collected measurements or supplied data.
Divide each element’s mass by the total sample mass and multiply by 100% to determine its evidence-based percent composition.
Compare evidence with a formula-based value carefully, use appropriate precision, and check that percentages add to about 100%.

Check your understanding

Question 1

A supplied data set gives 4.00 g of element A in a 16.00 g sample. What is the mass percent of A?

25.0%
4.00%
12.0%
400%

Show answer and explanation

25.0%

Divide the element mass by the total sample mass and multiply by 100%. The result is 25.0%.

Question 2

A two-element sample has supplied masses of 3.2 g and 6.6 g. The listed total sample mass is 10.0 g. What should you do first?

Check whether the element masses account for the listed total before calculating.
Change one mass so the percentages add to 100%.
Calculate both percentages using 3.2 g as the denominator.
Assume the difference proves the sample identity is wrong.

Show answer and explanation

Check whether the element masses account for the listed total before calculating.

The element masses add to 9.8 g, not 10.0 g. Check what the data include and report the discrepancy rather than altering the evidence.

Question 3

A planned investigation includes measuring the mass of each element, but no measurements have been made. Which statement is appropriate?

Report the planned values as measured results.
Describe the measurements as planned steps, not as collected evidence.
Choose values that make the total exactly 100%.
Claim the sample’s formula has been confirmed.

Show answer and explanation

Describe the measurements as planned steps, not as collected evidence.

A plan is not a completed measurement. Only collected or supplied data can be reported as evidence.

Key terms

Atomic mass: The average mass assigned to an atom of an element on the periodic table.
Formula mass: The sum of the atomic masses represented by a chemical formula.
Percent composition by mass: The percentage of a compound’s total mass that comes from a particular element.
Subscript: A small number in a chemical formula that shows how many atoms of the preceding element are represented.
Evidence: Measurements or supplied data used to answer an inquiry question.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Chemistry (SCH3U), expectation D2.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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