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General Chemistry I · Gases

Gas Mixtures and Dalton's Law

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

In a mixture of gases, each gas exerts its own pressure — its partial pressure — as if it were the only gas present. Dalton's law states that the total pressure is the sum of the partial pressures. The mole fraction of a gas is the fraction of all moles that it contributes, and it sets that gas's share of the total pressure.

Why this matters

Gas mixtures are everywhere — air is mostly N₂ and O₂ with traces of argon and CO₂. Dalton's law lets you compute the oxygen available at altitude, the makeup of breathing gases in diving and anesthesia, and the composition of industrial gas streams. Mole fraction is the standard way to report gas and solution compositions in chemistry and medicine.

The college version

Key Ideas

  • Partial pressure (Pᵢ) is the pressure one component would exert alone in the container.
  • Dalton's law: P_total = P₁ + P₂ + P₃ + … = ΣPᵢ.
  • Mole fraction: Xᵢ = nᵢ/n_total (dimensionless, ranges 0 to 1).
  • Partial pressure from mole fraction: Pᵢ = Xᵢ · P_total.
  • Independence: gas particles are far apart and interact little, so each gas's contribution doesn't depend on the others.

Equations and Variables

  • P_total = ΣPᵢ = P₁ + P₂ + … — total pressure equals the sum of partial pressures.
  • Xᵢ = nᵢ/n_total — mole fraction of component i.
  • Pᵢ = Xᵢ · P_total — partial pressure from mole fraction.
  • From the ideal gas law: Pᵢ = nᵢRT/V, so P_total = (n_total)RT/V.

How It Works

  1. Consider a container holding several gases at once. Each gas's molecules fill the whole volume and collide with the walls.
  2. Each component contributes pressure proportional to its number of moles, exactly as if the other gases weren't there.
  3. The total pressure is just the sum of those independent contributions (Dalton's law).
  4. The mole fraction tells you what fraction of the molecules belong to each gas.
  5. Because pressure splits in proportion to moles, Pᵢ = Xᵢ · P_total.

Worked Example

A container holds 0.20 mol O₂, 0.30 mol N₂, and 0.50 mol He, with a total pressure of 2.0 atm. Find each mole fraction and partial pressure. n_total = 0.20 + 0.30 + 0.50 = 1.00 mol. X(O₂) = 0.20/1.00 = 0.20; X(N₂) = 0.30/1.00 = 0.30; X(He) = 0.50/1.00 = 0.50. P(O₂) = 0.20 × 2.0 atm = 0.40 atm. P(N₂) = 0.30 × 2.0 atm = 0.60 atm. P(He) = 0.50 × 2.0 atm = 1.0 atm. Check: 0.40 + 0.60 + 1.0 = 2.0 atm. ✓

Common Confusions

  • "Partial pressures don't have to add up to the total" — they always do; that's Dalton's law.
  • "Mole fraction can be a percentage over 100" — mole fractions are fractions; they must sum to exactly 1.
  • "The heaviest gas contributes the most pressure" — pressure is set by the number of moles (and temperature), not by molar mass.
  • "Partial pressure means the gas occupies part of the volume" — no; each gas fills the entire volume; only its pressure contribution is "partial."
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a party in one big room where three different groups of people are each talking. The total noise is just everyone's talking added together. Each gas in a mixture is like one of those groups: it makes its own "noise" (pressure) as if the other groups weren't even there, and the total is simply the sum. The analogy's limit: real gases do interact slightly (that's why real-gas corrections exist), but for dilute gases the "each group acts alone" picture is essentially exact.

Key takeaways

  • Dalton's law: P_total = ΣPᵢ.
  • Mole fraction: Xᵢ = nᵢ/n_total.
  • Partial pressure: Pᵢ = Xᵢ · P_total.
  • Mole fractions in a mixture always sum to 1.
  • Each gas behaves as if it occupied the container alone.
  • Air at sea level: P_total ≈ 1 atm, with P(O₂) ≈ 0.21 atm (21%).
  • Dalton's law: total pressure = sum of partial pressures.
  • Xᵢ = nᵢ/n_total.
  • Pᵢ = Xᵢ · P_total.
  • Mole fractions sum to 1.
  • Each gas behaves independently of the others.

Keep learning

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Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • State Dalton's law of partial pressures.
  • Define mole fraction and use it to find partial pressures.
  • Calculate the total pressure of a gas mixture from its components.
  • Explain why each gas in a mixture behaves independently.

Sources & references

  1. OpenStax, "9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions," Chemistry 2e.
  2. Brown et al., "10.6 Gas Mixtures and Partial Pressures," Chemistry LibreTexts.
  3. Petrucci et al., "6.6 Mixtures of Gases," Chemistry LibreTexts.

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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