Key takeaways
- The ideal gas law rearranges to V = nRT ÷ P, giving volume in litres.
- Temperature must always be in kelvin, never Celsius, for the formula to work.
- At standard temperature and pressure (STP), one mole of gas occupies about 22.4 litres.
- R, the gas constant, is 8.314 J/(mol·K), fixed for every calculation.
In this guide
What is the ideal gas law?
The ideal gas law describes the relationship between a gas's pressure, volume, temperature, and amount. Rearranged to solve for volume, it tells you exactly how much space a gas will occupy under given conditions.
Why does the ideal gas law matter?
Gases don't have a fixed volume the way solids and liquids do. Squeeze them, heat them, or add more, and the volume changes predictably. This formula is how chemists calculate exactly how much.
At standard temperature and pressure, one single mole of any ideal gas, hydrogen, oxygen, or anything else, occupies almost exactly the same 22.4 litres. It's one of the most useful shortcuts in chemistry.
The formula
| Symbol | What it means | Example |
|---|---|---|
| V | The volume of the gas, in litres (L) | 22.4 L |
| n | The amount of gas, in moles (mol) | 1 mol |
| R | The gas constant, always 8.314 J/(mol·K) | 8.314 |
| T | The temperature, in kelvin (K) | 273 K |
| P | The pressure, in kilopascals (kPa) | 101.325 kPa |
How to calculate gas volume step by step
- 1Find the moles of gas. This is your amount, in mol.
- 2Convert temperature to kelvin. Add 273 to a Celsius reading.
- 3Find the pressure. Convert to kilopascals if needed.
- 4Multiply n × R × T, then divide by P. That gives the volume in litres.
Try the calculator below with your own moles, temperature, and pressure to see every step worked out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Mixing up pressure units. This formula expects kilopascals (kPa); convert from atmospheres by multiplying by 101.325, or from mmHg if needed.
- Forgetting the gas constant's units. R = 8.314 J/(mol·K) only gives correct results when moles, kelvin, and kPa are used together.
- Using a negative or zero pressure. Pressure must be a positive number, since a gas always exerts some pressure.
Tips and tricks
- 22.4 L is roughly the volume of eleven 2-litre soda bottles, a useful everyday-scale comparison.
- To estimate quickly, remember that volume grows with temperature and shrinks with pressure, in direct and inverse proportion.
- Once you have the gas's volume, comparing it to its mass gives you density, useful for identifying an unknown gas.
Where you'll use it in real life
- Chemistry labs: predicting how much space a gas sample will take up under given conditions.
- Weather balloons: balloons expand as they rise because pressure drops with altitude, increasing volume.
- Car tyres: tyre pressure rises on a hot day because temperature increases, even though the tyre's volume barely changes.
- Industrial engineering: gas storage and transport rely on this relationship to size tanks and pipelines safely.
Quick summary
To find gas volume, multiply moles by the gas constant (8.314) and the temperature in kelvin, then divide by the pressure in kPa. Remember: temperature must always be in kelvin. Use the calculator above to work through your own conditions.
Worked example
A chemistry student has 1 mole of an ideal gas at standard temperature (273 K, which is 0°C) and standard pressure (101.325 kPa). What volume does the gas occupy?
- 01PV = nRT → V = nRT / P (R = 8.314 J/mol·K)
- 02V = (1 × 8.314 × 273) / 101.325
- 03V = 2269.72 / 101.325
- 04V = 22.4 L
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate the volume of a gas?
Multiply the moles of gas by the gas constant (8.314) and the temperature in kelvin, then divide by the pressure in kPa: V = nRT ÷ P.
Why must temperature be in kelvin?
The gas law is based on absolute temperature, where zero means no thermal energy at all. Celsius has a different zero point, so it would give incorrect results.
What is standard temperature and pressure (STP)?
STP is commonly defined as 273 K (0°C) and 101.325 kPa (1 atmosphere). At STP, one mole of an ideal gas occupies about 22.4 litres.
What does 'ideal gas' mean?
An ideal gas is a simplified model where gas particles don't interact with each other. Real gases behave very close to this model at normal temperatures and pressures.
