Ideal Gas Volume PV nRT

Ideal gas volume: V = nRT / P

Rearrange the ideal gas law PV = nRT and you get V = nRT/P, the volume that n moles of an ideal gas take up at temperature T (kelvin) and pressure P. With R = 0.082057 L·atm/(mol·K), the classical "CNTP/STP" reference of 273.15 K and 1 atm gives 22.4 L for 1 mol of any ideal gas. Switch to the post-1982 IUPAC STP (273.15 K, 100 kPa) and the molar volume comes out to 22.7 L instead. The law tracks real gases well at low pressure and high temperature, but it starts to drift once intermolecular forces become significant. When that happens, reach for the van der Waals or Redlich–Kwong equations.

Applications

Teaching general chemistry, sizing industrial O₂, N₂ and H₂ storage tanks, working out the stoichiometry of gas-phase reactions like combustion or ammonia synthesis, HVAC and process engineering, atmospheric science, and quick lab estimates of how much gas was evolved or consumed.

FAQ

CNTP, STP or NTP — what is the difference? The old "CNTP" used in Brazil and the pre-1982 STP both ran on 273.15 K and 1 atm, giving 22.4 L/mol. IUPAC's modern STP shifted to 273.15 K and 100 kPa (22.7 L/mol). NTP, meanwhile, usually means 293.15 K and 1 atm (24.0 L/mol).

Does the gas identity matter? For an ideal gas, no. One mole of He, O₂ or CO₂ takes up the same volume at the same P and T. Identity only comes into play once you start applying non-ideal corrections.

Why must temperature be in kelvin? The law comes out of kinetic theory, which is built on absolute temperature. Plug in °C and you'd hit zero or negative values at low T, and the equation falls apart.