Dalton's Law: pressure adds up
Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases equals the sum of the partial pressures each gas would exert if it occupied the entire volume alone at the same temperature. In equation form: P_total = P₁ + P₂ + P₃ + ...
Each gas in a mixture behaves independently. Its partial pressure is determined by its mole fraction times the total pressure: Pᵢ = Xᵢ × P_total, where the mole fraction Xᵢ = nᵢ / n_total. John Dalton, the English chemist who also formulated modern atomic theory, published this law in 1801 after studying the behavior of gas mixtures and the solubility of gases in water.
Air: the classic example
Dry air at sea level is approximately 78.08% nitrogen, 20.95% oxygen, 0.93% argon, and 0.04% carbon dioxide, with trace amounts of neon, helium, methane, krypton, and hydrogen. At 1.000 atm total pressure, the partial pressures are: N₂ = 0.7808 atm, O₂ = 0.2095 atm, Ar = 0.0093 atm, and CO₂ = 0.0004 atm. These add to 1.0000 atm, consistent with Dalton's Law.
At high altitude, the total atmospheric pressure drops but the composition percentages remain approximately the same up to about 80 km. At the summit of Mount Everest (8,848 m), where barometric pressure is about 0.31 atm, the partial pressure of oxygen is roughly 0.31 × 0.2095 = 0.065 atm — low enough to require supplemental oxygen for most climbers.
Collecting gas over water
A common laboratory application: when a gas is collected by water displacement, the collected gas is a mixture of the desired gas and water vapor. The water vapor pressure depends only on temperature. At 25 °C, water vapor pressure is 23.8 torr. If the barometric pressure is 760.0 torr and the collected gas pressure inside the collection tube equals atmospheric pressure, then P_dry_gas = 760.0 - 23.8 = 736.2 torr. Failing to subtract water vapor pressure is a frequent source of error in general chemistry labs.
Scuba diving and Dalton's Law
Divers breathe compressed air at the ambient pressure of the surrounding water. At 30 m depth, the total pressure is about 4 atm. The partial pressure of nitrogen in the breathing gas is 4 × 0.78 = 3.12 atm, which is high enough to cause nitrogen narcosis. Technical divers replace some or all of the nitrogen with helium to reduce narcosis, using Dalton's Law to calculate the oxygen partial pressure and ensure it stays within safe limits — above 0.16 atm to avoid hypoxia, below about 1.4 atm to avoid oxygen toxicity.
John Dalton: the man behind the law
John Dalton (1766-1844) was an English chemist, physicist, and meteorologist. He formulated modern atomic theory in 1808, proposing that each element consists of unique atoms that combine in fixed ratios to form compounds. His work on gas mixtures grew from his lifelong interest in meteorology: understanding how the atmosphere, a mixture of gases, behaved required a theory of partial pressures.
Dalton's law of partial pressures appeared in his 1801 paper "On the Constitution of Mixed Gases." He argued that each gas in a mixture acts independently, as if the others were absent. This was controversial at the time — some chemists believed gases interacted chemically in mixtures — but Dalton's atomic theory provided a natural explanation: if gases consist of discrete particles with empty space between them, those particles should not affect each other's motion.
The mathematics of mixtures
For a gas mixture, the total pressure is the sum of partial pressures. If each component obeys the Ideal Gas Law, then P_total = (n_total × R × T) / V. The partial pressure of component i is Pᵢ = (nᵢ × R × T) / V = Xᵢ × P_total, where Xᵢ = nᵢ / n_total is the mole fraction. The mole fractions of all components must sum to 1. This relationship is independent of which gases are in the mixture.
A practical consequence: if you know the total pressure and the mole fractions, you can calculate each partial pressure. If air at 1.00 atm has X_O₂ = 0.2095, then P_O₂ = 0.2095 atm. This is often more useful than measuring each component individually, especially in industrial and medical gas monitoring.
Anesthesia and Dalton's Law
Anesthesiologists use Dalton's Law daily to deliver precise concentrations of gases. A typical anesthesia machine blends oxygen, nitrous oxide, and a volatile anesthetic (such as sevoflurane or isoflurane). The total fresh gas flow might be 4.0 L/min with 50% oxygen and 50% nitrous oxide, plus 2% sevoflurane. The partial pressure of oxygen in the circuit is 0.50 × ambient pressure. Monitoring each component's concentration ensures the patient receives the intended mixture.
At altitude, the partial pressure of oxygen in air drops even though the percentage stays constant at 21%. Cabin pressure in commercial aircraft at cruising altitude is typically equivalent to about 8,000 ft, where atmospheric pressure is roughly 0.75 atm. The partial pressure of oxygen in the cabin is therefore about 0.75 × 0.21 = 0.16 atm — adequate for healthy passengers but low enough to cause measurable desaturation in people with respiratory conditions.
More worked examples
Example 4: Lab gas collection. Hydrogen gas is collected over water at 25 °C and 750 torr barometric pressure. The water vapor pressure at 25 °C is 23.8 torr. Using Dalton's Law: P_H₂ = 750 - 23.8 = 726.2 torr. This is the pressure of dry hydrogen.
Example 5: Trimix diving. A technical diver uses trimix: 21% O₂, 35% He, 44% N₂ at 5 atm depth. PO₂ = 0.21 × 5 = 1.05 atm — below the 1.4 atm oxygen toxicity threshold. PHe = 1.75 atm, PN₂ = 2.20 atm. The helium reduces narcosis compared to air at the same depth (PN₂ would be 3.90 atm without helium).
Frequently asked questions
John Dalton (1766-1844) was an English chemist, physicist, and meteorologist. He formulated modern atomic theory in 1808, proposing that each element consists of unique atoms that combine in fixed ratios to form compounds. His work on gas mixtures grew from his lifelong interest in meteorology: understanding how the atmosphere, a mixture of gases, behaved required a theory of partial pressures.
Dalton's law of partial pressures appeared in his 1801 paper "On the Constitution of Mixed Gases." He argued that each gas in a mixture acts independently, as if the others were absent. This was controversial at the time — some chemists believed gases interacted chemically in mixtures — but Dalton's atomic theory provided a natural explanation: if gases consist of discrete particles with empty space between them, those particles should not affect each other's motion.
For a gas mixture, the total pressure is the sum of partial pressures. If each component obeys the Ideal Gas Law, then P_total = (n_total × R × T) / V. The partial pressure of component i is Pᵢ = (nᵢ × R × T) / V = Xᵢ × P_total, where Xᵢ = nᵢ / n_total is the mole fraction. The mole fractions of all components must sum to 1. This relationship is independent of which gases are in the mixture.
A practical consequence: if you know the total pressure and the mole fractions, you can calculate each partial pressure. If air at 1.00 atm has X_O₂ = 0.2095, then P_O₂ = 0.2095 atm. This is often more useful than measuring each component individually, especially in industrial and medical gas monitoring.
Anesthesiologists use Dalton's Law daily to deliver precise concentrations of gases. A typical anesthesia machine blends oxygen, nitrous oxide, and a volatile anesthetic (such as sevoflurane or isoflurane). The total fresh gas flow might be 4.0 L/min with 50% oxygen and 50% nitrous oxide, plus 2% sevoflurane. The partial pressure of oxygen in the circuit is 0.50 × ambient pressure. Monitoring each component's concentration ensures the patient receives the intended mixture.
At altitude, the partial pressure of oxygen in air drops even though the percentage stays constant at 21%. Cabin pressure in commercial aircraft at cruising altitude is typically equivalent to about 8,000 ft, where atmospheric pressure is roughly 0.75 atm. The partial pressure of oxygen in the cabin is therefore about 0.75 × 0.21 = 0.16 atm — adequate for healthy passengers but low enough to cause measurable desaturation in people with respiratory conditions.
Example 4: Lab gas collection. Hydrogen gas is collected over water at 25 °C and 750 torr barometric pressure. The water vapor pressure at 25 °C is 23.8 torr. Using Dalton's Law: P_H₂ = 750 - 23.8 = 726.2 torr. This is the pressure of dry hydrogen.
Example 5: Trimix diving. A technical diver uses trimix: 21% O₂, 35% He, 44% N₂ at 5 atm depth. PO₂ = 0.21 × 5 = 1.05 atm — below the 1.4 atm oxygen toxicity threshold. PHe = 1.75 atm, PN₂ = 2.20 atm. The helium reduces narcosis compared to air at the same depth (PN₂ would be 3.90 atm without helium).
What is Dalton's Law? P_total = P₁ + P₂ + P₃. The total pressure of a gas mixture equals the sum of component partial pressures.
What is partial pressure? The pressure a single gas in a mixture would exert if it occupied the entire volume alone at the same temperature.
How do you calculate mole fraction? Xᵢ = nᵢ / n_total. Then Pᵢ = Xᵢ × P_total.
Why subtract water vapor pressure? When collecting gas over water, the collected gas contains water vapor. Dalton's Law requires subtracting the water vapor pressure to get the pressure of the dry gas alone.