Ideal gas law calculator

The arithmetic in pV = nRT is trivial and the two ways to get it wrong are not. The first is the temperature: the law takes kelvin, and a Celsius figure dropped straight in gives an answer that is wrong by a factor of hundreds near room temperature. The second is what "standard conditions" means. IUPAC moved the standard pressure from 101.325 kPa to 100 kPa in 1982 and both numbers are still in circulation, so a mole of gas at 0 °C occupies 22.711 L or 22.414 L depending on which table your teacher learned from. This page shows both rather than picking one, and R comes from CODATA, where it is exact.

How it is calculated

pV = nRT, R = 8.314462618 J mol⁻¹ K⁻¹, T/K = t/°C + 273.15

With pressure in kilopascals and volume in litres the equation needs no conversion factor at all: a kilopascal-litre is a joule, so pV in kPa·L equals nRT in joules directly. R itself stopped being a measurement in 2019, when the redefinition of the SI fixed the Boltzmann constant and the Avogadro constant exactly; R is their product and CODATA now lists it as exact. Everything an ideal gas law answer can be wrong about therefore sits in the assumption that the gas is ideal, and in whether you used kelvin.

Source: IUPAC, Quantities, Units and Symbols in Physical Chemistry (the Green Book), 3rd edition, 2nd printing 2012, Sec. 2.10.1 (v), amount of substance and the specification of entities, p. 54 — "In the equation pV = nRT and in equations involving colligative properties, the entity implied in the definition of n should be an independently translating particle (a whole molecule for a gas)"

Questions people ask

Is a mole of gas 22.4 litres or 22.7 litres at STP?

Both, and which one is right depends on a decision IUPAC took in 1982. The Green Book puts it plainly: the standard pressure is 100 kPa, that value "is the IUPAC recommendation since 1982", and "prior to 1982 the standard pressure was usually taken to be p° = 101 325 Pa (= 1 atm, called the standard atmosphere)". At 0 °C the first gives 22.710 954 64 L/mol and the second 22.413 969 54 L/mol, both exact in CODATA. The familiar 22.4 is the older one. The Green Book adds the sentence that actually settles arguments: "In any case, the value for p° should be specified."

Why does the page ask for Celsius if the law needs kelvin?

Because that is what thermometers and exam papers give you, and the conversion is the single most common mistake in this calculation. The page converts by adding 273.15 — the zero of the Celsius scale, a defined value, not a rounded one — and shows you the kelvin figure it used, so you can check that the number going into the arithmetic is the one you meant.

How close is a real gas to this?

Close enough for a school exercise at ordinary pressure and well away from condensation, and not close at all near the boiling point or at high pressure. The ideal gas law assumes the molecules have no volume of their own and do not attract one another; both assumptions fail as you compress the gas, and the real molar volume comes out a few percent low. There is no correction applied here — this page answers the ideal gas question and does not pretend to be a van der Waals calculator.

What is NTP, and is it the same as STP?

No, and that is a third convention on top of the two above. "Normal temperature and pressure" usually means 20 °C or 25 °C rather than 0 °C, and it is not an IUPAC definition, so different fields use it differently. Because the ambiguity is real, this page does not offer an NTP button: set the temperature and pressure you actually mean, and the answer is unambiguous.

Why is R exact now?

Because since the 2019 revision of the SI, the Boltzmann constant and the Avogadro constant are both defined with fixed numerical values, and the molar gas constant is simply their product. CODATA lists R as 8.314 462 618... J mol⁻¹ K⁻¹ with the standard uncertainty given as "(exact)". Before 2019 it carried a measured uncertainty, which is why older tables show 8.314 472 with a parenthesised error.

Sources

The documents this page reads its numbers out of, linked so you can check them yourself.

1. IUPAC, Quantities, Units and Symbols in Physical Chemistry (the Green Book), 3rd edition, 2nd printing 2012, Sec. 2.10.1 (v), amount of substance and the specification of entities, p. 54 — "In the equation pV = nRT and in equations involving colligative properties, the entity implied in the definition of n should be an independently translating particle (a whole molecule for a gas)"
2. NIST, CODATA recommended values of the fundamental physical constants (2022 adjustment), molar volume of ideal gas (273.15 K, 100 kPa) — the molar volume of an ideal gas at 273.15 K and 100 kPa is given as "22.710 954 64... x 10⁻³ m³ mol⁻¹", exact
3. NIST, CODATA recommended values of the fundamental physical constants (2022 adjustment), molar volume of ideal gas (273.15 K, 101.325 kPa) — the molar volume of an ideal gas at 273.15 K and 101.325 kPa is given as "22.413 969 54... x 10⁻³ m³ mol⁻¹", exact
4. NIST, CODATA recommended values of the fundamental physical constants (2022 adjustment), molar gas constant R — the value is given as "8.314 462 618... J mol⁻¹ K⁻¹" with a standard uncertainty of "(exact)", because R is fixed by the definitions of the kelvin and the mole rather than measured

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