AP® Chemistry · Unit 3 · Topic 3.4
Partial Pressures and Mole Fraction
Each gas in a mixture contributes to the total pressure in proportion to its mole fraction, as if it alone filled the container. Partial pressure equals mole fraction times total pressure.
Gas particles are so spread out and far apart that one gas barely notices the others are there. Each gas's molecules zip around, hit the walls, and create pressure completely independent of what else is mixed in. That is Dalton's law of partial pressures: the total pressure of a mixture is just the sum of the pressures each gas would exert if it had the container all to itself.
Mole fraction is the fraction of all the gas particles that belong to one component: moles of that gas divided by total moles of gas. Since pressure comes from how often particles hit the walls, and mole fraction tells you what share of the particles belong to each gas, partial pressure is just mole fraction times total pressure: PA = XA times P_total. Mass never enters the formula, because temperature sets the average kinetic energy of all the particles equally, regardless of whether they are light or heavy.
This connects straight back to the ideal gas law, since PA V = nA R T works for each gas individually inside the same container. It also shows up whenever a gas is collected over water: the gas you want is mixed with water vapor, and you subtract the water's known vapor pressure at that temperature from the total measured pressure to isolate the partial pressure of your actual gas. That correction step appears constantly in lab-based gas problems.
Key terms
- Partial pressure
- The pressure one gas in a mixture would exert if it alone occupied the entire container.
- Mole fraction
- The moles of one component divided by the total moles of all components in the mixture.
- Dalton's law
- The total pressure of a gas mixture equals the sum of the partial pressures of each component gas.
- Vapor pressure correction
- Subtracting the known vapor pressure of water from total measured pressure to find the pressure of a gas collected over water.
Watch it explained
- How it worksHow does the mole fraction of a gas set its share of the total pressure?
- Worked exampleFind the partial pressure of oxygen in a 2.0 atm mixture that is 21 percent O2 by moles.
- Worked exampleWalk me through correcting for water vapor when a gas is collected over water at 25 degrees C.
- Common mistakeWhy isn't the heavier gas in a mixture responsible for a bigger share of the pressure?
Check yourself
End of topic.