PV = nRT
- P is the pressure, V the volume, n the amount of gas in moles and T the temperature in kelvin.
- R is the gas constant. Its value depends on the units: 8.314 J/(mol·K) with pascals and cubic meters, or 0.08206 L·atm/(mol·K) with liters and atmospheres.
Rearrange for whatever you need: V = nRT ÷ P, P = nRT ÷ V, n = PV ÷ RT, T = PV ÷ nR.
A worked example
What volume does 1 mol of gas take up at 0 °C and 1 atm? Convert the temperature first: 0 °C = 273.15 K. Then V = 1 × 0.08206 × 273.15 ÷ 1 = 22.4 L, the familiar molar volume at standard temperature and pressure.
Common mistakes
- Using degrees Celsius instead of kelvin. Add 273.15.
- Mixing units: an R in L·atm with a pressure in kPa gives a wrong answer. Convert first, or pick the R that matches.
- Forgetting that n is moles, not grams. Divide the mass by the molar mass.
When it stops working
The law assumes gas particles take up no space and do not attract each other. That holds well for most gases near room temperature and ordinary pressures, but not at very high pressures or low temperatures close to where a gas turns liquid.
The Ideal Gas Law Calculator solves for P, V, n or T with the units you use.