Calculate gas amounts with pV = nRT
Rearrange the ideal gas equation and keep pressure, volume, temperature and the gas constant in compatible units.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Keep pressure, volume, amount and absolute temperature consistent in gas calculations. Written practice is self-checked
Before you begin
- Rearrange a formula and convert between common metric volume units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which temperature scale is used in pV = nRT?
What you will learn
- State and rearrange pV = nRT
- Use pressure, volume and temperature to calculate gas amount
- Convert temperature to kelvin and volume to compatible units
Use absolute temperature and compatible units
The ideal gas equation is pV = nRT, where p is pressure, V is volume, n is amount in mol, R is the molar gas constant and T is absolute temperature in kelvin.
With R = 8.31 J mol⁻¹ K⁻¹, use p in pascals and V in cubic metres so pV is in joules. Convert Celsius to kelvin with T/K = t/°C + 273. Avoid mixing kPa with m³ or cm³ without an explicit conversion.
Rearrange before substituting values
For amount, n = pV/(RT). For a fixed amount of ideal gas, pV/T is constant between two states, provided the amount does not change.
Estimate whether the result is plausible: a higher pressure or volume at the same temperature corresponds to more gas particles; a higher absolute temperature increases the pV product for a fixed amount.
Pause and explain
With p in Pa, V in m³ and R in J mol⁻¹ K⁻¹, which expression gives n?
Worked example
Find n for a gas at 100 000 Pa, volume 2.493 × 10⁻³ m³ and temperature 300 K. Use R = 8.31 J mol⁻¹ K⁻¹.
Show the worked solution
- n = pV/(RT).
- pV = 100 000 × 0.002493 = 249.3 J.
- RT = 8.31 × 300 = 2493 J mol⁻¹; divide.
Answer n = 0.100 mol.
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.
Calculate n for p = 2.00 × 10⁵ Pa, V = 1.247 × 10⁻³ m³ and T = 300 K. Use R = 8.31 J mol⁻¹ K⁻¹.
Give me a hint
Use n = pV/(RT) and keep the SI units together.
Compare my reasoning
- pV = 2.00 × 10⁵ × 1.247 × 10⁻³ = 249.4 J.
- RT = 8.31 × 300 = 2493 J mol⁻¹.
- Divide pV by RT.
n ≈ 0.100 mol.
Look for these in your work
- Equation rearranged
- Units compatible
- Amount calculated
Convert 27 °C to kelvin and explain why it must be converted before using the gas equation.
Give me a hint
Add the Celsius temperature to 273 for this syllabus calculation.
Compare my reasoning
- T = 27 + 273.
- T = 300 K.
- The equation uses absolute temperature, not Celsius.
27 °C = 300 K. Kelvin is measured from absolute zero, so it is the temperature scale used in pV = nRT.
Look for these in your work
- Conversion correct
- Kelvin unit stated
- Absolute temperature explained
A fixed amount of ideal gas is heated from 300 K to 450 K at constant volume. Its initial pressure is 80.0 kPa. Find the final pressure.
Give me a hint
At fixed n and V, pressure is proportional to absolute temperature.
Compare my reasoning
- p₂/p₁ = T₂/T₁.
- p₂ = 80.0 × 450/300.
- Keep the pressure unit unchanged.
p₂ = 120 kPa.
Look for these in your work
- Temperature ratio used
- Kelvin temperatures used
- Pressure unit retained
Common mistakes
- Using Celsius directly
- Mixing cm³ and m³
- Using a pressure unit inconsistent with R
- Rearranging as n = RT/(pV)
What can you explain now?
Which temperature scale is used in pV = nRT?
Compare with the explanation
Kelvin
The equation uses absolute temperature.
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
What units make pV and nRT consistent when R is 8.31 J mol⁻¹ K⁻¹?
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.