Worked example 1
Calculate the percent composition of Ca(NO₃)₂.
Try it first: Expand the formula into an atom list before you calculate anything.
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StoichiometryPercent compositionContent level: Core 20 min
Percent Composition
What you'll be able to do: Find the mass percent of any element in a compound, and use percent composition to test whether a sample matches a formula.
Best after: The Mole and Molar Mass
Introduction
A chemical formula tells you how many atoms of each element are present. Percent composition turns that counting information into something you can weigh: what fraction of a sample's mass comes from each element. It is the bridge between a formula on paper and a balance reading in the laboratory.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Calculate the molar mass of a compound from its formula.
- Calculate the mass percent of each element in a compound.
- Use percent composition to decide whether an unknown sample is consistent with a proposed formula.
- Convert between mass percent and the mass of an element in a weighed sample.
Lesson
What percent composition actually measures
Percent composition answers a mass question, not a counting question. In one mole of water the two hydrogen atoms contribute only 2.016 g out of 18.015 g, so hydrogen is 11.19 % of the mass even though two out of every three atoms are hydrogen. Whenever an answer feels surprising, ask whether you were thinking about atom counts when the question asked about mass.
Percent by mass and percent by atoms are different numbers. Read the question carefully.
The three-step routine
1. Write the formula and expand it atom by atom. 2. Multiply each subscript by that element's atomic mass and add the results to get the molar mass. 3. Divide each element's total mass by the molar mass and multiply by 100. Keeping the arithmetic in this order means the molar mass is computed once and reused, which removes most rounding errors.
% element = (n x atomic mass of element) / M(compound) × 100 %
Parentheses and hydrates
A subscript outside parentheses multiplies every atom inside it, so Ca(NO₃)₂ contains 1 Ca, 2 N and 6 O. A dot in a hydrate formula means the water is part of the formula unit and its mass counts: CuSO₄ . 5 H₂O has a molar mass of 249.68 g/mol, not 159.61 g/mol.
Ca(NO₃)₂, CuSO₄ . 5 H₂O
Expand the formula into a short atom list before you touch the calculator.
Using percent composition in the laboratory
Percent composition is how a mass measurement becomes a chemical claim, but one element's percentage alone rarely identifies a unique compound. If a 5.00 g sample contains 2.06 g of sodium, it is 41.2% Na by mass. That is 1.86 percentage points from NaCl (39.34%) and 2.18 from Na₂CO₃ (43.38%): NaCl is numerically closer, but neither is a compelling match without considering uncertainty and other evidence. Compare multiple elements or a second property before naming an unknown.
Next: Empirical and Molecular FormulasChecking your answer
The percentages of all elements in a compound must sum to 100 % within rounding. If they sum to 97 % or 104 %, an atomic mass was mistyped or a subscript was missed. A second check: the element with the largest total mass contribution must have the largest percentage, which is not always the element with the most atoms.
Composition can rule out a formula without identifying one
A measured mass percent can be compared with a proposed formula, but one element's percentage rarely proves a unique identity. First calculate the theoretical percent from each candidate formula, then compare numerical differences with the experiment's precision. A 5.00 g sample containing 2.06 g Na is 41.2% sodium. That is 1.86 percentage points from NaCl's 39.34% and 2.18 points from Na₂CO₃'s 43.38%: NaCl is slightly closer, yet neither is a convincing match if the measurement is precise. A second element's percentage, the sample's purity, or another test is needed to decide.
Key ideas
Definition
Percent composition
The mass percent of each element in a compound, calculated from one mole of that compound.
Rule
Mass, not count
Percent composition weighs atoms. A light element with many atoms can still be a small percentage of the mass.
Rule
Percentages sum to 100
Every element's percentage added together must give 100 % within rounding. Use this as a built-in check.
Assumption
Pure substance
The formula describes the whole sample. A mixture has no single percent composition, each component must be handled separately.
Equation
Mass percent of an element
% X = (nX x AX) / M x 100 %
- nX = number of atoms of element X in one formula unit (exact)
- AX = atomic mass of X in g/mol
- M = molar mass of the whole compound in g/mol
- use when = you know the formula and want a mass fraction
- limits = the sample must be the pure compound; impurities shift every percentage
Equation
Mass of an element in a sample
mX = (% X / 100) x msample
- mX = mass of element X in the sample, in g
- msample = total mass of the weighed sample, in g
- use when = a question asks how much of one element a weighed sample contains
- limits = assumes the sample is entirely the named compound
Worked examples
Worked example 2
A fertiliser is pure ammonium sulfate, (NH₄)₂SO₄. How many grams of nitrogen are in a 50.0 g sample?
Try it first: Decide whether you need a percentage or a direct mass ratio, both routes work.
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Worked example 3
A 10.00 g sample believed to be pure CaCO₃ contains 3.80 g Ca. Is that result consistent with the proposed formula? Use M(CaCO₃) = 100.09 g/mol and M(Ca) = 40.08 g/mol.
Try it first: Compare the measured calcium fraction with the formula's predicted fraction.
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Common mistakes
Counting only some of the atoms inside parentheses, for example 3 O in Ca(NO₃)₂.
Why it's wrong: The outside subscript multiplies every atom inside the parentheses, so there are 6 O and 2 N.
Check instead: Write the expanded atom list on its own line before adding masses.
Reporting the fraction of atoms instead of the fraction of mass.
Why it's wrong: Hydrogen is 2 of the 3 atoms in water but only 11.19 % of its mass, because atoms have very different masses.
Check instead: Ask whether the question says percent by mass; if so, every term must be a mass.
Leaving the water of crystallisation out of a hydrate's molar mass.
Why it's wrong: The waters are part of the formula unit, so CuSO₄ . 5 H₂O has M = 249.68 g/mol, not 159.61 g/mol.
Check instead: Treat everything after the dot as extra atoms in the formula.
Accepting percentages that do not add to about 100 %.
Why it's wrong: A sum well away from 100 % means an atomic mass or subscript is wrong, the individual answers cannot all be right.
Check instead: Add your percentages as the last step, every time.
Letting periodic-table masses set the significant figures of the final answer.
Why it's wrong: Atomic masses are reference data known to more digits than the measured sample mass.
Check instead: Count significant figures from the measured quantities in the problem.
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Independent practice
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What you should now know
Percent composition is the mass of one element in one mole of a compound divided by the molar mass of that compound, expressed as a percentage. Compute the molar mass first, keep the element masses as mass per mole, and check that all the percentages add to 100 %.
- Percent composition is a mass fraction calculated from one mole of the compound.
- Expand parentheses and hydrate waters before computing the molar mass.
- All element percentages must sum to 100 % within rounding.
- Percent composition is independent of sample size, so it scales directly to any mass.
Sources and further reading
- Chemistry 2e, Section 3.1: Formula Mass and the Mole ConceptPaul Flowers, Klaus Theopold, Richard Langley, William R. Robinson, et al. · OpenStax, Rice University · Chapter 3.1 · pp. Section 3.1 (web edition)View source
Adapted from "Chemistry 2e" by OpenStax, Rice University, licensed CC BY 4.0. Changes were made. License