Why are atom fractions and mass fractions different answers?

Support map

Model diagram

Use only paper, a calculator and supplied data. Do not carry out reactions, generate gases, heat substances or mix household chemicals.

Situation and question

A water molecule contains two H atoms and one O atom. A learner concludes that hydrogen contributes two thirds of the mass. Is that correct? Compare atom counts with mass contributions using H=1 and O=16 in the supplied teaching model.

New terms, fully explained

An element’s mass fraction w is its mass in a compound divided by the mass of the compound. For a known formula, w(E) = kAᵣ(E)/Mᵣ, where k counts E atoms in the formula. The fraction is dimensionless; multiply by 100% for a percentage. This describes a pure compound’s composition, not solution concentration.

Predict first

Predict which element contributes most of the mass of H₂O. Would the mass fraction change between 18 g and 36 g of pure water with the same composition? Explain the difference between a constant fraction and an increasing mass of an element.

Investigate or analyse given data

For water, list the contributions: H contributes 2×1=2, O contributes 16, total 18. For CO₂, C contributes 12 and O contributes 32, total 44. Find fractions first and percentages second. Rounding may make the percentages add to slightly more or less than 100%.

Worked example

In water, w(H)=2/18≈0.111, or 11.1%, and w(O)=16/18≈88.9%. In 36 g of water, the hydrogen mass represented by its composition is 36×2/18=4 g. This is a composition calculation, not an instruction to extract hydrogen from water.

A common mistake

Mistake: using atom counts instead of mass contributions, or confusing 11.1% with 11.1. To multiply by a mass, use 0.111… or divide the percentage by 100. Oxygen mass in water does not mean free O₂ gas is present inside it.

Transfer to a new case

Find the mass fractions of C and O in CO₂. Then find the carbon mass corresponding to 22 g of pure CO₂. As an additional case, find the Ca fraction in CaCO₃ with Mᵣ≈100 and Aᵣ(Ca)=40.

Answer and recall

Check: CO₂ contains approximately 27.3% C and 72.7% O by mass; 22 g corresponds to 6 g of C in its composition. The Ca fraction in CaCO₃ is about 40%. Check the fraction sum and label whether you describe composition or the whole sample mass.

Exercise

What is the O mass fraction in CaCO₃? What O mass corresponds to 25 g CaCO₃?

Answers

When to revisit

Close the page and, after 10 minutes, reconstruct the map, define the terms in your own words and solve the new case. Repeat without hints after a day and a week. If an error persists, return to the worked example and write down the missing step.

Sources and limits

• OpenStax: composition and formulas

How do we move from mass to particle count without confusion?

How do equation coefficients connect amounts of substances?