How this instrument works
The ideal gas law treats a gas as a swarm of point particles that never interact except by bouncing off the container walls. Combine three older relations — Boyle's law (volume falls as pressure rises), Charles's law (volume rises with temperature), and Avogadro's principle (equal amounts of any gas occupy equal volume at the same temperature and pressure) — and rearranging PV = nRT for volume gives V = nRT ⁄ P. Every quantity on the right pulls the answer the direction physical intuition expects: more molecules or more heat needs more room, more squeeze needs less.
The constant R, the molar gas constant, is 8.31446261815324 joules per mole-kelvin — not measured to that many digits but defined to be exact, since the 2019 redefinition of the SI fixed the Boltzmann constant and Avogadro's number by decree and R is simply their product. Before 2019 it was an experimentally determined figure with uncertainty in its last few digits; now that uncertainty has moved elsewhere in the constant system, and R itself is as exact as the metre.
The model is a limit, not a law of everything. It assumes molecules take up no volume of their own and exert no forces on each other beyond a collision, which is nearly true for a dilute gas at ordinary temperature and badly wrong as a gas nears the pressure and cold where it would condense. Carbon dioxide behaves close to ideal at one atmosphere and room temperature but deviates noticeably at the tens of atmospheres inside a fire extinguisher; helium, with its weak intermolecular attraction, stays close to ideal over a far wider range.
- Enter the Amount, in moles — this is n, how much gas you have, independent of what the gas actually is.
- Enter the Temperature in kelvin — the field wants the absolute scale, not Celsius; 0°C is 273.15 K.
- Enter the Pressure — the unit menu defaults to kPa but also accepts Pa or atm; switch it to match your reading.
- Read the Volume — it defaults to litres; switch to millilitres for a small sample or cubic metres for a full tank.
Worked example — one mole at 0°C and standard pressure
Set Amount to 1 mol, Temperature to 273.15 K (0°C), and Pressure to 101.325 kPa (101325 Pa, one standard atmosphere) — the 'standard conditions' chemistry courses quote before ever explaining where 22.4 litres comes from. The formula gives V = (1)(8.31446261815324)(273.15) ⁄ 101325 = 0.022413969545 m³, which the Volume field reads out as 22.414 litres once its unit is switched — the molar volume constant, derived here rather than pulled from memory.
The figure is specific to the older convention of standard pressure as exactly one atmosphere, 101.325 kPa. IUPAC's current definition of standard temperature and pressure uses 100 kPa instead, which, run through the same formula, gives 22.711 litres per mole — the reason two textbooks can both be right about 'the' molar volume while disagreeing in the third digit. Double the Temperature field to 546.3 K with everything else unchanged and Volume doubles too, to 0.044828 m³, exactly as Charles's law predicts.
Questions
Why must Temperature be entered in kelvin rather than Celsius?
Because the formula is a direct proportionality, V proportional to T at fixed n and P, and that only holds on a scale where zero really means zero volume in the limit. Celsius has an arbitrary zero at the freezing point of water; enter 0 directly for a 0°C reading and the formula would predict zero volume for gas that obviously still fills the container. Kelvin fixes that by setting zero at absolute zero, so 273.15 K, not 0, is what belongs in the field.
Why do some sources say one mole of gas is 22.4 litres and others say 22.7?
Both are correct for different definitions of standard pressure. The older, still common convention fixes standard pressure at exactly one atmosphere, 101.325 kPa, which is what the worked example above uses and what gives 22.414 litres. IUPAC's current standard, adopted in 1982, instead fixes standard pressure at 100 kPa exactly, which lowers the pressure slightly and raises the volume to 22.711 litres. Enter either pressure into the Pressure field and compare.
Does the ideal gas law work for any real gas, like carbon dioxide or steam?
Reasonably well at ordinary pressure and temperature, and increasingly badly as a gas is compressed or cooled toward the point where it would condense. Carbon dioxide near one atmosphere and room temperature tracks the ideal prediction within a fraction of a percent; the same gas at the tens of atmospheres inside a fire extinguisher, or steam near its boiling point, deviates enough that engineers switch to a real-gas equation of state with a compressibility correction.
What happens to Volume if I double the Pressure?
It halves, holding Amount and Temperature fixed — the inverse relationship Robert Boyle described in 1662, built directly into the formula's division by P. Squeeze the same one mole of gas at 0°C from 101.325 kPa to 202.65 kPa and the Volume field drops from 22.414 litres to 11.207 litres. The reverse also holds: halve the pressure and the volume doubles.
What does an Amount of zero mean physically?
No gas, no volume — the instrument returns exactly 0 regardless of Temperature or Pressure, since every term in V = nRT ⁄ P scales with n. It looks like a trivial result, but it is a useful sanity check: any formula claiming to describe a gas's volume has to collapse to zero the moment there is no gas left to fill it, and this one does, cleanly, at every combination of the other two fields.