Dalton’s Law of Partial Pressures: Complete Explanation with Examples
Every breath you take is a mixture of gases — roughly 78% nitrogen, 21% oxygen, 0.9% argon, and 0.04% carbon dioxide. Each of those gases exerts its own pressure on your lungs independently of the others. The total pressure of the air you breathe is simply the sum of those individual pressures.
This is Dalton’s Law of Partial Pressures — one of the foundational principles of gas chemistry — and it governs everything from scuba diving safety to the design of hospital oxygen systems.
What Is Dalton’s Law of Partial Pressures?
Dalton’s Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas in the mixture.
The partial pressure of a gas is the pressure that gas would exert if it alone occupied the entire volume of the container at the same temperature. It is the gas’s individual contribution to the total pressure.
The law was formulated by English chemist and physicist John Dalton in 1801 — the same Dalton who proposed the atomic theory of matter. Dalton observed that gases in a mixture behave independently of one another, each following the ideal gas law as if the other gases were not present. This independence is the physical basis of his law.
The Partial Pressure Formula
There are two equivalent ways to calculate the partial pressure of a gas in a mixture:
Method 1: From the Ideal Gas Law
Since each gas behaves independently, you can apply the ideal gas law (PV = nRT) to each component:
Method 2: From Mole Fraction
The partial pressure of a gas equals its mole fraction multiplied by the total pressure:
The mole fraction is simply the fraction of all gas molecules that belong to component i. Since mole fractions must add up to 1, and partial pressures add up to total pressure, these two equations are entirely consistent.
How to Calculate Partial Pressure — Step-by-Step Examples
Example 1: Air Composition at Sea Level
Problem: At sea level, total atmospheric pressure is 101.325 kPa (1 atm). Air is approximately 78.09% N₂, 20.95% O₂, and 0.93% Ar by mole fraction. Find the partial pressure of each gas.
Given: χ(N₂) = 0.7809, χ(O₂) = 0.2095, χ(Ar) = 0.0093
Step 2: Apply P = χ × P_total:
P(N₂) = 0.7809 × 101.325 = 79.12 kPa
P(O₂) = 0.2095 × 101.325 = 21.23 kPa
P(Ar) = 0.0093 × 101.325 = 0.94 kPa
Use our Partial Pressure Calculator to solve this for any gas mixture instantly.
Example 2: Gas Mixture from Moles
Problem: A container holds 2.0 mol N₂, 3.0 mol O₂, and 1.0 mol CO₂ at a total pressure of 600 kPa. Find the partial pressure of each gas.
Given: P_total = 600 kPa
Step 2: Calculate mole fractions:
χ(N₂) = 2.0/6.0 = 0.333
χ(O₂) = 3.0/6.0 = 0.500
χ(CO₂) = 1.0/6.0 = 0.167
Step 3: Find partial pressures:
P(N₂) = 0.333 × 600 = 200 kPa
P(O₂) = 0.500 × 600 = 300 kPa
P(CO₂) = 0.167 × 600 = 100 kPa
Example 3: Finding Total Pressure from Individual Partial Pressures
Problem: A gas mixture in a 5.0 L flask at 25°C contains 0.50 mol He, 0.30 mol Ne, and 0.20 mol Ar. Find the total pressure.
Given: n(He) = 0.50 mol, n(Ne) = 0.30 mol, n(Ar) = 0.20 mol
R = 8.314 L·kPa/(mol·K)
P(He) = (0.50 × 8.314 × 298) / 5.0 = 1238.9/5.0 = 247.8 kPa
P(Ne) = (0.30 × 8.314 × 298) / 5.0 = 743.3/5.0 = 148.7 kPa
P(Ar) = (0.20 × 8.314 × 298) / 5.0 = 495.5/5.0 = 99.1 kPa
Step 2: Add partial pressures:
P_total = 247.8 + 148.7 + 99.1 = 495.6 kPa
P_total = (1.00 mol × 8.314 × 298) / 5.0 = 495.6 kPa ✓ (same answer — confirms Dalton’s Law)
Example 4: Collecting Gas Over Water
Problem: When a gas is collected by displacing water in a test tube (a common lab technique), the collected gas is always mixed with water vapour. The partial pressure of the dry gas must be calculated by subtracting the vapour pressure of water.
Given: P_total = 101.3 kPa
Given: P_water vapour = 3.17 kPa (at 25°C)
P(H₂) = 98.1 kPa
The Mole Fraction — Understanding χ
The mole fraction χᵢ is one of the most useful concepts in mixture chemistry. Key properties:
- Always between 0 and 1 (or 0% and 100%)
- Sum of all mole fractions in a mixture = exactly 1
- Dimensionless — no units
- Independent of temperature and pressure (unlike concentration in mol/L)
- Directly proportional to partial pressure at constant total pressure
The mole fraction is related to volume fraction for ideal gases — at the same temperature and pressure, the fraction of volume occupied by a gas equals its mole fraction. This is why air being “21% oxygen” means both 21% by moles AND 21% by volume.
Why Dalton’s Law Works — The Physics Behind It
Dalton’s Law holds because ideal gas molecules are assumed to:
- Have negligible volume compared to the container
- Exert no forces on each other between collisions
- Move independently
Under these conditions, each gas molecule hits the container walls with a force that depends only on its own kinetic energy — not on what other gas molecules are doing nearby. The total pressure is simply the sum of all those individual impacts.
In real gases at high pressures or low temperatures, intermolecular forces become significant and Dalton’s Law becomes an approximation. It works best for:
- Gases at low to moderate pressures (below ~10 atm)
- Gases at high temperatures (far above their boiling points)
- Gases with weak intermolecular forces (noble gases, N₂, H₂)
It works less well for polar gases (H₂O vapour, NH₃) at high concentrations.
Real-World Applications of Dalton’s Law
Scuba Diving and Nitrogen Narcosis
At 30 metres depth, water pressure is approximately 4 atm total. The partial pressure of each gas in air is four times its surface value: P(N₂) = 0.79 × 4 = 3.16 atm (surface: 0.79 atm), P(O₂) = 0.21 × 4 = 0.84 atm (surface: 0.21 atm). At these elevated partial pressures, nitrogen dissolves in blood and tissue at higher concentrations, causing nitrogen narcosis (an intoxicating effect) at depths beyond roughly 30 metres, and decompression sickness if the diver ascends too quickly. Professional divers use mixed gases — trimix (N₂, O₂, He) or heliox (He, O₂) — specifically to reduce the partial pressure of nitrogen.
Hospital Oxygen Therapy
Medical oxygen is delivered at a specific partial pressure of O₂ to treat respiratory conditions. Normal air delivers P(O₂) ≈ 21 kPa. Supplemental oxygen raises the fraction of O₂ in the breathing gas, increasing P(O₂) without changing total pressure. A patient breathing 40% O₂ at atmospheric pressure receives P(O₂) = 0.40 × 101.3 = 40.5 kPa — nearly double the normal amount.
Anaesthesia
Anaesthetic gases (isoflurane, sevoflurane, nitrous oxide) work by achieving a specific partial pressure in the blood and brain tissue, not a specific concentration. Anaesthesiologists dial in the percentage of anaesthetic gas in the breathing mixture, which sets its partial pressure via Dalton’s Law. This is why anaesthetic dosing is expressed in minimum alveolar concentration (MAC) — a partial pressure measurement.
Atmospheric Science and Weather
The water vapour content of air is expressed as its partial pressure (vapour pressure). When water vapour’s partial pressure reaches the saturation vapour pressure at a given temperature, condensation occurs — forming clouds, fog, and rain. Relative humidity is defined as the ratio of actual water vapour partial pressure to saturation vapour pressure, expressed as a percentage.
Industrial Gas Blending
Manufacturers of specialty gas mixtures (calibration gases, welding gases, medical gases) use Dalton’s Law to calculate the amount of each component needed. If you need a 500 L cylinder of gas at 200 bar containing 10% CO₂ in N₂, Dalton’s Law tells you the CO₂ partial pressure must be 20 bar and N₂ must be 180 bar.
Dalton’s Law vs Henry’s Law — What Is the Difference?
Students sometimes confuse these two gas laws, both of which involve partial pressure:
🟢 Dalton’s Law
P_total = P₁ + P₂ + P₃ + …Describes gas mixtures in the gas phase — how individual gases contribute to total gas pressure. Each gas behaves as if it alone occupied the container.
🔵 Henry’s Law
C = kH × PDescribes how gases dissolve in liquids — the amount of gas dissolved is proportional to its partial pressure above the liquid.
Common Mistakes with Dalton’s Law
❌ Adding Pressures Without Checking Units
All pressures must be in the same unit before adding. Mix kPa and atm and the answer will be wrong. Always convert first.
❌ Forgetting Water Vapour When Collecting Gas Over Water
In any lab collection experiment, the gas collected is wet. Subtract vapour pressure of water at the experimental temperature to get the dry gas partial pressure.
❌ Confusing Mole Fraction with Mass Fraction
21% oxygen by moles (volume) does not mean 21% by mass. Oxygen’s molar mass (32 g/mol) differs from nitrogen’s (28 g/mol), so the mass percentage of oxygen in air is approximately 23%, not 21%.
❌ Applying Dalton’s Law to Reacting Gases
Dalton’s Law requires the gases to not react with each other. H₂ and O₂ at high temperature would react to form water — their mixture does not follow Dalton’s Law in the same way. The law states “non-reacting gases” for this reason.
Frequently Asked Questions
In a mixture of gases, each gas acts as if it were alone in the container. The total pressure is just the sum of each gas’s individual pressure. Think of it as: total = P₁ + P₂ + P₃ + …
The partial pressure of a gas in a mixture is the pressure it would exert if it alone occupied the entire volume at the same temperature. It equals its mole fraction multiplied by the total pressure: Pᵢ = χᵢ × P_total.
Dalton’s Law is exact only for ideal gases. Real gases deviate at high pressures (above ~10 atm) and low temperatures, when intermolecular forces become significant. For most practical situations at near-atmospheric pressure, Dalton’s Law is an excellent approximation.
Vapour pressure is the partial pressure of water vapour in equilibrium with liquid water at a given temperature. At 25°C it is 3.17 kPa; at 100°C it equals atmospheric pressure (101.3 kPa) — that is why water boils at 100°C at sea level. In gas collection experiments, water vapour always adds to the total pressure measured, so it must be subtracted to find the dry gas pressure.
At depth, total pressure increases with water depth (~1 atm per 10 metres). Dalton’s Law shows that partial pressures of all gases in the breathing mixture increase proportionally. High partial pressures of N₂ cause narcosis; high P(O₂) above 1.6 atm causes oxygen toxicity. Mixed gases like trimix are used to keep each component’s partial pressure within safe limits.
🧪 Calculate Partial Pressures Instantly
Rather than working through mole fraction calculations by hand, our Partial Pressure Calculator solves for the partial pressure of any gas in a mixture. Enter the mole fractions or moles of each component and total pressure, and it applies Dalton’s Law automatically with step-by-step working shown. For problems involving grams of gas, use our Grams to Moles Calculator first to convert mass to moles.