What this calculator does
Weighing a known volume of gas at a known pressure and temperature identifies it. A gram and a quarter occupying one litre at standard conditions gives 28.03 g/mol, which is nitrogen.
The method works because the ideal gas law fixes how many moles are present regardless of what the gas is. One litre at 1 atm and 273.15 K contains 0.0446 moles of anything, so the mass measurement alone determines the molar mass.
The formula
The ideal gas law gives the moles as PV over RT, using R of 0.0821 L·atm/(mol·K). Dividing the measured mass by that mole count gives the molar mass. Accuracy depends on the gas behaving ideally, which is reasonable near ambient conditions and degrades at high pressure or near condensation.
| Term | Meaning |
|---|---|
| Ideal gas law | PV = nRT, relating pressure, volume, moles and temperature. |
| Molar volume | 22.4 L per mole at 0 °C and 1 atm, which is the same relationship expressed differently. |
| Vapour density | A related historical method comparing a gas density with hydrogen. |
| Compressibility factor | How far a real gas departs from ideal behaviour. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass of gas (g) | Mass of gas in grams, measured by weighing the container full and empty. |
| Pressure (atm) | Pressure in atmospheres. |
| Volume (L) | Volume in litres. |
| Temperature (K) | Temperature in kelvin. |
When to use it
Identifying an unknown gas
The molar mass narrows the candidates immediately, often to one.
Confirming a synthesis
A gaseous product molar mass confirms its identity against the expected formula.
Teaching the gas laws
It is the classic practical application of PV = nRT, combining a physical measurement with a calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What molar mass does each measured mass give?
Different masses occupying the same volume at the same conditions.
| Mass of gas | Molar mass | Moles of gas (n = PV/RT) | Note |
|---|---|---|---|
| 0.5 g | 11.21 g/mol | 0.0446 mol | Assumes ideal-gas behaviour; real gases deviate at high pressure or low temperature. |
| 1.25 g | 28.03 g/mol | 0.0446 mol | Assumes ideal-gas behaviour; real gases deviate at high pressure or low temperature. |
| 2 g | 44.85 g/mol | 0.0446 mol | Assumes ideal-gas behaviour; real gases deviate at high pressure or low temperature. |
| 3 g | 67.28 g/mol | 0.0446 mol | Assumes ideal-gas behaviour; real gases deviate at high pressure or low temperature. |
Questions
Why is the mole count the same for every gas?
Because the ideal gas law contains no term for molecular identity. Equal volumes of any gas at the same temperature and pressure contain equal numbers of molecules, which is Avogadro law. The mass then varies entirely with the molar mass.
How accurate is this?
Good to a percent or so near ambient conditions for gases well above their boiling points. Accuracy falls at high pressure or near condensation, where molecular volume and intermolecular attraction matter. Weighing errors usually dominate in practice, since a litre of gas weighs very little.
What is molar volume?
22.4 litres per mole at 0 °C and 1 atm, which is the same relationship expressed as a constant. It gives a quick check: a litre at those conditions is one over 22.4 of a mole, which is the 0.0446 this calculator reports.
Which value of R should I use?
0.0821 L·atm/(mol·K) for pressure in atmospheres and volume in litres, which is what this uses. Using 8.314 J/(mol·K) requires pressure in pascals and volume in cubic metres. Mismatched units are the usual source of a wildly wrong answer.
For comparing effusion rates, see the Graham’s law calculator. For gas mixtures, see the partial pressure calculator.