The ideal gas law
The ideal gas law, PV = nRT, ties together the pressure P, volume V, amount n (in moles) and absolute temperature T of a gas. The molar gas constant is R = 8.314462618 J·mol⁻¹·K⁻¹ — an exact value since the 2019 revision of the SI, which fixed the Boltzmann and Avogadro constants (NIST/CODATA). The law unifies Boyle’s, Charles’s, Gay-Lussac’s and Avogadro’s laws into one equation of state.
When it holds and when it fails
The ideal gas law is most accurate at low pressure and high temperature, where molecules are far apart, their own volume is negligible and intermolecular forces are weak. Real gases deviate near condensation — at high pressure or low temperature — where a corrected equation of state such as van der Waals is needed. At standard conditions (IUPAC STP: 0 °C and 100 kPa), one mole of an ideal gas occupies about 22.71 L.
How to use the calculator
Fix any three of P, V, n and T and read the fourth, or vary one input to see how another responds at constant conditions. Temperature must be absolute (kelvin) in the equation; the tool converts for you.
Note: temperature in PV = nRT is always absolute (kelvin). Using the value of R above requires SI units (pascals, cubic metres, moles, kelvin); the tool converts common lab units (atm, L, °C) internally.
Frequently asked questions
What is the ideal gas law?
PV = nRT, relating the pressure, volume, amount (in moles) and absolute temperature of an ideal gas through the molar gas constant R. It is the equation of state for a hypothetical gas of non-interacting point particles.
What is the value of the gas constant R?
R = 8.314462618 J/(mol*K), an exact value since the 2019 SI revision. In other units it is about 0.082057 L*atm/(mol*K) or 8.314 J/(mol*K).
When does the ideal gas law fail?
At high pressure and low temperature, where gas molecules are close together, their finite size and mutual attractions matter. Near condensation the ideal gas law breaks down and a real-gas model such as van der Waals is used.
What is STP and the molar volume?
IUPAC standard temperature and pressure is 0 C (273.15 K) and 100 kPa; one mole of an ideal gas then occupies about 22.71 L. The older STP of 1 atm gives a molar volume of 22.41 L.
References
- Molar gas constant R = 8.314462618 J·mol⁻¹·K⁻¹, exact since the 2019 SI revision (NIST/CODATA).
- P. Atkins & J. de Paula, Atkins’ Physical Chemistry (Oxford University Press) — equations of state and the ideal gas.
- B. P. É. Clapeyron (1834), consolidation of Boyle’s, Charles’s, Gay-Lussac’s and Avogadro’s laws into PV = nRT.