Learning Objectives
1 objectiveBy the end of this note, you should be able to:
- 1.4.AExplain the quantitative relationship between the elemental composition by mass and the composition of substances in a mixture.
Pure Substances Versus Mixtures
Pure substances contain atoms, molecules, or formula units of only a single type, whereas mixtures contain two or more types whose relative proportions can vary.
Every sample of water, for instance, contains hydrogen and oxygen in a 2 : 1 atomic ratio regardless of the sample’s origin. This constancy means that any pure substance always yields the same percent composition by mass. Iron(III) oxide, Fe₂O₃, always contains 69.94% iron and 30.06% oxygen by mass — no matter how much or how little is present.
A mixture, by contrast, combines two or more pure substances in proportions that are not fixed. A saltwater solution could be 3% NaCl or 10% NaCl; both are saltwater, but their elemental compositions by mass differ because the ratio of NaCl to H₂O differs.
If the percent composition by mass of a mixture is known, the mass fraction of each component substance can be calculated. Conversely, if the identities and amounts of the component substances are known, the overall elemental composition by mass can be determined by summing each element’s contribution from every component.
| Feature | Pure Substance | Mixture |
|---|---|---|
| Composition | Fixed ratio of atoms/molecules/formula units | Variable ratio of two or more pure substances |
| Elemental % by mass | Constant for a given substance | Changes with proportions of components |
| Examples | H₂O, NaCl, Fe₂O₃ | Saltwater, air, bronze |
MisconceptionStudents sometimes assume that any sample with more than one element must be a mixture. A compound such as NaCl is a pure substance — it contains one type of formula unit, even though two elements are present.
Elemental Analysis and Purity
Elemental analysis determines the relative numbers of atoms in a substance and can verify whether that substance is pure.
Because every pure compound has a unique and fixed percent composition by mass, experimentally measuring the mass percentages of each element provides a chemical fingerprint. If an unknown sample’s elemental analysis matches the theoretical percent composition of a known compound, the sample is likely that compound. If the experimental values deviate from the theoretical values, the sample may be impure — meaning it is a mixture rather than a single pure substance.
From mass percentages, moles of each element can be calculated, and dividing by the smallest number of moles yields the simplest whole-number (empirical) ratio.
To determine purity quantitatively, compare the experimental mass percent of a key element with its theoretical value in the pure compound. A sample of NaCl that shows only 58.0% chlorine by mass instead of the expected 60.66% likely contains an impurity that dilutes the chlorine content.
Worked Example — Determining Mass Percent from a Mixture
A 10.00 g mixture contains only NaCl and KCl. Elemental analysis shows the mixture contains 4.200 g of chlorine. Determine the mass of NaCl in the mixture.
Let x = mass of NaCl and (10.00 − x) = mass of KCl.
Molar masses needed:
$${M}_{\text{NaCl}}=58.44{\text{ g mol}}^{-1}$$
$${M}_{\text{KCl}}=74.55{\text{ g mol}}^{-1}$$
$${M}_{\text{Cl}}=35.45{\text{ g mol}}^{-1}$$
Mass fraction of Cl in NaCl:
$$\frac{35.45}{58.44}=0.6066$$
Mass fraction of Cl in KCl:
$$\frac{35.45}{74.55}=0.4756$$
Set up the mass-balance equation for chlorine:
$$0.6066x+0.4756(10.00-x)=4.200$$
Expand:
$$0.6066x+4.756-0.4756x=4.200$$
Combine like terms:
$$0.1310x=4.200-4.756$$
$$0.1310x=-0.556$$
Recheck — the negative result indicates less Cl than pure KCl alone would provide, so let’s verify: 10.00 g of pure KCl contains 4.756 g Cl, while 10.00 g of pure NaCl contains 6.066 g Cl. The mixture contains 4.200 g Cl, which is less than even pure KCl would give, so let’s re-examine the problem setup.
Corrected worked example with realistic data:
A 10.00 g mixture contains only NaCl and KCl. Elemental analysis shows the mixture contains 5.200 g of chlorine. Determine the mass of NaCl in the mixture.
Mass fraction of Cl in NaCl:
$$\frac{35.45}{58.44}=0.6066$$
Mass fraction of Cl in KCl:
$$\frac{35.45}{74.55}=0.4756$$
Set up the mass-balance equation for chlorine, where x = mass of NaCl:
$$0.6066x+0.4756(10.00-x)=5.200$$
Expand:
$$0.6066x+4.756-0.4756x=5.200$$
Combine like terms:
$$0.1310x=0.444$$
Solve for x:
$$x=\frac{0.444}{0.1310}$$
$$x=3.39\text{ g NaCl}$$
The mixture therefore contains 3.39 g NaCl and 6.61 g KCl.
Practice Problem
A 5.00 g sample is believed to be pure CaCO₃ (theoretical: 40.04% Ca, 12.00% C, 47.96% O by mass). Elemental analysis shows only 38.50% calcium by mass. Calculate the mass of calcium detected and explain what the result suggests about purity.
Answer
Mass of calcium detected:
Equation used
$${m}_{\text{Ca}}=\text{total mass}\times \text{mass fraction of Ca}$$
Given
$$\text{total mass}=5.00\text{ g}$$
$$\text{mass fraction of Ca}=0.3850$$
Working
$${m}_{\text{Ca}}=5.00\times 0.3850$$
$${m}_{\text{Ca}}=1.93\text{ g}$$
The theoretical mass of calcium in 5.00 g of pure CaCO₃ would be 5.00 × 0.4004 = 2.00 g. The detected value (1.93 g) is lower than expected, which indicates the sample is not pure CaCO₃ — it likely contains an impurity that either lacks calcium or has a lower calcium mass percent than CaCO₃.
Examiner InsightAP free-response questions frequently provide elemental analysis data and ask students to determine whether a sample is pure or a mixture. Always compare experimental mass percentages to theoretical values and state the direction of the discrepancy.
QUICK RECAP
Key Points
- Pure substances have one type of particle; mixtures have two or more types.
- Pure substances have fixed percent composition by mass.
- Mixtures have variable composition depending on component proportions.
- Elemental analysis measures mass percentages of each element experimentally.
- Comparing experimental to theoretical mass percent reveals sample purity.
- Deviations from theoretical values indicate the sample is a mixture.
- Mass-balance equations relate component masses to total elemental mass.
- Mass fraction of an element equals its atomic mass divided by the compound’s molar mass.
- Increasing one component in a mixture shifts overall composition toward that component’s values.
- Percent composition connects directly to empirical formula determination.
CAN I…? PROGRESS CHECK
Self-Assessment
- Distinguish between a pure substance and a mixture using particulate-level descriptions.
- Calculate the percent composition by mass of any element in a pure compound from its formula.
- Determine whether a sample is pure by comparing experimental and theoretical mass percentages.
- Set up and solve a mass-balance equation to find the composition of a two-component mixture.
- Predict how changing the proportion of one component in a mixture affects overall elemental composition.
- Explain how elemental analysis reveals the relative numbers of atoms in a substance.