Ideal Gas Laws
Senior 2 · Physics
Ideal Gas Laws
Lesson 5 of 5
22 min
Air is not one gas but a mixture: about 78% nitrogen, 21% oxygen and 1% argon and other gases. Climbers on Mount Karisimbi feel short of breath even though the air up there is still 21% oxygen. Hospitals give patients extra oxygen. Divers, pilots and athletes all have to think about the oxygen in a mixture. John Dalton's law of partial pressures explains how each gas in a mixture contributes to the pressure.
The partial pressure of a gas in a mixture is the pressure it would exert if it filled the whole container on its own, at the same temperature.
Dalton's law: the total pressure of a mixture of gases that do not react with each other equals the sum of the partial pressures of the gases in it.
P(total) = P₁ + P₂ + P₃ + …
In the particle picture this is natural: each kind of particle hits the walls independently, so the pressures simply add. Because pressure is proportional to the number of particles (PV = nRT), each gas's share of the pressure equals its share of the particles:
partial pressure of A = (fraction of the particles that are A) × P(total)
Worked example 1. A container holds 2 mol of nitrogen and 1 mol of oxygen at a total pressure of 90 kPa. Oxygen is 1 of the 3 moles, so p(O₂) = ⅓ × 90 = 30 kPa, and p(N₂) = ⅔ × 90 = 60 kPa. Check: 30 + 60 = 90 kPa.
Oxygen makes up about 21% of the particles in air at every height. What changes with height is the total pressure.
Your lungs take in oxygen according to its partial pressure, not its percentage. On Karisimbi each breath delivers about 30% less oxygen than in Kigali, and that is why climbers breathe hard.
In the laboratory, hydrogen is often collected by bubbling it into an upside-down jar of water. The jar then contains hydrogen and water vapour. At 25 °C the vapour pressure of water is 3.17 kPa. If the total pressure in the jar is 85.0 kPa, then by Dalton's law p(H₂) = 85.0 − 3.17 ≈ 81.8 kPa.
| Application | What happens | Law |
|---|---|---|
| Breathing | The diaphragm moves down, lung volume increases, pressure inside falls below air pressure, air flows in | Boyle |
| Syringes and bicycle pumps | Changing the volume changes the pressure of the trapped air | Boyle |
| Diving | Air in the lungs expands as a diver rises, so she must breathe out on the way up | Boyle |
| Hot-air balloons | Heated air expands, so the balloon's air is less dense than the air outside and it rises | Charles |
| Tyres and aerosol cans | Heating a gas in a fixed volume raises its pressure; this is why cans say "Do not incinerate" | Gay-Lussac |
| Weather balloons | Pressure and temperature both fall with height; the balloon expands until it bursts | Combined law |
| Altitude sickness and medical oxygen | Lower total pressure means lower oxygen partial pressure; extra oxygen raises it again | Dalton |
On the Ideal screen of Gas Properties, set "Hold Constant" to Temperature. Use the Particles panel to add 50 heavy particles and note the pressure. Reset, add 50 light particles instead and note that pressure. Finally put both sets in together. The pressure of the mixture is close to the sum of the two separate pressures (the reading flickers, so average it by eye): Dalton's law.
Tip
Percentage is not pressure. A gas's percentage in a mixture tells you its share; multiply by the total pressure to get its partial pressure. For a gas collected over water, always subtract the water-vapour pressure from the total.
Name the law and the constant quantity when you explain an application: "the volume is fixed, so by Gay-Lussac's law the pressure rises".
A mixture contains nitrogen at 60 kPa, oxygen at 25 kPa and carbon dioxide at 5 kPa. What is the total pressure?
Solution: By Dalton's law, P = 60 + 25 + 5 = 90 kPa.
Air is 21% oxygen. Find the partial pressure of oxygen (a) in Kigali, where air pressure is 85 kPa, and (b) at sea level, 101.3 kPa.
Solution: (a) 0.21 × 85 ≈ 17.9 kPa. (b) 0.21 × 101.3 ≈ 21.3 kPa.
Oxygen is collected over water at 20 °C. The total pressure is 84.0 kPa and the vapour pressure of water at 20 °C is 2.34 kPa. Find the partial pressure of the oxygen.
Solution: p(O₂) = 84.0 − 2.34 ≈ 81.7 kPa.
Name the gas law that best explains each: (a) a hot-air balloon rises; (b) a tyre bursts on a very hot road; (c) you breathe in when your chest expands; (d) climbers carry oxygen on very high mountains.
Solution: (a) Charles's law: heated air expands and becomes less dense. (b) Gay-Lussac's law: at nearly fixed volume, the pressure rises with temperature. (c) Boyle's law: larger lung volume, lower pressure, so air flows in. (d) Dalton's law: lower total pressure means lower oxygen partial pressure.
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