The Ideal Gas Law Explained: PV = nRT, R in Every Unit, and Where It Breaks

What each symbol means, and why T is never in degrees Celsius

P is the absolute pressure of the gas, V the volume it fills, n the amount of substance in moles, and T the thermodynamic temperature. Rearranged, the law says any one of the four follows from the other three: P = nRT/V, V = nRT/P, n = PV/RT, T = PV/nR. Take 2.00 mol of a gas held in a 10.0 L vessel at 25 °C. Convert first: 25 °C is 298.15 K. Then P = 2.00 × 0.0820574 × 298.15 / 10.0 = 4.89 atm, or in SI units 2.00 × 8.314463 × 298.15 / 0.0100 = 496 kPa. The two routes are the same calculation wearing different units.

The single most common wrong answer comes from typing the Celsius reading straight into T. Feed 25 instead of 298.15 into the same example and the pressure collapses to 0.41 atm — 11.9 times too small, because 298.15 divided by 25 is 11.93. Kelvin is the only scale on which zero means zero: doubling the absolute temperature really does double the pressure at fixed volume, whereas doubling a Celsius reading is arithmetic without physical meaning. The tell is that the error grows as the temperature approaches 0 °C and becomes catastrophic below it, where a negative T would hand you a negative pressure.

Molar volume: 22.414 L or 22.711 L depends on which standard you mean

Set n = 1 and the law gives the volume of one mole directly: V = RT/P. At 0 °C (273.15 K) and 1 atm that is 22.414 L/mol, the figure most school books print. At the same 0 °C but 100 kPa it is 22.711 L/mol, and 100 kPa has been the IUPAC definition of standard pressure since 1982. The gap is 1.3 percent, which is enough to change the second significant figure of any gas volume you report. At 25 °C and 100 kPa, sometimes labelled standard ambient conditions, a mole fills 24.790 L.

The practical rule is to stop writing STP and start writing the conditions. An exam paper that says standard temperature and pressure and expects 22.4 is using the pre-1982 convention; a data table headed 100 kPa expects 22.7. Neither is wrong, and the tools on this site label the conditions rather than the acronym for exactly that reason. If a question gives you a gas volume and no temperature or pressure, it has not given you enough information, and the honest move is to state which convention you assumed.

Where the ideal gas law stops being true

PV = nRT is an idealisation, not a law of nature, and it assumes two things that are never exactly true: that molecules occupy no volume of their own, and that they do not attract one another. Both assumptions survive at low density and fail as the gas is squeezed or cooled towards condensation. The usual measure of the damage is the compressibility factor Z = PV/(nRT), which equals 1 for a perfect gas. Using van der Waals with the standard constants for carbon dioxide at 300 K, Z is 0.996 at 1 bar, 0.957 at 10 bar and 0.733 at 50 bar — so at 50 bar the ideal law overstates the volume by more than a quarter.

Which gas it is matters as much as the pressure. Nitrogen at the same 300 K is far better behaved: Z is 0.9994 at 1 bar and still 0.974 at 50 bar, because its molecules attract each other weakly and it is nowhere near condensing at room temperature. Carbon dioxide misbehaves precisely because 300 K is close to its critical region. A workable rule of thumb: below about 10 bar and well above the boiling point, the ideal gas law is good to roughly one percent and you can use it without apology. Near or above the critical pressure, or within a few tens of kelvin of the boiling point, reach for a real-gas equation or a compressibility chart instead.

Frequently asked questions

Is one mole of gas 22.4 L or 22.7 L?

Both, under different conditions. At 0 °C and 1 atm the molar volume is 22.414 L/mol; at 0 °C and 100 kPa it is 22.711 L/mol. IUPAC redefined standard pressure from 1 atm to 100 kPa in 1982, so newer sources give 22.711 while many school books still print 22.4. Check which pressure the question states and compute V = RT/P yourself rather than recalling a number whose conditions you no longer remember.

What is the difference between the ideal gas law and the combined gas law?

The combined gas law, P₁V₁/T₁ = P₂V₂/T₂, compares one fixed sample of gas in two states and never mentions how much gas there is, so R cancels out and no molar quantity is needed. The ideal gas law describes a single state and does contain n, which lets you go from a pressure and a volume to a number of moles or a mass. Use the combined form when a sample is heated, compressed or moved between conditions; use PV = nRT whenever the question asks how much gas, or gives you a mass.

Does the ideal gas law work for air, or only for pure gases?

It works for mixtures, and air at ordinary conditions is one of its better customers. In a mixture, n is the total amount of substance of all components, and each gas separately obeys the same law at its own partial pressure — that is Dalton's law of partial pressures. Air near 1 bar and 300 K is dominated by nitrogen and oxygen, both far above their boiling points, so the deviation from ideality is well under one percent. The exception is water vapour: once air is near saturation, the condensing component stops behaving ideally, which is why humid-air calculations use dedicated psychrometric relations rather than PV = nRT alone.