Dalton’s law

6 min read Last updated April 8, 2026

Clinical relevance in anaesthesia

  • Underpins how we interpret and deliver oxygen and volatile agents: inspired, alveolar and arterial partial pressures drive diffusion and clinical effect.
    • Oxygenation: PAO2 and PaO2 depend on FiO2 and barometric pressure (PB), not on % alone.
    • Volatile uptake/partial pressure: effect-site is related to partial pressure; changes in PB alter delivered partial pressure for a given % setting.
  • Explains why humidification matters: water vapour exerts its own partial pressure and reduces available partial pressure for other gases.
    • At 37 °C, saturated water vapour pressure PH2O ≈ 6.3 kPa (47 mmHg).
  • Altitude/hyperbaric environments: same FiO2 gives different inspired PO2; anaesthetic vapourisers and MAC considerations depend on whether control is by % or partial pressure.
    • At altitude PB falls → inspired PO2 falls even if FiO2 unchanged.
    • Hyperbaric: PB rises → inspired PO2 rises; oxygen toxicity risk increases for a given FiO2.

Common clinical calculations

  • Inspired oxygen partial pressure (dry gas): PIO2 = FiO2 × PB.
    • At sea level PB ≈ 101 kPa: PIO2 (air) ≈ 0.21 × 101 ≈ 21 kPa.
  • Inspired oxygen partial pressure (humidified): PIO2 = FiO2 × (PB − PH2O).
    • At sea level: (101 − 6.3) ≈ 94.7 kPa; with FiO2 0.21 → PIO2 ≈ 19.9 kPa.
  • Alveolar gas equation (to link Dalton’s law to PAO2): PAO2 = FiO2 × (PB − PH2O) − (PaCO2 / R).
    • R (respiratory quotient) typically ≈ 0.8.

Statement and key definitions

  • Dalton’s law: In a mixture of non-reacting gases, the total pressure equals the sum of the partial pressures of each component.
  • Partial pressure (Pi): the pressure that gas i would exert if it alone occupied the entire volume at the same temperature.
  • For ideal gases: Pi = Fi × PTotal (where Fi is the fractional concentration).

Assumptions and limitations

  • Applies best to ideal gases (low pressure, high temperature, minimal intermolecular forces).
  • Real gases deviate at high pressures/low temperatures; partial pressure concept remains clinically useful but exact linearity may be reduced.
  • In gas mixtures with chemical interaction (e.g., reactive gases), Dalton’s law may not hold strictly.

Humidification and water vapour

  • Water vapour contributes to total pressure; in the trachea/alveoli at 37 °C, PH2O ≈ 6.3 kPa regardless of altitude (provided full saturation).
  • Therefore, the maximum available pressure for other gases in fully humidified alveolar gas is (PB − PH2O).
  • Clinical implication: at altitude, PH2O is a larger fraction of PB, further reducing inspired and alveolar PO2.

Anaesthesia-specific applications

  • Volatile agents: clinical effect relates to partial pressure (brain/alveolar), not % per se.
    • At lower PB (altitude), a given vaporiser dial setting (% by volume) may produce a lower partial pressure of agent, potentially reducing anaesthetic depth if not compensated (device-dependent).
  • Oxygen delivery: FiO2 must be interpreted with PB and humidification; use PIO2 and PAO2 concepts when reasoning about hypoxaemia.
  • Gas analysis: measured end-tidal concentrations are fractions; converting to partial pressure requires multiplication by ambient pressure (and considering water vapour if relevant to the measurement system).
  • Decompression/aviation: reduced PB lowers partial pressures of all gases; hypoxia risk despite unchanged percentage oxygen in air.

Worked examples (typical FRCA numeracy)

  • Example 1 (dry inspired gas): PB 100 kPa, FiO2 0.5 → PIO2 = 0.5 × 100 = 50 kPa.
  • Example 2 (humidified): PB 101 kPa, FiO2 1.0 → PIO2 = 1.0 × (101 − 6.3) ≈ 94.7 kPa.
  • Example 3 (alveolar gas equation): FiO2 0.21, PB 101 kPa, PH2O 6.3 kPa, PaCO2 5.3 kPa, R 0.8 → PAO2 ≈ 0.21×(94.7) − (5.3/0.8) ≈ 19.9 − 6.6 ≈ 13.3 kPa.
State Dalton’s law and define partial pressure.

Core definitions expected early in a viva.

  • Dalton’s law: total pressure of a mixture of non-reacting gases equals the sum of the partial pressures of the individual gases.
  • Partial pressure: the pressure a gas would exert if it alone occupied the container at the same temperature.
  • For ideal gases: Pi = Fi × PTotal.
A previous FRCA-style question: Calculate the inspired oxygen partial pressure in the trachea for a patient breathing air at sea level.

Examiners usually want you to include humidification.

  • Use PIO2 = FiO2 × (PB − PH2O) for fully humidified inspired gas.
  • At sea level PB ≈ 101 kPa, PH2O at 37 °C ≈ 6.3 kPa, FiO2 = 0.21.
  • PIO2 ≈ 0.21 × (101 − 6.3) = 0.21 × 94.7 ≈ 19.9 kPa (≈ 150 mmHg).
A previous FRCA-style question: Why does humidification reduce inspired oxygen partial pressure?

Link Dalton’s law to water vapour pressure.

  • Total pressure is fixed at PB; adding water vapour contributes PH2O to the total pressure.
  • By Dalton’s law, the partial pressures of the other gases must sum to (PB − PH2O).
  • Therefore, for a given FiO2, PIO2 is lower when gas is fully humidified.
A previous FRCA-style question: Use the alveolar gas equation to estimate PAO2 on air at sea level (PaCO2 5.3 kPa, R 0.8).

Common short calculation in written/viva.

  • PAO2 = FiO2 × (PB − PH2O) − (PaCO2 / R).
  • FiO2 0.21; (PB − PH2O) ≈ 94.7 kPa → first term ≈ 19.9 kPa.
  • PaCO2/R ≈ 5.3/0.8 ≈ 6.6 kPa.
  • PAO2 ≈ 19.9 − 6.6 ≈ 13.3 kPa.
Explain the difference between concentration (%) and partial pressure, and why partial pressure is more physiologically relevant.

This is a frequent viva line of questioning.

  • Concentration (fraction) is the proportion of a gas in a mixture; partial pressure is that fraction multiplied by total pressure (Pi = Fi × PTotal).
  • Diffusion and gas exchange depend on partial pressure gradients (e.g., alveolar-to-capillary PO2).
  • At different barometric pressures, the same % gives different partial pressures and therefore different physiological effects.
A previous FRCA-style question: At altitude, why can a patient become hypoxaemic even though the percentage of oxygen in air is unchanged?

Dalton’s law applied to atmospheric pressure.

  • FiO2 remains ~0.21, but PB decreases with altitude.
  • Therefore PIO2 = FiO2 × (PB − PH2O) decreases, reducing PAO2 and ultimately PaO2.
  • PH2O is fixed by temperature (~6.3 kPa at 37 °C), so it becomes a larger fraction of PB at altitude, further reducing available pressure for oxygen.
How does Dalton’s law relate to delivery of volatile anaesthetics and MAC at different barometric pressures?

Examiners want the concept: effect tracks partial pressure.

  • Anaesthetic potency is related to partial pressure in the brain; alveolar partial pressure is a surrogate.
  • MAC is defined as an alveolar concentration at 1 atm, but the underlying driver is partial pressure; at lower PB, the same % corresponds to a lower partial pressure.
  • Practical implication depends on the vaporiser/agent delivery system: if it delivers a set %, partial pressure delivered falls with PB; if it targets partial pressure, the required % would rise as PB falls.
A previous FRCA-style question: A cylinder contains 50% O2 and 50% N2 at a total pressure of 200 bar. What are the partial pressures?

Straight Dalton calculation.

  • PO2 = 0.5 × 200 = 100 bar; PN2 = 0.5 × 200 = 100 bar.
  • Assumes ideal behaviour; at very high pressures real gas deviation may occur, but this is the expected exam answer.
Describe how you would calculate the partial pressure of oxygen from a gas analyser reading of 40% O2 in theatre at sea level.

They want multiplication by ambient pressure and a note about humidification context.

  • If the sample is dry (typical side-stream analysers dry the sample), PO2 ≈ 0.40 × PB ≈ 0.40 × 101 ≈ 40 kPa.
  • If considering fully humidified gas at 37 °C, use PO2 ≈ 0.40 × (PB − PH2O) ≈ 0.40 × 94.7 ≈ 37.9 kPa.
Give two limitations of Dalton’s law in clinical practice/physics terms.

Keep it simple: ideal vs real gases and reactivity.

  • Real gases deviate from ideal behaviour at high pressures and low temperatures (intermolecular forces, finite molecular volume).
  • If gases react chemically, the assumption of non-reacting components fails and partial pressures may not sum in the simple way.

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