Worked example 1
A flask holds 0.200 mol N₂, 0.100 mol O₂ and 0.200 mol He at a total pressure of 2.50 atm. Find the partial pressure of oxygen.
Try it first: Find the total number of moles before doing anything else.
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Gases, Solutions & SpectroscopyPartial PressuresContent level: Core 20 min
Dalton's Law and Partial Pressures
What you'll be able to do: Calculate partial pressures from mole fractions and correct a gas collected over water for water vapour.
Introduction
Air is a mixture, and so is almost every gas sample you will collect in a lab. Dalton's law says each component pushes on the walls as though the others were not there.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- State the law of partial pressures
- Calculate mole fractions and use them to find partial pressures
- Correct a wet gas measurement for the vapour pressure of water
- Explain why partial pressure, not total pressure, drives gas behaviour in a mixture
Lesson
Adding the pressures
Because ideal particles do not interact, each gas in a mixture contributes pressure independently. The total pressure is Ptotal = P1 + P2 + P3 and so on. Nothing about the identity of the gases matters, only how many moles of each are present.
Ptotal = P1 + P2 + ... + Pn
Mole fractions
The mole fraction of a component, written as chi, is its moles divided by the total moles. Multiplying the mole fraction by the total pressure gives the partial pressure of that gas. Mole fractions have no units and always sum to one, which is a fast way to check your work.
PA = chiA * Ptotal
For gases at the same temperature and volume, mole ratio, volume ratio and pressure ratio are all the same number. That equivalence saves a lot of arithmetic.
Gas collected over water
When a gas is bubbled into an inverted container of water, the trapped sample is a mixture of the gas and water vapour. The measured total pressure therefore includes the vapour pressure of water at that temperature, which you look up in a table. Subtract it to obtain the pressure of the dry gas.
Pgas = Ptotal - Pwater
Why partial pressure matters
Rates, equilibria and biological transport all respond to the partial pressure of a gas rather than the total. Oxygen at high altitude is still about 21 percent of the air by moles, but the low total pressure lowers its partial pressure, which is why breathing is harder.
Key ideas
Definition
Partial pressure
The pressure one component of a mixture would exert alone in the same container at the same temperature.
Definition
Mole fraction
Moles of one component divided by the total moles; unitless and summing to one.
Rule
Wet gas correction
Always subtract the tabulated vapour pressure of water when a gas is collected over water.
Key concept
Independence
Ideal components ignore each other, which is why the pressures simply add.
Equation
Law of partial pressures
Ptotal = P1 + P2 + ... + Pn
- Pi = partial pressure of component i
Equation
Mole fraction form
PA = chiA * Ptotal
- chiA = moles of A divided by total moles
- Ptotal = total pressure of the mixture
Worked examples
Worked example 2
Hydrogen is collected over water at 25 °C. The total pressure is 755 mmHg and the vapour pressure of water at that temperature is 23.8 mmHg. What is the pressure of the dry hydrogen?
Try it first: Decide which pressure the barometer reading actually represents.
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Common mistakes
Using mass fractions instead of mole fractions.
Why it's wrong: Pressure counts particles, not grams, so a heavy gas would be overweighted.
Check instead: Convert every mass to moles before finding fractions.
Forgetting the water vapour correction.
Why it's wrong: The collected sample is saturated with vapour, so the raw reading overstates the gas.
Check instead: Look up the vapour pressure at the stated temperature and subtract it.
Assuming a heavier gas contributes more pressure.
Why it's wrong: Ideal partial pressure depends only on moles, not on molar mass.
Check instead: Compare mole counts alone.
Practice this skill
No practice questions are available for this topic yet. You can still practice the whole unit.
What you should now know
In an ideal mixture, the total pressure is the sum of the partial pressures, and each partial pressure equals the mole fraction of that gas times the total. Gases collected over water are saturated with water vapour, so the vapour pressure of water must be subtracted before the dry gas is analysed.
- Total pressure is the sum of the partial pressures
- PA = chiA x Ptotal
- Mole fraction uses moles, never masses
- Subtract the vapour pressure of water for gases collected over water
- At fixed T and V, mole ratio equals pressure ratio
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.