Library / Chemical / CHE-02
Chemical
Ideal gas law
Pressure of a gas from amount, temperature and volume.
- Ref
- CHE-02
- Rev
- v1
- Field
- Chemical
- Result
- p [kPa]
p absolute pressure, V volume, n amount in moles, Ru = 8.314 J/(mol·K) the universal gas constant, T absolute temperature in kelvin. Shown here for p in kPa and V in litres (1 J/L = 1 kPa).
For a gas, pressure rises when you add more gas, heat it, or squeeze it into a smaller space. This law ties those together.
Calculator
- Pressure in bar0.9977 bar
- Gas density for M = 29 g/mol1.16 kg/m³
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 0 °C and 101.325 kPa one mole of gas takes 22.4 L, a useful anchor value.
- Always use absolute temperature. 0 °C is 273.15 K, not zero.
- At high pressure or low temperature, real gases deviate; use a compressibility factor Z.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| n Amount of gas | 0.1 to 100 mol | 4.988 | 4,988 | 4,983 | +10% | +10 % |
| V Volume | 1 to 1,000 L | 4.988 | 4,988 | 4,983 | +10% | −9.09 % |
| T Temperature | 200 to 600 K | 66.51 | 199.5 | 133 | +10% | +10 % |
Sweep of Temperature
| Temperature (K) | Absolute pressure (kPa) |
|---|---|
| 200 | 66.51 |
| 250 | 83.14 |
| 300 | 99.77 |
| 350 | 116.4 |
| 400 | 133 |
| 450 | 149.7 |
| 500 | 166.3 |
| 550 | 182.9 |
| 600 | 199.5 |
Sweep one variable
Variables and how each one contributes
Absolute pressure
What the equation gives you. Everything else feeds it.
Amount of gas
Number of moles. Directly proportional.
Temperature
Absolute temperature (°C + 273.15). Directly proportional: 10% hotter means 10% higher pressure.
Volume
Container volume. Inversely proportional.
Worked example with the values above
- n R T = 2 × 8.314 × 300 = 4,988 J.
- Divide by the volume in litres: 4,988 / 50 = pressure in kPa.
- p = 99.77 kPa.
Assumptions and limits
- Ideal gas behaviour (low pressure, moderate temperature).
- Absolute pressure and absolute temperature.
- Closed container.
Common mistakes
- Using gauge pressure or °C.
- Mixing litres and m³.
- Using the law near condensation.
Statistics and uncertainty
Real gases deviate by 1% or less at atmospheric pressure but several per cent above about 10 bar. Temperature in kelvin carries a small relative error, so measurement uncertainty mostly comes from the volume and the moles.
Where it is used
- Gas cylinder contents and pressure with temperature.
- Pneumatic system sizing.
- Combustion and propellant gas calculations.
Maths you need
- Absolute temperature: kelvin
- Moles: amount of gas