Rule of thumb · Materials and ElementsNº 94 / 238

A mole of any gas fills about 24 litres at room temperature and pressure

How much space does a mole of gas take?

A mole of any gas fills about 24 litres at 20 °C and 1 atm (22.4 litres at 0 °C), so a litre of gas at room conditions is about 0.04 mol and weighs about 0.04 times its molar mass in grams.

Why it works

PV = nRT gives a volume per mole of RT/P = 8.314 × 293.15 / 101,325 = 0.02406 m³, 24.06 litres, and it does not depend on the gas, because the molecules are so far apart that their size and the pull between them hardly matter. A litre of nitrogen at those conditions is 1.16 g, a litre of carbon dioxide 1.83 g and a litre of helium 0.17 g.

When it fails

It is for an ideal gas: a real one at 200 atm or near its boiling point is far off, and water vapour at room temperature condenses. And the standard conditions differ: 22.41 litres at 0 °C and 1 atm, 22.71 at 0 °C and 1 bar, 24.79 at 25 °C and 1 bar, so say which.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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