1.4 Composition

Composition of Mixtures

Weigh out a two-component mixture such as NaCl and KCl and watch the particle box refill by mole ratio. Switch to elemental analysis to sort every atom by element, then read one measured percent back into the mass of each component.

Pure vs MixtureElemental AnalysisPercent by Mass5 Mixtures
Topic 1.4

Composition of Mixtures

Explain the quantitative relationship between the elemental composition by mass and the composition of substances in a mixture.

A pure substance contains atoms, molecules, or formula units of a single type. A mixture contains two or more types whose relative proportions can vary. That variability is the whole distinction: you can make salt water at any concentration you like, but you cannot make water that is 50% hydrogen by mass.

Mixtures are further split by uniformity:

  • Homogeneous (a solution) — composition is uniform throughout; a sample from anywhere looks the same. Air, salt water, brass.
  • Heterogeneous — properties depend on where you sample. Sand in water, oil and vinegar, granite.

Elemental analysis measures the mass of each element in a sample. For a pure compound that gives you the empirical formula. For a mixture it lets you back-solve the amount of each component, or judge purity: if a sample of "pure" CaCO₃ analyzes as 38.2% Ca instead of the theoretical 40.0%, something else is in there.

The standard two-component problem is a system of two equations: total mass, and total mass of one element.

Key points

  • Compounds have fixed composition; mixtures do not. That single sentence answers most conceptual questions in this topic.
  • Homogeneous means uniform at the particulate level, not that it looks uniform to your eye.
  • A two-component mixture problem is two equations in two unknowns: mass balance plus one element balance.

Equations

  • not on the sheet

Common mistakes

  • Air is a mixture, not a compound. Its N₂ : O₂ ratio can and does vary.
  • A solution is a mixture. Being homogeneous does not make it a pure substance.
  • Mass fractions add to 1, mole fractions add to 1 — but they are not the same number unless the molar masses happen to match.
  • Alloys are mixtures (solid solutions), which is why their composition and properties are tunable.

Worked example

A 10.00 g mixture contains only NaCl and KCl. Analysis shows the mixture is 52.8% chlorine by mass. What mass of NaCl is present?

Let x = mass of NaCl; then (10.00 − x) = mass of KCl.

Chlorine mass fraction in NaCl = 35.45/58.44 = 0.6066
Chlorine mass fraction in KCl = 35.45/74.55 = 0.4756

Total Cl = 0.528 × 10.00 = 5.28 g

0.6066x + 0.4756(10.00 − x) = 5.28
0.6066x + 4.756 − 0.4756x = 5.28
0.1310x = 0.524
x = 4.00 g NaCl (and 6.00 g KCl)

Check: 0.6066(4.00) + 0.4756(6.00) = 2.43 + 2.85 = 5.28 g Cl ✓

Full notes for topic 1.4 →