Calculate mole fractions and partial pressures
Use gas amount fractions to find partial pressures for mixtures and equilibrium systems.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Equilibrium constants apply at a fixed temperature; include only gaseous or aqueous species in the relevant expressions. For acid–base work, distinguish strength from concentration. Written practice is self-checked
Before you begin
- Balance equations, interpret reversible arrows and use concentration in mol dm⁻³.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How is mole fraction calculated?
What you will learn
- Define mole fraction
- Calculate a gas partial pressure from mole fraction and total pressure
- Use partial pressure as the amount measure in a gas mixture
Mole fraction is a fraction of total gas amount
The mole fraction of gas A is xA = nA / ntotal. It has no unit, and the mole fractions in a mixture sum to 1.
A mole fraction uses amounts of gas particles, not masses or concentrations. If all gases are measured in the same mixture, the fraction can be calculated from their mole amounts.
Partial pressure is the gas's share of total pressure
For an ideal gas mixture, the partial pressure of A is pA = xA × ptotal. The total pressure is the sum of component partial pressures.
Keep pressure units consistent. A component with twice the mole fraction has twice the partial pressure at the same total pressure.
Pause and explain
How do you calculate a component's partial pressure?
Worked example
A mixture contains 2.0 mol N₂ and 1.0 mol H₂ at total pressure 300 kPa. Find x(H₂) and its partial pressure.
Show the worked solution
- Total amount = 3.0 mol.
- x(H₂)=1.0/3.0=1/3.
- p(H₂)=x×ptotal=(1/3)×300 kPa.
Answer x(H₂)=0.333; p(H₂)=100 kPa.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A gas mixture has 0.50 mol O₂ and 1.50 mol N₂. Find x(O₂).
Give me a hint
Divide O₂ amount by total gas amount.
Compare my reasoning
- Total amount = 0.50+1.50=2.00 mol.
- x(O₂)=0.50/2.00.
- Check that the result is between 0 and 1.
x(O₂)=0.250.
Look for these in your work
- Total amount correct
- Fraction calculated
- Plausibility checked
A gas has mole fraction 0.20 in a mixture at 250 kPa. Find its partial pressure.
Give me a hint
Multiply its fraction by total pressure.
Compare my reasoning
- p = 0.20×250 kPa.
- Keep the supplied pressure unit.
- Check that the component pressure is below the total.
p = 50 kPa.
Look for these in your work
- Relationship used
- Multiplication correct
- Unit correct
A mixture at 400 kPa contains gases with mole fractions 0.10, 0.25 and 0.65. Find all three partial pressures and show the total check.
Give me a hint
Multiply each fraction by total pressure.
Compare my reasoning
- First: 0.10×400=40 kPa.
- Second: 0.25×400=100 kPa; third: 0.65×400=260 kPa.
- Add the three pressures.
Partial pressures are 40 kPa, 100 kPa and 260 kPa; their sum is 400 kPa.
Look for these in your work
- Each fraction applied
- All partial pressures found
- Sum matches total
Common mistakes
- Using mass fraction instead of mole fraction
- Forgetting to include all gases in total amount
- Multiplying total pressure by the wrong gas's fraction
- Assuming partial pressures do not sum to total pressure
What can you explain now?
How is mole fraction calculated?
Compare with the explanation
Amount of one gas divided by total gas amount
It is that gas's share of the mixture's moles.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
How do amount fraction and total pressure combine to give the partial pressure?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.