How it works
The ideal gas law relates the pressure, volume, amount, and temperature of a gas in a single equation: PV = nRT. Rearranged for whichever value you don't already know, it lets you solve for pressure, volume, moles, or temperature from the other three.
P = nRT ÷ V
V = nRT ÷ P
n = PV ÷ RT
T = PV ÷ nR
R is the ideal gas constant, 0.0821 L·atm/(mol·K) when pressure is in atmospheres and volume is in litres. Temperature must always be in kelvin — not Celsius or Fahrenheit — since the law depends on an absolute temperature scale.
Worked example
One mole of gas at 273 K occupying 22.4 litres — what's the pressure?
- Use the formula P = nRT ÷ V.
- Substitute: P = (1 × 0.0821 × 273) ÷ 22.4.
- That's 22.4133 ÷ 22.4.
- Which gives 1.0006 atm.
The pressure is 1.0006 atm — this is the standard molar volume at STP, a useful sanity-check value.
Common questions
What does each letter in PV = nRT stand for?
P is pressure (atm), V is volume (litres), n is the amount of gas (moles), R is the gas constant (0.0821 L·atm/mol·K), and T is temperature in kelvin. Together they describe how an ideal gas behaves.
Why does temperature have to be in kelvin?
The ideal gas law only works with an absolute temperature scale, where zero really means zero energy — kelvin, not Celsius or Fahrenheit. Using °C directly would give a wrong answer, since 0°C isn't 0 on an absolute scale. Convert first: K = °C + 273.15.
How accurate is the ideal gas law for real gases?
It's a close approximation for most gases at ordinary pressures and temperatures, but it breaks down at very high pressure or very low temperature, where intermolecular forces and molecular volume start to matter — that's where the van der Waals equation is used instead.