Dalton's law of partial pressures explains how gases behave when they are mixed in the same container. Each gas contributes its own pressure as if it were alone at the same temperature and volume. This idea matters in chemistry, weather, scuba diving, respiration, and lab experiments that collect gases.
It lets you connect the total pressure of a gas mixture to the amount of each gas present.
In a mixture, gas particles move independently and collide with the container walls, creating pressure. The total pressure is the sum of the partial pressures from all gases in the mixture. For ideal gases, a gas's partial pressure depends on its mole fraction, so Pgas = Xgas Ptotal.
When a gas is collected over water, water vapor also adds pressure, so it must be subtracted to find the dry gas pressure.
Understanding Chemistry: Dalton's Law of Partial Pressures
The key reason the rule works is the motion of particles. Gas particles are far apart compared with their size. Most of the time, a particle travels freely until it hits another particle or a wall.
Pressure comes from repeated impacts on the wall. Nitrogen particles make their own set of impacts. Oxygen particles make another set.
The wall receives every impact, so the effects add together. A particle does not need to know which other gases are present. This independence is a useful model, not a claim that gases never interact.
The model is most accurate for gases at ordinary temperatures and fairly low pressures. Under these conditions, the particles have little attraction to each other and take up very little space. At high pressure, particles are crowded.
At low temperature, attractions become more important. Then a real gas can produce a pressure that differs slightly from the ideal prediction.
In most school calculations, the ideal model is accurate enough. It is still important to state the temperature and pressure conditions, especially when comparing experimental results.
Air gives a familiar example. Its pressure changes with altitude, but its composition stays fairly similar near Earth’s surface. This means the pressure due to oxygen falls as total air pressure falls.
A person high on a mountain may breathe the same fraction of oxygen in each breath, yet receive fewer oxygen particles. Divers face the opposite change. Water pressure raises the total pressure around them, which raises the pressures of gases they breathe.
Nitrogen can then dissolve into blood and body tissues. Careful ascent gives that dissolved nitrogen time to leave safely.
A good calculation starts by listing every gas that is actually present. Convert all pressures to the same unit before combining them. Common units include atmospheres, kilopascals, millimetres of mercury, and torr.
Next, check whether the question gives amounts of gas, fractions of a mixture, or measured pressures. Amounts can be turned into mole fractions by dividing each amount by the total amount. A common error is using mass fraction instead of mole fraction.
Another is forgetting water vapour in a wet gas sample. The water vapour pressure depends strongly on temperature, so a table value must match the stated temperature.
Finally, check that the separate gas pressures add back to the measured total. This simple check catches many sign, unit, and rounding mistakes.
Key Facts
- Dalton's law: Ptotal = P1 + P2 + P3 + ...
- Partial pressure is the pressure one gas would exert if it occupied the container alone at the same temperature.
- Mole fraction: Xi = ni / ntotal
- Partial pressure from mole fraction: Pi = Xi Ptotal
- For ideal gases in the same container, Pi = niRT / V
- Gas collected over water: Ptotal = Pgas + PH2O, so Pgas = Ptotal - PH2O
Vocabulary
- Partial pressure
- The pressure contributed by one gas in a mixture of gases.
- Dalton's law
- The rule that the total pressure of a gas mixture equals the sum of the partial pressures of its gases.
- Mole fraction
- The ratio of moles of one gas to the total moles of all gases in the mixture.
- Ideal gas
- A model gas whose particles have negligible volume and no attractions, so it follows PV = nRT.
- Water vapor pressure
- The pressure exerted by water vapor, which must be included when gas is collected over water.
Common Mistakes to Avoid
- Adding mole fractions to pressure values directly is wrong because mole fraction has no units and must be multiplied by total pressure to get partial pressure.
- Forgetting water vapor pressure in gas collection is wrong because the collected gas mixture contains both the desired gas and water vapor.
- Using the wrong temperature unit in gas law calculations is wrong because PV = nRT requires temperature in kelvins, not degrees Celsius.
- Assuming the largest-volume gas always has the largest partial pressure is wrong because partial pressure depends on moles and temperature in a shared container, not just visual volume.
Practice Questions
- 1 A container holds N2 at 0.40 atm, O2 at 0.25 atm, and CO2 at 0.10 atm. What is the total pressure of the gas mixture?
- 2 A gas mixture has 2.0 mol He, 3.0 mol Ne, and 5.0 mol Ar at a total pressure of 1.20 atm. What is the partial pressure of Ar?
- 3 A student collects oxygen gas over water and reads a total pressure of 748 mmHg. The water vapor pressure is 23 mmHg. Explain why the oxygen pressure is not 748 mmHg and state how to find the correct value.